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World History/Causes and course of the Second World War

Causes of World War II
France, Great Britain, and the U.S. had attained their wartime objectives in 1919. They had reduced Germany to a military cipher and had reorganized Europe and the world as they saw fit. The French and the British frequently disagreed on policy in the postwar period, however, and were unsure of their ability to defend the peace settlement. Disillusionment with war led to the practice of appeasement, or giving into an aggressor's demands to keep the peace. The U.S., disillusioned by the Europeans' failure to pay their war debts, retreated into isolationism. The Treaty of Versailles left many countries dissatisfied. Adverse conditions, such as reparations and unemployed veterans from World War I led to the circulation of new, radical ideas and solutions, such as fascism in Italy. This Fascist party, as Mussolini called it, later became a model for Hitler in Germany.

The Failure of Peace Efforts
During the 1920s, attempts were made to achieve a stable peace. The first was President Woodrow Wilson's idea to establish the League of Nations (1920) as a forum in which nations could settle their disputes. The League's powers were limited to persuasion and various levels of moral and economic sanctions that the members were free to carry out as they saw fit. The United States never joined the League and Germany and the USSR were also never members. At the Washington Conference of 1921-2, the principal naval powers agreed to limit their navies according to a fixed ratio. The Locarno Conference (1925) produced a treaty guarantee of the German-French boundary and an arbitration agreement between Germany and Poland. In the Kellogg-Briande Pact (1928), 63 countries including all the Great Powers except the USSR, renounced war as an instrument of national policy and pledged to resolve all disputes among them "by pacific means." The signatories had agreed beforehand to exempt wars of "self-defense."

The Rise of Fascism
One of the victors' stated aims in World War I had been "to make the world safe for democracy," and postwar Germany adopted a democratic constitution, as did most of the other states restored or created after the war. In the 1920s, however, the wave of the future appeared to be a form of nationalistic, militaristic totalitarianism known by its Italian name, fascism. It promised to minister to peoples' wants more effectively than democracy and presented itself as the one sure defense against communism. Benito Mussolini established the first Fascist, European dictatorship during the inter war period in Italy in 1922.

Formation of the Axis Coalition
Adolf Hitler, the Leader of the German National Socialist (Nazi) party, preached a racist brand of fascism. Hitler promised to overturn the Versailles Treaty and secure additional Lebensraum ("living space") for the German people, who he contended deserve more as members of a superior race. In the early 1930s, the Great Depression hit Germany. The moderate parties could not agree on what to do about it, and large numbers of voters turned to the Nazis and Communists. In 1933 Hitler became the German Chancellor, and in a series of subsequent moves established himself as dictator. Japan did not formally adopt fascism, but the armed forces' powerful position in government enabled them to impose a similar type of totalitarianism. As dismantlers of the world status quo, the Japanese were well ahead of Hitler. They used a minor clash with Chinese troops near Mukden, also known as the Mukden or Manchurian crisis, in 1931 as a pretext for taking over all of Manchuria, where they proclaimed the puppet state of Manchukuo in 1932. In 1937-8 they occupied the main Chinese ports. Having denounced the disarmament clauses of the Versailles Treaty, created a new air force, and reintroduced conscription, Hitler tried out his new weapons on the side of right-wing military rebels in the Spanish civil war (1936-9). This venture brought him into collaboration with Mussolini who was also supporting the Spanish revolt after having seized (1935-6) Ethiopia in a small war. Treaties between Germany, Italy, and Japan in 1936-7 brought into being the Rome-Berlin-Tokyo Axis. For example, Japan and Germany signed the Anti-Comintern pact in 1936 and then Italy joined in 1937. This pact denounced communism and it showed their unity in the matter. The Axis thereafter became the collective term for those countries and their allies.

German Aggression in Europe
Hitler launched his own expansionist drive with the annexation of Austria in March 1938. The way was clear: Mussolini supported him; and the British and French, overawed by German rearmament, accepted Hitler's claim that the status of Austria was an internal German affair. The U.S. had impaired its ability to act against aggression by passing a neutrality law that prohibited material assistance to all parties in foreign conflicts. In September 1938 Hitler threatened war to annex the western border area of Czechoslovakia, the Sudetenland and its 3.5. million ethnic Germans. The British Prime Minister Neville Chamberlain initiated talks that culminated at the end of the month in the Munich Pact, by which the Czechs, on British and French urging, relinquished the Sudetenland in return for Hitler's promise not to take any more Czech territory. Chamberlain believed he had achieved "peace for our time," but the word Munich soon implied abject and futile appeasement. Less than six months later, in March 1939, Hitler seized the remainder of Czechoslovakia. Alarmed by this new aggression and by Hitler's threats against Poland, the British government pledged to aid that country if Germany threatened its independence. A popular joke ran at the time: "A guarantee a day keeps Hitler away". France already had a mutual defense treaty with Poland. The turn away from appeasement brought the Soviet Union to the fore. Joseph Stalin, the Soviet dictator, had offered military help to Czechoslovakia during the 1938 crisis, but had been ignored by all the parties to the Munich Agreement. Now that war threatened, he was courted by both sides, but Hitler made the more attractive offer. Allied with Britain and France, the Soviet Union might well have had to fight, but all Germany asked for was its neutrality. In Moscow, on the night of August 23, 1939, the Nazi-Soviet Pact was signed. In the part published the next day, Germany and the Soviet Union agreed not to go to war against each other. A secret protocol gave Stalin a free hand in Finland, Estonia, Latvia, eastern Poland, and eastern Romania.

The Worldwide Great Depression

The costs of carrying out World War I, as well as the costs to rebuild Western Europe after years of fighting, resulted in enormous debts on the part of the Western European powers to the United States. The enormous reparations put on Germany in the Treaty of Versailles also increased the debts. Coupled with ineffective governments in many of these European States (notably the Weinmar Republic, pre-Mussolini Italy and Socialist France) led to slow reconstruction and poor economic growth.

With the crash of the New York Stock Market on 29 October, 1929, the United States recalled all foreign loans in the following days. Unable to repay these loans, the economies of the West collapsed, beginning the Great Depression.

War in Europe
The German invasion of Poland on September 1, 1939 is regarded as the start of World War II. Due to official League of Nations law, France and the UK were obligated to intervene, but in reality did very little in a period known as the phony war. In Poland, however, fighting had begun. Germany was extremely successful in this war due to their new strategy known as blitzkrieg (meaning "lightning war"). This strategy involved the use of tanks, a relatively new technology at the time, to quickly overrun a country before they could set up their defenses properly. This strategy worked amazingly for Germany, with the German troops arriving near the Polish capitol of Warsaw in just 7 days. Germany and the USSR had made a nonaggression pact in the days leading up to the invasion, which was essentially an agreement to split eastern Europe between the two countries. The agreement was initially a shock to the world, as the two countries were governed by ideologies that were about as far apart from each other as possible. However, this fragile agreement did not last. Before that, though, the USSR used this opportunity to annex the Baltic states, parts of Romania, and tried to take land Finland in a disastrous campaign for the Russians known as the winter war. Germany then proceeded to take out Denmark and Norway in order to secure positions in the north sea. Then Germany shifted their attention to France. French strategy relied on using the Maginot line, a massive line of forts stretching the entirety of their border with Germany to protect their border with relatively few troops while positioning their best forces along the border with Belgium, as Germany had attacked through Belgium in the first world war. However, they left the Ardennes forest undefended, as they believed that the dense forest would provide enough of a natural barrier. Knowing this, Germany launched a daring attack that sent 50 tank divisions through the Ardennes. The Germans broke through, and managed to cut off the allied forces. The French forces there were wiped out, but they were able to defend long enough to let British forces escape through Dunkirk. But for France, all was lost. The bulk of their army had been wiped out, and within weeks France had to surrender. This was far from the end of French resistance, though, as aside from civilian resistance efforts, and forces fighting under the banner of "Free France" played a major role in the north African front in the coming years. In Europe, however, Germany had set up a puppet state called Vichy France in the south, while the north was fully annexed for defense purposes. Germany tried to make the odds seem as far in their favor as they could in the hopes that Britain would try to make peace, but the new Prime Minister Winston Churchill refused to give up. In order to take over the British Isles, Germany would first have to gain control of the English channel in both the air and sea to be able to land troops on the island. After intense air fighting over England that resulted in the bombing of major English cities, Britain stopped any chance of a naval invasion.

The War in the Pacific

 * Note that this is only a rough outline. Change it as needed.

Mukden Incident and the Invasion of Manchuria (1931)
After winning the Russo-Japanese War in 1905, Japan quickly became the dominant power in its region. Russia recognized Korea as a Japanese sphere of influence and removed all of its forces from there and Manchuria, the sparsely populated northeastern region of China. In 1910, Japan annexed Korea as its own with little protest or resistance. Still, Japan was a quickly growing country, both population-wise and economically. It founded the South Manchuria Railway company in Manchuria in 1906, and with that company was able to gain government-like control of the area.

By 1931, the Depression had struck a blow to Japan. The government did little to help Japan's economy, and in the eyes of its citizens, was weak and powerless. Instead, the public favored the Japanese army, and soon the civilian government had lost control of its military. To the army, Manchuria seemed like an obvious solution to many of Japan's problems. Manchuria was vast and thinly populated, and would serve as excellent elbow room for an already overcrowded Japan. It was also thought that Manchuria was rich in forests, natural resources, and fertile land. The fact that the Japanese believed themselves to be far superior to the Chinese only moved Japan towards conflict faster. Additionally, the warlord of Manchuria went against Japanese expectations and declared his allegiance to a growing Chinese military movement. So, in 1931, the army staged an explosion at a section of railway near Mukden, a city in Manchuria, as a pretext to invade and annex China. Japan met little resistance, although it did not have support of its own government, and Manchuria was completely occupied by the end of the year. Japan subsequently set up the puppet state of Manchukuo to oversee the newly acquired region. The League of Nations vehemently protested Japan's aggression, but Japan then withdrew from it.

Japan invades China (1937)
The 1920s saw a weak and politically chaotic China. Warlords of the many provinces of China constantly feuded, and the central government was weak and decentralized, unable to do anything to stop conflict. In 1927 Chiang Kai-Shek gained control of the Kuomintang (the Chinese government) and its National Revolution Army. Chiang led an expedition to defeat southern and central Chinese warlords and gain the allegiance of northern warlords. He was successful, and he soon focused on what he perceived to be a greater threat than Japan, which was communism. But in 1937, the deposed warlord general of Manchuria kidnapped Chiang and refused to release him until he at least temporarily united with the communists against the Japanese threat. The Japanese army responded by staging the Battle of Lugou Bridge, which was supposed to provoke open war between China and Japan. It worked and the Sino-Japanese War began. The beginning of the conflict was marked by the Chinese strategy of giving up land in order to stall the Japanese. It is important to note that the Japanese was not to completely take over China; rather, the Japanese wanted to set up puppet governments in key regions that would protect and advance Japanese interests. The fall of Nanjing in the early stages of this conflict saw the beginning of Japanese war atrocities. 100,000-300,000 were killed in the six weeks after Nanjing was captured. Other war crimes committed included widespread rape, arson, and looting.

Anti-Comintern Pact and Tripartite Pact
These were pacts between Germany, Italy, and Japan. The Anti-Comintern pact had been a pact that denounced communism and it was initially signed by Japan and Germany. However, later, as German and Italian relations improved, Italy also signed and this was made stronger later by the Rome-Berlin-Tokyo Axis in 1938. The Tripartite Pact also strengthened the alliance and it was basically a confirmation of the Rome-Berlin-Toyko Axis.

Pearl Harbor and Simultaneous Invasions (early December 1941)
On December 7, 1941, Japanese warplanes commanded by Vice Admiral Chuichi Nagumo carried out a surprise air raid on Pearl Harbor, Hawaii, the largest U.S. naval base in the Pacific. The Japanese forces met little resistance and devastated the harbor. This attack resulted in 8 battleships either sunk or damaged, 3 light cruisers and 3 destroyers sunk as well as damage to some auxiliaries and 343 aircraft either damaged or destroyed. 2408 Americans were killed including 68 civilians; 1178 were wounded. Japan lost only 29 aircraft and their crews and five midget submarines. However, the attack failed to strike targets that could have been crippling losses to the US Pacific Fleet such as the aircraft carriers which were out at sea at the time of the attack or the base's ship fuel storage and repair facilities. The survival of these assets have led many to consider this attack a catastrophic long term strategic blunder for Japan.

The following day, the United States declared war on Japan. Simultaneously to the attack on Pearl Harbor, Japan also attacked U.S. air bases in the Philippines. Immediately following these attacks, Japan invaded the Philippines and also the British Colonies of Hong Kong, Malaya, Borneo and Burma with the intention of seizing the oilfields of the Dutch East Indies.

Following the Japanese attack on Pearl Harbor, Germany declared war on the United States on December 11, 1941, even though it was not obliged to do so under the Tripartite Pact of 1940. Hitler made the declaration in the hopes that Japan would support him by attacking the Soviet Union. Japan did not oblige him, and this diplomatic move proved a catastrophic blunder which gave President Franklin D. Roosevelt the pretext needed for the United States joining the fight in Europe with full commitment and with no meaningful opposition from Congress. Some historians mark this moment as another major turning point of the war with Hitler provoking a grand alliance of powerful nations, most prominently the UK, the USA and the USSR, who could wage powerful offensives on both East and West simultaneously.

Allied Defeats in the Pacific and Asia (late December 1941-1942)
Simultaneous with the dawn raid on Pearl Harbor, the Japanese carried out an invasion of Malaya, landing troops at Kota Bharu on the east coast, supported by land based aircraft from bases in Vietnam and Taiwan. The British attempted to oppose the landings by dispatching Force Z, comprising the battleship HMS Prince of Wales and the battlecruiser HMS Repulse, with their escorting destroyers, from the naval base in Singapore, but this force was intercepted and destroyed by bombers before even reaching their objective.

In a series of swift maneuvers down the Malay peninsula, thought by the British to be "impassable" to an invading force landing so far north, the Japanese advanced down to the Johor Straits at the southernmost tip of the peninsula by January 1942. The Japanese were even using tanks, which the British had incorrectly thought would not be able to penetrate the jungles.

During a short two week campaign the Japanese crossed the Straits of Johor by amphibious assault and conducted a series of sharp battles, notably the battle of Kent Ridge when the Royal Malay Regiment put up a brave but futile effort to stem the tide. Singapore fell on February 15, 1942 and with its fall, Japan was now able to control the sea approaches from the Indian Ocean through the Malacca Straits. The natural resources of the Malay peninsula, in particular rubber plantations and tin mines, were now in the hands of the Japanese.

Other Allied possessions, especially in the oil rich East Indies (Indonesia) were also swiftly captured, and all organised resistance effectively ceased, with attention now shifting to events closer to Midway, the Solomon Islands, the Bismark Sea and New Guinea.

Allies Regroup and the Battle of Midway (1942)
Following the attack on Pearl Harbour, the US military sought to strike back at Japan, and a plan was formulated to bomb Tokyo. As Tokyo could not be reached by land based bombers, it was decided to use an aircraft carrier to launch the attack close to Japanese waters. The Doolittle Raid was carried out by James H. (Jimmy) Doolittle and his squadron of B-25 medium bombers, launched from the USS Hornet. The raid achieved little strategically, but was a tremendous morale booster in the dark days of 1942. It also led to the decision by the Japanese military to attack the only logical base of the attackers, the tiny atoll of Midway.

A powerful force of warships, with four large fleet carriers at its core (Akagi, Kaga, Hiryu and Soryu) attacked Midway. The US navy, with the aid of intercepted and decoded Japanese signals, were ready and launched a counter attack with the carriers USS Enterprise and USS Yorktown, destroying all four of the Japanese fleet carriers. This was a devastating blow to the Japanese and is considered the turning point of the Pacific War. The Japanese had largely roamed the Pacific Ocean, the South China Sea, the Malacca Straits and the Indian Ocean with impunity, launching raids from these same four carriers on Allied bases in these areas including Darwin, Colombo and along the Indian east coast. With the loss of these carriers and more importantly their cadre of irreplaceable hard core highly trained naval aviators, the Japanese could no longer maintain an effective offensive and became largely defensive from then on.

Island Hopping (1943- Late 1944)
Island hopping was a campaign of capturing key islands in the Pacific that were used as prerequisites, or stepping stones, to the next island with the eventual destination being Japan, rather than trying to capture every island under Japanese control. Allied forces often assaulted weaker islands first, while starving out the Japanese strongholds before attacking them.

The Atomic Bomb (August 1945)
On August 6, 1945, a lone B-29 bomber, named the Enola Gay, appeared over the skies of Hiroshima. Air raid sirens went off around the city and people ran for their shelters. However, minutes later, the all-clear symbol was given. Although it had been a seemingly harmless run, the B-29 had, in fact, dropped a single bomb (this bomb was called "Little Boy"). This bomb detonated about 1,900 feet over Hiroshima and leveled much of the city within a few thousandths of a second. Tens of thousands were killed immediately and many more would eventually die from the radiation poisoning.

However, Japan did not surrender to the United States, so three days later, on August 9, 1945, a B-29 named Boxcar dropped an atom bomb on the city of Nagasaki (this bomb was called "Fat Man"). Although the bomb was actually more powerful than the Hiroshima bomb, the foggy weather conditions and the hilly terrain of Nagasaki somewhat shielded a portion of the city from the worst effects.

This, in conjunction with other factors affecting the state of the war, led to a ceasefire with Japan, and surrender a month later.


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World History/Consequences of the Second World War

The Second World War saw the most far-reaching transformation of world politics to date. The destructive technologies introduced during the war – foremost, the atomic bomb – made it very unlikely that a land-based conflict of similar scale and duration among the major nations could ever happen again, because of the potential for total destruction of all combatants.

No advanced industrial nation has been invaded since 1945, and all wars since that time have been guerrilla conflicts in less-developed countries, conflicts involving less-developed countries with more advanced ones, or some combination of these two scenarios.

From an economic standpoint, the war and its aftermath consumed much of the real and potential industrial production of the world over the period 1940–1960 (with the exception that the United States, its homeland untouched, was able to expand both its defense industries and its civilian economy very rapidly after 1945). Europe and Japan lay in ruins and would spend 15–20 years rebuilding the basis for economic life, with much assistance from the U.S. The Soviet Union and China, though victorious in the war, were also ravaged.

Splitting of the world
Europe was split into two main camps by the "Iron Curtain", which divided Germany in half and separated Austria from Czechoslovakia and Hungary, and Italy from Yugoslavia. The Soviet Union absorbed eastern Poland, and "reassigned" large areas of German territory to Polish rule by way of compensation. Moscow intervened directly to install Communist parties in power in Poland, eastern Germany, Hungary and Czechoslovakia. Finland was able to keep its independence, but did not regain the lands it lost to the Soviets in the 1940 Winter War. Yugoslavia under Marshal Tito, already Communist, did not submit to direct influence from Moscow, choosing a more independent path and greatly angering Stalin. Elsewhere in the Balkans, Bulgaria, Romania and Albania also were brought into the Soviet bloc. To the west were the democracies allied to the USA: the UK, France, Italy, the Netherlands, Belgium, Norway, and West Germany. Washington became quite concerned, however, that local Communist parties might gain power in France, Italy and Greece in the late 1940s, given the battered state of the postwar European economy and the proximity of the Soviet Union. French leader Charles DeGaulle received strong backing from the U.S., and anti-Communist parties in Italy were heavily financed. In the end neither nation left the Western sphere of influence.

In Asia, China, Vietnam, Korea and Mongolia were communist countries. Japan, first under occupation by the USA after WWII, had to reform its system – moving away from from militarism and expansionism and into democratic reforms. Military alliances were formed on both sides: First NATO, on April 4, 1949 in the USA geopolitical sphere and as a direct response due to the Cold War the Soviet Union (USSR), on May 14, 1955 created the Organization of Warsaw treaty, better known as Warsaw Pact.

In an attempt to set up a body for possible dialog between Western, Eastern, and Developing countries and establish international law, the Organization of United Nations was established in 1945 by USA initiative. The failing of the League of Nations, also initiated by the USA was one of several precursor stages for WWII. Special consideration must be given to the geopolitical interests behind these organizations, especially who they favor. Even if ultimately, they are a stabilizing force. Other USA international initiatives include: the International Monetary Fund (IMF), the World Bank and more recently the World Trade Organization (WTO), that has its roots in the discussions to form the International Trade Organization (ITO) as an evolution from the General Agreement on Tariffs and Trade (GATT) of 1947.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Talk:World History

http://en.wikibooks.org/wiki/World_History:An_Age_of_Empires_-_Rome%2C_Han_China%2C_and_the_Silk_Road has been split into two different chapters (The Roman Empire needs it's own chapter for sure) but the links are now broken. Planned Stages of Development
 * 1) Humble Beginnings- Intial exploratory action and structural plans Accomplished
 * 2) Operation: Blank Check- Finalization of structure and basic articles- See The Rise of Dictatorship and Totalitarianism for an example of the type of article completeness desired Current
 * 3) Exapand-a-lot- Addition of information concerning cultural, artistic, architectural, and societal conditions/achievements for cultures, especially noting the interactions between them, pointing out little known phenomen (i.e. North-South trade patterns are often ignored versus the ever-prevalent East-West trade)
 * 4) It's a fixer-upper- Error-proofing, addition of multiple-choice review to each article and to the entire project, addition of material and accuracy checking
 * 5) The Home Stretch- Final accuaracy checking, error-proofing, etc.
 * 6) Exit Stage-Left- The completion of the project and advertising- contacting AP World History teachers, the College Board, etc. and turning the project into a regular source of information to students, teachers, and interested persons

Old talk (pre-Standard change)

Oh what fun, I've now added a section the Weimar Republic (it seems appropriate here) tomorrow I'll spruce up ol' Mussolini and finish up Hitler. Then on to World War II! Oh, I think I'll tackle some ancient history tomorrow as well. But where to put the Great Depression? I guess it's own article is the way to go. And since I'm the only big contributor for a month...I am kind of giving myself free reign to take the reins (inline assonance intentional :-) of power for the time being. I think however, I will begin to aim for AP World History standards (I achieved a 5, so I will call myself well-qualified for the task) rather than the very regional California standards (although they provide an excellent baseline) I will give a week's notice before I unilaterally make the standards change. Please comment--Naryathegreat 04:13, 6 Nov 2004 (UTC)

So what'd I get done today? Let's see, I redid much of the structure of the historical contents page and moved some pages around. I added potential sections. I added info on the AP World History Standard. I added a disclaimers page and a Golden Rule, to help keep us on track. As soon as the Standard change is official, I'm taking the California standards out of the articles and will probably replace them with the appropriate AP World History Standard material. I redid ol' Mussolini and made the Maya something to be proud of, as well as restructuring the Precolumbian page. It now takes into account all the cultures likely you'll want to know about. You personally probably haven't heard of them, and I've got some more, if we get to that eventuality. I created World History 101, a clever introduction and explanation that should help streamline the process of getting FAQs out of the way. I mean it about rapid progression over the next month. I beleive by that time it will be at least half finished, and worthy of an "orange" two-block recognition. You deserve commendation for putting the project into place and giving it some initial vitality. But now, it's time to get moving, abandon the regional standard, and I pray, make it a good enough page that I'm not just always talking to thin air.--Naryathegreat 23:51, 6 Nov 2004 (UTC)

Okay, well, I'm back after my extended leave of abscence for personal reasons. Actually I've been back for a while but I just haven't done major edits. I added a large amount to the Roman Republic part of that article and I plan to add some more to other parts over the next few weeks. A few people have shown actual interest in helping now so I hope this project becomes further advanced. Thanks for you interst in our project if you're reading this! Also, I choose to stay with the AP World History Standard for now because whoever it was that was upset a few months back never turned up again or spoke to me personally so...Anwyway, if you want to help and don't know where to start, then drop me a line and I'll give you some starting places. We don't just need contributors-- we need proofreaders and reviewers too (reviewers check for consistency and smooth transition of ideas, all that sort of thing). I'd love your help!--Naryathegreat

Naming convention
Hi, I assembled the Top active list of Wikibooks. Unfortunately, World History does not follow any naming convention, so the contributions can not be attributed easily to a book. If somebody is still working on this book, please consider a consistent naming convention, so that all pages belonging to World History can be recognized by a computer script.

It is up to you to choose either World History World History:Ancient Civilizations

or the more modern version (since subpages have been activated on Wikibooks recently) World History World History/Ancient Civilizations

(subpages give additional navigational advantages, e.g. an automatic link to the parent page, etc.)

Logged in users can easily move pages by the "move" command. Thanks! --Andreas 06:09, 12 Mar 2005 (UTC)

Frustration
I'm dissapointed. A WikiProject entitled WORLD history turns out to be exclusivley HUMAN history. Were this a fair and balanced representation of the history of our species, I'd be satisfied. However, this project is culturally-one sided.

This project dismisses the first 99.5% of human history in 1 'chapter', less than 20 sentances. This summary effectivley throws out the overwhelming majority of the history of our species as trash: not worth writing about, not worth reading about, not worth learning about. More or less, this project makes this point:

"Around 10,000 years ago agriculture... effectivly started civilization and the begining of the nation-state."

Which implies:

"Nothing worthwhile happened until agriculture was developed 10,000 years ago"

and

"The initial 99% of the history of our species was spent building UP to our civilized state."

Honestley.

The 'history' book you are writing has been written before, in every text book across the globe. This in an opportunity to BREAK THE MOLD, and write a history of our species that does not dismiss "prehistory" as worthless. You guys are throwing this opportunity away.

 * Don't view this as the 'final essay'. If you have information to add--add it!  Wiki projects like this are ongoing and information is only available as people add it.  Obviously, there is an overwhelming amount of data that needs to be added.  So contact whatever history experts you know and have them insert the missing data!  Don't complain about it--fix it. That's what Wiki is all about.

 * To add on - If you honestly feel the need to have a difference in perspective, it would be beneficial to all for you to include it within the book's framework (or as a totally new wikibook). However, the standards that wikibooks should aspire to should still be maintained, especially with regards to facuality and NPOV.I do not believe the original author(s) intended this to be a totally biased POV article; it's just that, humans have only seen history from our own POV, and even then records of ancient times have been badly maintained if at all. Certainly if you have insights to the areas you mentioned, I believe wikibooks will welcome your contributions (within reasons, of course). Lynx7725 17:19, 21 Jun 2005 (UTC)

 * If you want anthropology, write and anthropology book. Don't get your shorts in a wad because you can't change definitions to suit your prejudices.  History is a record of HUMAN events, particularly human WRITTEN events. we need to make this like the U.S. history book

 * Isn't this supposed to be a HISTORY book? Pre-history is not history at all, and the first chapter really should be scrapped. It might be ok in a Science book, or anthropology, or mythology, or something--but the fact remains it's really not history! It can't be history unless we have written records.--Linesdata 17:54, 31 October 2007 (UTC)

First chapter on China started
I'm new to editing Wikibooks, but after reading some of them - specifically this one - and noticing missing content, I decided to do some personal research. As a result, I typed up "The Mythical Period" in Chapter 5: The First Chinese Dynasties. I'm not sure if it conforms to AP standards, but I hope it fits well. Thanks!

--Ccny930

Christian first chapter
How about having an optional first chapter that has origins from a Christian perspective, so that this can be developed as homeschoole friendly, and the instructor can choose which chapter to use.?

All Wiki's are written from a non buyist perspective and therefore the most scientific perspective (except for the buyist wikis of course) It would be extremely inappropiate to write a christian point of view because the bible states that the Earth is only  about 5000 years old. your best bet would be to come up with your own first chapter, skip it, or use an entirely different source of information.

I believe I can speak for a great number of people who would also find it totally unacceptable to write any history from a specifically Christian perspective. Does "homeschoole(sic)friendly" mean that children who are homeschooled are mostly being taught history, and other subjects, from a "Christian perspective?" Does this mean they are being sheltered from "non-Christian" education in public schools? If this is the case, I don't think you are going to find a great deal of "creationist" literature or other media on Wikibooks in Wikimedia, unless it is to explain creationism. I'm sure Wiki-people come from all backgrounds, but I believe we all agree that the scientific method is one construct of reality from which learning materials in "academic" topics are best oriented. Of course, I am not saying that religious topics should or would be kept out of Wikibooks or Wikimedia at all.

Brazil content
Brazilian History page up for deletion can you use it in this project? ChessCreator (talk) 16:53, 15 February 2008 (UTC)

Some remarks regarding structure of project
I notice that material regarding early chinese dynasties is duplicated in Ancient Civilisations and The First Chinese dynasties. Also the structure of Ancient Civilisations could do with some tidying up; The Hittites,Kassites and Assyrians should be moved into the Mesopotamian section as there is a clear linear sequence between these civilisations and events in southern Mesopotamia. Besides, should the Kassites be seen as an independent civilisation.

Material regarding the Persians should be moved from the Ancient Civilisations section and moved to the Greek Section where it is contemporaneous, (also alter the title of the Greek section as well to include Persians). The Persians signify the end of Mesopotamian dominance and therefore should not be included in that section, they are not as ancient as the New Babylonians.

I would like to contribute to this project but until the overall structure is decided upon, I don't know whether my work is duplicated or not, or whether it will be eventually deleted. I read a chapter on Mesopotamian history and made copious notes on the Amorites,Kassites,Hittites and Assyrians without realising the text had information on them at the end of the Ancient Civilisations section. I might add something at another time.

I hesitate on making the changes myself without some discussion beforehand.

Also see my remarks in the talk page of Ancient Civilisations.

Zfishwiki (talk) 18:19, 28 April 2010 (UTC)

anyone still here
if no one else seems to be active I have some big ideas which involve moving/creating/combing chapters and other large structural changes. I received a five on the AP exam myself and know a few of its secrets.

If their is no opposition I propose a new table of contents that i believe better fits AP standards and flows better
 * 1) Ancient civilizations
 * 2) Migrations and complications
 * 3) The Axial Age
 * 4) Greece and Persia
 * 5) Rome
 * 6) Classical Asia
 * 7) Islam
 * 8) Darkness in Europe
 * 9) The golden age of Asia
 * 10) Hemispheric interaction
 * 11) Mongols and aftermath
 * 12) The ancient Americas
 * 13) Empires of Gunpowder
 * 14) Global transformation: Early modern interactions
 * 15) The European transformation
 * 16) The Russian emergence
 * 17) Asia and Africa in transition
 * 18) The enlightenment  and revolution
 * 19) The revolution of everyday life, the industrial revolution
 * 20) The European world order
 * 21) The Japanese reaction
 * 22) Into the trench: World War one
 * 23) Depression and dictators
 * 24) The War of the world
 * 25) The cold war
 * 26) Latin America
 * 27) The African emergence
 * 28) The New Asia
 * 29) Globalization

Plagiarism
I was suspicious that large amounts of this were not original content I am right, copying and pasting random paragraphs of this book into google I found that most of them were cut and paste out of other books and never did a see a citation, therefore the majority of this book should be removed for copyright violations it seems.

Format of textbook
The entire format of the textbook is probably outdated and it doesn't match the 2016 AP World History course format. For example,other then Egypt, most of Africa doesn't play a big role in ancient river valley civilizations. The AP exam focuses much more on the Indus, Chinese, Egypt and Mesopotamia civilizations. But there is still an entire section about the African continent that was in the beginning of the textbook. So I will try to rearrange the sections to make it unanimous with the AP World History course format.RenaissanceMan2144 (discuss • contribs) 03:07, 7 December 2016 (UTC)

title: Talk:World History


text:
Spanish/Lesson 6

Direct Object Pronouns
While the subject of a sentence initiates an action (the verb), the direct object is the one that is affected by the action. A direct object pronoun is used to refer to the direct object of a previous sentence:

The following table shows the six types of direct object pronouns:

In spanish tú is used for informal situations, and usted must be used when a formal treatment is needed.

Note: In Spain, le and les are used as the masculine direct object pronoun only when referring to people. If the antecedent of a direct object is masculine but non-human, lo or los are used instead. In most other Spanish speaking places, lo and los are used instead of le and les.

Indirect Object Pronouns
An indirect object is an object that would be asked for with To whom...? or From whom...?. It is called indirect because it occurs usually together with a direct object which is affected directly by the action:

The apple is given by the woman (direct). The boy gets the given apple (indirect - depends on the apple being given).

Here is a table with all of the Spanish indirect object pronouns:

Position Of Object Pronouns (Double Object Pronouns)
So far we have only seen sentences with one object pronoun. If there is both a direct and an indirect object pronoun, the indirect pronoun usually comes first:

Also, when both object pronouns are in the third person (either singular or plural), the indirect pronoun changes from le/les to se:

In sentences that contain an infinitive or a participle, the object pronoun may be either placed before the conjugated verb or it maybe attached to the infinitive/participle:

It is possible to have the two rules above working at the same time: A combination of direct and indirect pronouns that is attached to an infinitive/participle:

Exercise:Object Pronouns

Vocabulario (Vocabulary) - La comida (Food)
In Spain and some other countries, comida is the midday meal.

In other countries, for example Chile, comida is the last meal in the day.

Instead of saying desayuno, comida y cena (Spain) or desayuno, almuerzo y comida (Chile, Colombia), it's safer to say desayuno, almuerzo y cena.

The word comida has several meanings
 * food Me gusta la comida mexicana
 * meal El desayuno es la principal comida del día
 * lunch La comida es a las 2 PM
 * dinner La comida es a las 9 PM

Note that due to the pervasive influence of English, in many supermarkets there is a section called Vegetales instead of Verduras. They mistranslate vegetable, forgetting that this is not the same as English vegetal (relating to plants).

 * Legumbres means the same thing as verduras (vegetables).

title: Spanish/Lesson 6


text:
Perl Programming

These books describe and explain Perl, a high-level, general-purpose, interpreted, dynamic programming language. Perl is noted for its idiomatically rich syntax, its extensive use of regular expressions and the large module archive CPAN.

Contents

 * /About Perl//

Beginning Perl

 * /Getting started/
 * /Editors and IDEs/
 * /Perl Installation and Setup/
 * First program
 * /Basic variables/
 * /Strings/
 * /Numbers/
 * /Comments/
 * /Conditionals/
 * /Control flow/
 * /Declarations/
 * /Operators/
 * /Variables/
 * /Data types/
 * /Scalar variables/
 * /Array variables/
 * /Hash variables/
 * /References and data structures/
 * /User input-output/
 * /Advanced output/
 * /Filehandles/
 * Statement modifiers
 * /Functions/
 * /Perl 5.10 additions/
 * Exercises

More Perl

 * /Regular expressions/
 * /Regular expression operators/
 * /Regular expressions reference/
 * /Code reuse (modules)/
 * Perl objects
 * /Structure and style/

Interfacing Perl

 * GUI and desktop programming
 * /CPAN/
 * Using a Bitcard account
 * /DBI - Perl database interface/

Web development

 * /CGI/
 * /FastCGI/
 * mod_perl
 * /HTML::Mason/
 * /HTTP::Engine/
 * /PSGI/
 * /Unicode UTF-8/

Perl and beyond

 * /Perl 6/
 * /Humour/

Sample code

 * First example code to get you started
 * Second example code to get you started

Reference

 * /Concept index/
 * /Function reference/
 * /Keywords/
 * Quick-reference cards
 * /Useful modules/
 * /Websites/

Related Wikibooks

 * Perl 6 Programming
 * Apache/mod perl

Perl-Programmierung Programación en Perl Programmation Perl Perl Perl Perl Perl

title: Perl Programming


text:
Talk:Spanish/Lesson 6

I have a question about the format in the vocabulary. In my opinion, the correct translation for "la manzana" (for instance) is "the applet" and not "applet". Is perfectly correct to say in Spanish "manzana". I think that if we want to use "el" or "la" with the words for make more clear the genre we should translate that like "the applet". That sounds more correct for me.

Wintermute 19:47 8 Aug 2003 (UTC)

 * I think the sentence "Quiero mostrar una casa a ti." can be written as "Quiero mostrarte una casa." The first form is correct, but it sounds somewhat foolish or childish.

 * OASO (Octavio Salguero)

 * I've changed the sentence OASO, (btw. feel free to just go and edit the pages right away if you see something that is incorrect and/or stylistically bad). Thomas Strohmann

Platano and/or Banano?
Hlasso 22:22, 30 March 2006 (UTC) In some countries the words 'banano' and 'platano' are used for different fruits. Banano is very similar to platano, however, platano is bigger and requires cooking to be eaten. In several countries the green 'platano' (not reap yet) is fried to make 'Patacón'.

Articles in Spanish
Hlasso 22:27, 30 March 2006 (UTC) I agree that translating "la manzana" to "apple" is incorrect. And I think this small error can be found throughout the document. For example: "El Vocabulario" is not common in spanish, books having a vocabulary usually have that section named "Vocabulario".

I'd help modifying the pages, but I'd like to hear the main author point of view before doing so.

title: Talk:Spanish/Lesson 6


text:
Lojban/Colours

 * gusni illumine `light'
 * Rafsi: gus, gu'i
 * Definition: x1 [energy] is light/illumination illuminating x2 from light source x3
 * Notes: x3 illuminates/lights x2 with light/illumination x1; x2 is lit/illuminated by illumination x1 from source x3 (= selgu'i for reordered places); light/lamp (= tergu'i) See also dirce, manku, solri, carmi, ctino, kantu.
 * viska see `vision'
 * Rafsi: vis, vi'a
 * Definition: x1 sees/views/perceives visually x2 under conditions x3
 * Notes: Also (adjective:) x1 is visual; x3 can include ambient lighting, background, etc. which may affect what is perceived; note that English "see" often means "look" or a more generic "observe", or even "understand, know". See also catlu, jvinu, kanla, minra, simlu, djuno, jimpe, zgana, ganse.
 * catlu look
 * Rafsi: cta
 * Definition: x1 looks at/examines/views/inspects/regards/watches/gazes at x2
 * Notes: Also look through (= grecta, ravycta, bacycta); note that English "look" often means a more generic "observe". See also jvinu, minra, simlu, viska, lanli, zgana, setca, viska.
 * jvinu view
 * Rafsi: vin, ji'u
 * Definition: x1 is the view/scene/panorama/sight/prospect of x2 (object/location) from point-of-view x3
 * Notes: Also x1 is on display to x2/x3. See also catlu, kanla, viska, canko, jarco.
 * manku dark
 * Rafsi: man
 * Definition: x1 is dark/lacking in illumination
 * Notes: (cf. blabi, gusni, ctino; use kandi or xekri with colors, ctino)
 * ctino shadow `shade'
 * Rafsi: ti'o
 * Definition: x1 is a shadow/the shade of object x2, made by light/energy source x3
 * Notes: See also manku, gusni.
 * skari color
 * Rafsi: ska
 * Definition: x1 is/appears to be of color/hue x2 as perceived/seen by x3 under conditions x4
 * Notes: Conditions may include lighting, background, etc.. See also blanu, bunre, cicna, cinta, crino, grusi, narju, nukni, pelxu, xunre, zirpu, carmi, kandi, xekri, blabi.
 * xekri black
 * Rafsi: xek, xe'i
 * Definition: x1 is black/extremely dark-colored [color adjective]
 * Notes: See also blabi, grusi, manku, skari, xekri, kandi, carmi, blanu, bunre, cicna, crino, narju, nukni, pelxu, xunre, zirpu.
 * blabi white
 * Rafsi: lab
 * Definition: x1 is white/very-light colored [color adjective]
 * Notes: Pale forms of other colors are a compound of white; e.g. pink (= labyxu'e, xunblabi) (whereas kandi is used for pale = dimness, lack of intensity). See also skari, xekri, grusi, kandi, manku, carmi, bakri, blanu, bunre, cicna, crino, narju, nukni, pelxu, xunre, zirpu.
 * grusi gray
 * Rafsi: rus
 * Definition: x1 is gray [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi.
 * xunre red
 * Rafsi: xun, xu'e
 * Definition: x1 is red/crimson/ruddy [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, nukni, narju, rozgu, zirpu.
 * pelxu yellow
 * Rafsi: pel
 * Definition: x1 is yellow/golden [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, narju, solji.
 * crino green
 * Rafsi: ri'o
 * Definition: x1 is green/verdant [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, cicna.
 * blanu blue
 * Rafsi: bla
 * Definition: x1 is blue [color adjective]
 * Notes: See also skari, blabi, xekri, zirpu, kandi, carmi, cicna.
 * bunre brown
 * Rafsi: bur, bu'e
 * Definition: x1 is brown/tan [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi.
 * cicna cyan
 * Rafsi: (none)
 * Definition: x1 is cyan/turquoise/greenish-blue [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, crino, blanu.
 * narju orange
 * Rafsi: naj
 * Definition: x1 is orange [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, xunre, pelxu, solji.
 * nukni magenta `fuchsin'
 * Rafsi: nuk
 * Definition: x1 is magenta/fuchsia/purplish-red [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, xunre, zirpu.
 * zirpu purple
 * Rafsi: zir, zi'u
 * Definition: x1 is purple/violet [color adjective]
 * Notes: See also skari, blabi, xekri, kandi, carmi, nukni, blanu, xunre.

title: Lojban/Colours


text:
Lojban/Foods and beverages

Beverages

 * djacu water
 * Rafsi: jac jau
 * Definition: x1 is made of/contains/is a quantity/expanse of water; (adjective:) x1 is aqueous/[aquatic]
 * Notes: [aquatic (= jaupli)]; (cf. lalxu, rirxe, xamsi, limna, litki, lumci, bumru, jinto)
 * xalka alcohol
 * Rafsi: xal
 * Definition: x1 is a quantity of/contains/is made of alcohol of type x2 from source/process x3
 * Notes: See also birje, jikru, vanju.
 * jikru liquor
 * Rafsi: (none)
 * Definition: x1 is made of/contains/is a quantity of liquor/spirits distilled from x2
 * Notes: See also barja, vanju, birje, xalka.
 * vanju wine
 * Rafsi: van
 * Definition: x1 is made of/contains/is a quantity of wine from fruit/grapes x2
 * Notes: See also barja, birje, xalka, jikru, fusra.
 * birje beer
 * Rafsi: (none)
 * Definition: x1 is made of/contains/is a amount of beer/ale/brew brewed from x2
 * Notes: See also pinxe, barja, jikru, vanju, xalka, fusra.
 * jisra juice
 * Rafsi: (none)
 * Definition: x1 is made of/contains/is a quantity of juice/nectar from-source/of-type x2
 * Notes: Water-based extract from a (generally) biological source. See also pinxe, djacu, grute, stagi.
 * sodva soda
 * Rafsi: sod
 * Definition: x1 is made of/contains/is a quantity of a carbonated beverage/soda of flavor/brand x2
 * Notes: Also: soft drink (though this sometimes includes tea and coffee as distinct from alcoholic beverages which are "hard drinks"). See also jilka, jinme.
 * ckafi coffee
 * Rafsi: kaf
 * Definition: x1 is made of/contains/is a quantity of coffee from source/bean/grain x2
 * Notes: Brew based on a seed/bean/grain; e.g. also chicory coffee, decaf, postum. See also tcati, brewed from a leaf, barja, cakla.
 * tcati tea
 * Rafsi: (none)
 * Definition: x1 is made of/contains/is a quantity of tea brewed from leaves x2
 * Notes: See also ckafi.

Foods

 * sanmi meal
 * Rafsi: sai
 * Definition: x1 (mass) is a meal composed of dishes including x2
 * Notes: x2 is a course/dish of meal x1 (= selsai for reordered places). See also barja, stasu, gusta, sanso.
 * rectu meat `flesh'
 * Rafsi: rec, re'u
 * Definition: x1 is a quantity of/contains meat/flesh from source/animal x2
 * Notes: See also sluji.
 * grasu grease
 * Rafsi: ras
 * Definition: x1 is a quantity of/is made of/contains grease/fat/oil from source x2
 * Notes: See also ctile, matne, plana.
 * ladru milk `lactic'
 * Rafsi: lad
 * Definition: x1 is made of/contains/is a quantity of milk from source x2; (adjective:) x1 is lactic/dairy
 * Notes: See also lanbi, mabru, tatru, cirla, kruji.
 * kruji cream
 * Rafsi: ruj
 * Definition: x1 is made of/contains/is a quantity of cream/emulsion/puree [consistency] of composition x2
 * Notes: [x2: composition including x2, which need not be complete specification]; See also ladru, matne.
 * matne butter
 * Rafsi: (none)
 * Definition: x1 is a quantity of/contains butter/oleo/margarine/shortening from source x2
 * Notes: (adjective:) x1 is buttery; an edible fat, solid but spreadable at normal temperatures; dairy butter (= ladmatne). See also grasu, kruji.
 * cirla cheese
 * Rafsi: (none)
 * Definition: x1 is a quantity of/contains cheese/curd from source x2
 * Notes: See also ladru.
 * sakta sugar `sucrose'
 * Rafsi: sat
 * Definition: x1 is made of/contains/is a quantity of sugar [sweet edible] from source x2 of composition x3
 * Notes: Also sucrose, fructose, glucose, galactose, lactose, etc.; saccharine/aspartame/sugar substitute (basysakta or sakybasti, ticysakta); x3: composition including x3, which need not be complete specification. See also silna, titla.
 * cakla chocolate
 * Rafsi: (none)
 * Definition: x1 is made of/contains/is a quantity of chocolate/cocoa
 * Notes: See also ckafi.
 * nanba bread
 * Rafsi: nab
 * Definition: x1 is a quantity of/contains bread [leavened or unleavened] made from grains x2
 * Notes: See also gurni, panlo, toknu.
 * salta salad
 * Rafsi: (none)
 * Definition: x1 (mass) is a quantity of salad [food] with ingredients/components including x2
 * Notes: x2 is in x1, an ingredient/part/component of x1. See also mixre, stasu.
 * sanso sauce
 * Rafsi: (none)
 * Definition: x1 is a sauce/topping/gravy/frosting for use with x2, containing ingredient(s) including x3
 * Notes: x3 is in x1, an ingredient/part/component of sauce x1. See also sanmi, mixre, stasu.
 * stasu soup `stew'
 * Rafsi: (none)
 * Definition: x1 is a quantity of soup/stew/olla/olio [food] of ingredients including x2
 * Notes: x2 is in x1, an ingredient/part/component of x1. See also sanmi, mixre, salta, sanso.
 * tsapi seasoning
 * Rafsi: (none)
 * Definition: x1 is a seasoning/condiment/spice causing flavor/effect x2 (event/property)
 * Notes: Also: x1 flavors x2 (tu'a). See also vrusi.
 * sigja cigar
 * Rafsi: sig
 * Definition: x1 is a cigar/cigarette/cigarillo made from tobacco/smokable substance x2 by x3
 * Notes: See also danmo, jelca, tanko, marna.

Vegetables

 * kobli cabbage `cole-'
 * Rafsi: kob, ko'i
 * Definition: x1 is a quantity of cabbage/lettuce/leafy vegetable of species/strain x2
 * Notes: See also stagi.
 * tamca tomato
 * Rafsi: (none)
 * Definition: x1 is a tomato [fruit/vegetable/plant] of species/strain x2
 * Notes: See also grute, stagi.
 * sluni onion
 * Rafsi: (none)
 * Definition: x1 is a quantity of/contains onions/scallions of type/cultivar x2
 * Notes: See also stagi.
 * sunga garlic
 * Rafsi: sug
 * Definition: x1 is a quantity of garlic [bulb] of species/strain x2
 * Notes: See also stagi.
 * patlu potato
 * Rafsi: (none)
 * Definition: x1 is a potato [an edible tuber] of variety/cultivar x2
 * Notes: (use samcu for starchy/tuberous roots that do not reproduce from eyes of tuber); See also genja, jalna, samcu.
 * samcu cassava `yam'
 * Rafsi: (none)
 * Definition: x1 is a quantity of cassava/taro/manioc/tapioca/yam [edible starchy root] of species/strain x2
 * Notes: See also patlu, genja, jalna.

Fruits

 * badna banana
 * Rafsi: (none)
 * Definition: x1 is a banana/plantain [fruit/plant] of species/breed x2
 * Notes: See also grute.
 * nimre citrus `lime'
 * Rafsi: (none)
 * Definition: x1 is a quantity of citrus [fruit/tree, etc.] of species/strain x2
 * Notes: See also grute, slari, slami, xukmi.
 * plise apple
 * Rafsi: (none)
 * Definition: x1 is an apple [fruit] of species/strain x2
 * Notes: See also grute.
 * perli pear
 * Rafsi: per
 * Definition: x1 is a pear [fruit] of species/strain x2
 * Notes: See also grute.
 * guzme melon
 * Rafsi: guz zme
 * Definition: x1 is a melon/squash [fruit/plant] of species/strain x2
 * Notes: See also grute.
 * figre fig
 * Rafsi: fig
 * Definition: x1 is a fig [fruit/tree] of species/strain x2
 * Notes: See also grute.

Digestion

 * pinxe drink
 * Rafsi: pix
 * Definition: x1 (agent) drinks/imbibes beverage/drink/liquid refreshment x2 from/out-of container/source x3
 * Notes: See also cidja, citka, taske, tunlo, xaksu, barja, birje.
 * cidja food `feed'
 * Rafsi: dja
 * Definition: x1 is food/feed/nutriment for x2; x1 is edible/gives nutrition to x2
 * Notes: See also citka, nitcu, pinxe, xagji, cpina.
 * vindu poison `venom'
 * Rafsi: vid
 * Definition: x1 is poisonous/venomous/toxic/a toxin to x2
 * Notes: See also since.
 * vikmi excrete
 * Rafsi: vim, vi'i
 * Definition: x1 [body] excretes waste x2 from source x3 via means/route x4
 * Notes: See also cigla, kalci, pinca, xasne.
 * kalci feces `shit'
 * Rafsi: (none)
 * Definition: x1 is a/the feces/excrement/dung/shit of x2 (animal/person); (adjective:) x1 is fecal (matter)
 * Notes: Also crap. See also ganxo, pinca, vikmi, mabla, festi.
 * pinca urine `piss'
 * Rafsi: (none)
 * Definition: x1 is a/the urine/piss/pee of x2
 * Notes: See also vikmi, xasne, kalci, mabla, festi.
 * vamtu vomit
 * Rafsi: vat
 * Definition: x1 vomits/regurgitates x2; x1 throws x2 up; [violent] digestive expulsion
 * Notes: (x2 is non-gaseous); See also rigni, jetce, kafke, sputu.

title: Lojban/Foods and beverages


text:
Waves/1D Solutions

As you have learned in the previous sections, the linear waves you studied in the previous section tend to disperse. However, there are nonlinear waves described by nonlinear partial differential equations (PDE) which admits solutions with nondispersing wave packets.

Here are two primary examples:

Sine-Gordon
This is described by the PDE

$$\partial^2_x\phi-\partial^2_t\phi=\sin(\phi)$$.

The equation of a wave travelling along the positive x direction is given by y=0.25 x 0.001sin(500t-0.025x)determine the angular frequence

title: Waves/1D Solutions


text:
Calculus/Differentiation/Differentiation Defined

What is Differentiation?
Differentiation is a process of finding a function that outputs the rate of change of one variable with respect to another variable.

Informally, we may suppose that we're tracking the position of a car on a two-lane road with no passing lanes. Assuming the car never pulls off the road, we can abstractly study the car's position by assigning it a variable, $$x$$. Since the car's position changes as the time changes, we say that $$x$$ is dependent on time, or $$x=f(t)$$. This tells where the car is at each specific time. Differentiation gives us a function $$\frac{dx}{dt}$$ which represents the car's speed, that is the rate of change of its position with respect to time.

Equivalently, differentiation gives us the slope at any point of the graph of a non-linear function. For a linear function, of form $$f(x)=ax+b$$, $$a$$ is the slope. For non-linear functions, such as $$f(x)=3x^2$$, the slope can depend on $$x$$ ; differentiation gives us a function which represents this slope.

The Definition of Slope
Historically, the primary motivation for the study of differentiation was the tangent line problem: for a given curve, find the slope of the straight line that is tangent to the curve at a given point. The word tangent comes from the Latin word tangens, which means touching. Thus, to solve the tangent line problem, we need to find the slope of a line that is "touching" a given curve at a given point, or, in modern language, that has the same slope. But what exactly do we mean by "slope" for a curve?

The solution is obvious in some cases: for example, a line $$y=mx+c$$ is its own tangent; the slope at any point is $$m$$. For the parabola $$y=x^2$$, the slope at the point $$(0,0)$$ is $$0$$ ; the tangent line is horizontal.

But how can you find the slope of, say, $$y=\sin(x)+x^2$$ at $$x=1.5$$ ? This is in general a nontrivial question, but first we will deal carefully with the slope of lines.

The Slope of a Line
The slope of a line, also called the gradient of the line, is a measure of its inclination. A line that is horizontal has slope 0, a line from the bottom left to the top right has a positive slope and a line from the top left to the bottom right has a negative slope.

The slope can be defined in two (equivalent) ways. The first way is to express it as how much the line climbs for a given motion horizontally. We denote a change in a quantity using the symbol $$\Delta$$ (pronounced "delta"). Thus, a change in $$x$$ is written as $$\Delta x$$. We can therefore write this definition of slope as:
 * $${\rm Slope}=\frac{\Delta y}{\Delta x}$$

An example may make this definition clearer. If we have two points on a line, $$P(x_1,y_1)$$ and $$Q(x_2,y_2)$$, the change in $$x$$ from $$P$$ to $$Q$$ is given by:
 * $$\Delta x=x_2-x_1$$

Likewise, the change in $$y$$ from $$P$$ to $$Q$$ is given by:
 * $$\Delta y=y_2-y_1$$

This leads to the very important result below.

Alternatively, we can define slope trigonometrically, using the tangent function:
 * $${\rm Slope}=\tan(\alpha)$$

where $$\alpha$$ is the angle from the rightward-pointing horizontal to the line, measured counter-clockwise. If you recall that the tangent of an angle is the ratio of the y-coordinate to the x-coordinate on the unit circle, you should be able to spot the equivalence here.

Of a graph of a function
The graphs of most functions we are interested in are not straight lines (although they can be), but rather curves. We cannot define the slope of a curve in the same way as we can for a line. In order for us to understand how to find the slope of a curve at a point, we will first have to cover the idea of tangency. Intuitively, a tangent is a line which just touches a curve at a point, such that the angle between them at that point is 0. Consider the following four curves and lines:

 The line $$L$$ crosses, but is not tangent to $$C$$ at $$P$$ . The line $$L$$ crosses, and is tangent to $$C$$ at $$P$$ . The line $$L$$ crosses $$C$$ at two points, but is tangent to $$C$$ only at $$P$$ . There are many lines that cross $$C$$ at $$P$$, but none are tangent. In fact, this curve has no tangent at $$P$$ .

A secant is a line drawn through two points on a curve. We can construct a definition of a tangent as the limit of a secant of the curve taken as the separation between the points tends to zero. Consider the diagram below.

As the distance $$h$$ tends to 0, the secant line becomes the tangent at the point $$x_0$$. The two points we draw our line through are:
 * $$P(x_0,f(x_0))$$

and
 * $$Q(x_0+h,f(x_0+h))$$

As a secant line is simply a line and we know two points on it, we can find its slope, $$m_h$$, using the formula from before:
 * $$m=\frac{y_2-y_1}{x_2-x_1}$$

(We will refer to the slope as $$m_h$$ because it may, and generally will, depend on $$h$$ .) Substituting in the points on the line,
 * $$m_h=\frac{f(x_0+h)-f(x_0)}{(x_0+h)-x_0}$$

This simplifies to
 * $$m_h=\frac{f(x_0+h)-f(x_0)}{h}$$

This expression is called the difference quotient. Note that $$h$$ can be positive or negative — it is perfectly valid to take a secant through any two points on the curve — but cannot be $$0$$.

The definition of the tangent line we gave was not rigorous, since we've only defined limits of numbers — or, more precisely, of functions that output numbers — not of lines. But we can define the slope of the tangent line at a point rigorously, by taking the limit of the slopes of the secant lines from the last paragraph. Having done so, we can then define the tangent line as well. Note that we cannot simply set $$h$$ to 0 as this would imply division of 0 by 0 which would yield an undefined result. Instead we must find the limit of the above expression as $$h$$ tends to 0:

This last equation is just the point-slope form for the line through $$(x_0,f(x_0))$$ with slope $$m$$.

Exercises
Solutions

The Rate of Change of a Function at a Point
Consider the formula for average velocity in the $$x$$ direction, $$\frac{\Delta x}{\Delta t}$$, where $$\Delta x$$ is the change in $$x$$ over the time interval $$\Delta t$$. This formula gives the average velocity over a period of time, but suppose we want to define the instantaneous velocity. To this end we look at the change in position as the change in time approaches 0. Mathematically this is written as: $$\lim_{\Delta t\to 0}\frac{\Delta x}{\Delta t}$$, which we abbreviate by the symbol $$\frac{dx}{dt}$$. (The idea of this notation is that the letter $$d$$ denotes change.) Compare the symbol $$d$$ with $$\Delta$$. The idea is that both indicate a difference between two numbers, but $$\Delta$$ denotes a finite difference while $$d$$ denotes an infinitesimal difference. Please note that the symbols $$dx$$ and $$dt$$ have no rigorous meaning on their own, since $$\lim_{\Delta t\to 0}\Delta t=0$$, and we can't divide by 0.

(Note that the letter $$s$$ is often used to denote distance, which would yield $$\frac{ds}{dt}$$ . The letter $$d$$ is often avoided in denoting distance due to the potential confusion resulting from the expression $$\frac{dd}{dt}$$.)

The Definition of the Derivative
You may have noticed that the two operations we've discussed — computing the slope of the tangent to the graph of a function and computing the instantaneous rate of change of the function — involved exactly the same limit. That is, the slope of the tangent to the graph of $$y=f(x)$$ is $$\frac{dy}{dx}$$. Of course, $$\frac{dy}{dx}$$ can, and generally will, depend on $$x$$, so we should really think of it as a function of $$x$$. We call this process (of computing $$\frac{dy}{dx}$$) differentiation. Differentiation results in another function whose value for any value $$x$$ is the slope of the original function at $$x$$. This function is known as the derivative of the original function.

Since lots of different sorts of people use derivatives, there are lots of different mathematical notations for them. Here are some:
 * $$f'(x)$$ (read "f prime of x") for the derivative of $$f(x)$$ ,
 * $$D_x[f(x)]$$ ,
 * $$Df(x)$$ ,
 * $$\frac{dy}{dx}$$ for the derivative of $$y$$ as a function of $$x$$ or
 * $$\frac{d}{dx}\big[y\big]$$, which is more useful in some cases.

Most of the time the brackets are not needed, but are useful for clarity if we are dealing with something like $$D(f\cdot g)$$, where we want to differentiate the product of two functions, $$f$$ and $$g$$.

The first notation has the advantage that it makes clear that the derivative is a function. That is, if we want to talk about the derivative of $$f(x)$$ at $$x=2$$, we can just write $$f'(2)$$.

In any event, here is the formal definition:

Examples
Example 1

The derivative of $$f(x)=\frac{x}{2}$$ is
 * $$f'(x)=\lim_{\Delta x\to 0}\left(\frac{\frac{x+\Delta x}{2}-\frac{x}{2}}{\Delta x}\right)=\lim_{\Delta x\to 0}\left(\frac{\frac{x}{2}+\frac{\Delta x}{2}-\frac{x}{2}}{\Delta x}\right)=\lim_{\Delta x\to 0}\left(\frac{\frac{\Delta x}{2}}{\Delta x}\right)=\lim_{\Delta x\to 0}\left(\frac{\Delta x}{2\Delta x}\right)=\lim_{\Delta x\to 0}\left(\frac12\right)=\frac12$$

no matter what $$x$$ is. This is consistent with the definition of the derivative as the slope of a function.

Example 2

What is the slope of the graph of $$y=3x^2$$ at $$(4,48)$$ ? We can do it "the hard (and imprecise) way", without using differentiation, as follows, using a calculator and using small differences below and above the given point:

When $$x=3.999$$, $$y=47.976003$$.

When $$x=4.001$$, $$y=48.024003$$.

Then the difference between the two values of $$x$$ is $$\Delta x=0.002$$.

Then the difference between the two values of $$y$$ is $$\Delta y=0.048$$.

Thus, the slope $$\frac{\Delta y}{\Delta x}=24$$ at the point of the graph at which $$x=4$$.

But, to solve the problem precisely, we compute

We were lucky this time; the approximation we got above turned out to be exactly right. But this won't always be so, and, anyway, this way we didn't need a calculator.
 * $$\lim_{\Delta x\to 0}\frac{3(4+\Delta x)^2-48}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}\frac{(4+\Delta x)^2-16}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}\frac{16+8\Delta x+(\Delta x)^2-16}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}\frac{8\Delta x+(\Delta x)^2}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}(8+\Delta x)$$
 * $$=3(8)$$
 * $$=24$$
 * }
 * $$=3\lim_{\Delta x\to 0}(8+\Delta x)$$
 * $$=3(8)$$
 * $$=24$$
 * }
 * $$=3(8)$$
 * $$=24$$
 * }
 * $$=24$$
 * }
 * }

In general, the derivative of $$f(x)=3x^2$$ is

 * $$f'(x)$$
 * $$=\lim_{\Delta x\to 0}\frac{3(x+\Delta x)^2-3x^2}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}\frac{(x+\Delta x)^2-x^2}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}\frac{x^2+2x\Delta x+(\Delta x)^2-x^2}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}\frac{2x\Delta x+(\Delta x)^2}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}(2x+\Delta x)$$
 * $$=3(2x)$$
 * $$=6x$$
 * }
 * $$=3\lim_{\Delta x\to 0}\frac{2x\Delta x+(\Delta x)^2}{\Delta x}$$
 * $$=3\lim_{\Delta x\to 0}(2x+\Delta x)$$
 * $$=3(2x)$$
 * $$=6x$$
 * }
 * $$=3(2x)$$
 * $$=6x$$
 * }
 * $$=6x$$
 * }
 * $$=6x$$
 * }

Example 3

If $$f(x)=|x|$$ (the absolute value function) then $$f'(x)=\frac{x}{|x|}$$, which can also be stated as
 * $$f'(x)=\left\{\begin{matrix}-1&x<0\\ {\rm undefined}&x=0\\ 1&x>0\end{matrix}\right.$$

Finding this derivative is a bit complicated, so we won't prove it at this point.

Here, $$f(x)$$ is not smooth (though it is continuous) at $$x=0$$ and so the limits $$\lim_{x\to 0^+}f'(x)$$ and $$\lim_{x\to 0^-}f'(x)$$ (the limits as 0 is approached from the right and left respectively) are not equal. From the definition, $$f'(0)=\lim_{\Delta x\to 0}\frac{|\Delta x|}{\Delta x}$$, which does not exist. Thus, $$f'(0)$$ is undefined, and so $$f'(x)$$ has a discontinuity at 0. This sort of point of non-differentiability is called a cusp. Functions may also not be differentiable because they go to infinity at a point, or oscillate infinitely frequently.

Understanding the derivative notation
The derivative notation is special and unique in mathematics. The most common notation for derivatives you'll run into when first starting out with differentiating is the Leibniz notation, expressed as $$\frac{dy}{dx}$$. You may think of this as "rate of change in $$y$$ with respect to $$x$$". You may also think of it as "infinitesimal value of $$y$$ divided by infinitesimal value of $$x$$". Either way is a good way of thinking, although you should remember that the precise definition is the one we gave above. Often, in an equation, you will see just $$\frac{d}{dx}$$, which literally means "derivative with respect to x". This means we should take the derivative of whatever is written to the right; that is, $$\frac{d}{dx}(x+2)$$ means $$\frac{dy}{dx}$$ where $$y=x+2$$.

As you advance through your studies, you will see that we sometimes pretend that $$dy$$ and $$dx$$ are separate entities that can be multiplied and divided, by writing things like $$dy=x^4dx$$. Eventually you will see derivatives such as $$\frac{dx}{dy}$$, which just means that the input variable of our function is called $$y$$ and our output variable is called $$x$$ ; sometimes, we will write $$\frac{d}{dy}$$ , to mean the derivative with respect to $$y$$ of whatever is written on the right. In general, the variables could be anything, say $$\frac{d\theta}{dr}$$.

All of the following are equivalent for expressing the derivative of $$y=x^2$$
 * $$\frac{dy}{dx}=2x$$
 * $$\frac{d}{dx}x^2=2x$$
 * $$dy=2x\,dx$$
 * $$f'(x)=2x$$
 * $$D(f(x))=2x$$

Exercises
Solutions

Differentiation Rules
The process of differentiation is tedious for complicated functions. Therefore, rules for differentiating general functions have been developed, and can be proved with a little effort. Once sufficient rules have been proved, it will be fairly easy to differentiate a wide variety of functions. Some of the simplest rules involve the derivative of linear functions.

Derivative of a constant function
For any fixed real number $$c$$ , $\frac{d}{dx}[c]=0$

Intuition
The graph of the function $$f(x)=c$$ is a horizontal line, which has a constant slope of 0. Therefore, it should be expected that the derivative of this function is zero, regardless of the values of $$x$$ and $$c$$.

Proof
The definition of a derivative is
 * $$\lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$

Let $$f(x)=c$$ for all $$x$$. (That is, $$f$$ is a constant function.) Then $$f(x+\Delta x)=c$$. Therefore
 * $$\frac{d}{dx}[c]=\lim_{\Delta x\to 0}\frac{c-c}{\Delta x}=\lim_{\Delta x\to 0}\frac{0}{\Delta x}$$

Let $$g(\Delta x)=\frac{0}{\Delta x}$$. To prove that $$\lim_{\Delta x\to 0}g(\Delta x)=0$$, we need to find a positive $$\delta$$ such that, for any given positive $$\varepsilon$$ , $$\Big|g(\Delta x)-0\Big|<\varepsilon$$ whenever $$0<|\Delta x-0|<\delta$$. But $$\Big|g(\Delta x)-0\Big|=0$$, so $$\Big|g(\Delta x)-0\Big|<\varepsilon$$ for any choice of $$\delta$$.

Examples

 * 1) $$\frac{d}{dx}[3]=0$$
 * 2) $$\frac{d}{dx}[z]=0$$

Note that, in the second example, $$z$$ is just a constant.

Derivative of a linear function
For any fixed real numbers $$m$$ and $$c$$ , $\frac{d}{dx}[mx+c]=m$ The special case $$\frac{dx}{dx}=1$$ shows the advantage of the $$\frac{d}{dx}$$ notation—rules are intuitive by basic algebra, though this does not constitute a proof, and can lead to misconceptions to what exactly $$dx$$ and $$dy$$ actually are.

Intuition
The graph of $$y=mx+c$$ is a line with constant slope $$m$$.

Proof
If $$f(x)=mx+c$$, then $$f(x+\Delta x)=m(x+\Delta x)+c$$. So,

 * $$f'(x)$$
 * $$=\lim_{\Delta x\to 0}\frac{m(x+\Delta x)+c-mx-c}{\Delta x}$$
 * $$=\lim_{\Delta x\to 0}\frac{m(x+\Delta x)-mx}{\Delta x}$$
 * $$=\lim_{\Delta x\to 0}\frac{mx+m\Delta x-mx}{\Delta x}$$
 * $$=\lim_{\Delta x\to 0}\frac{m\Delta x}{\Delta x}$$
 * $$=m$$
 * }
 * $$=\lim_{\Delta x\to 0}\frac{mx+m\Delta x-mx}{\Delta x}$$
 * $$=\lim_{\Delta x\to 0}\frac{m\Delta x}{\Delta x}$$
 * $$=m$$
 * }
 * $$=m$$
 * }
 * $$=m$$
 * }

Constant multiple and addition rules
Since we already know the rules for some very basic functions, we would like to be able to take the derivative of more complex functions by breaking them up into simpler functions. Two tools that let us do this are the constant multiple rule and the addition rule.

The Constant Rule
For any fixed real number $$c$$ , $\frac{d}{dx}\big[c\cdot f(x)\big]=c\cdot\frac{d}{dx}\big[f(x)\big]$ The reason, of course, is that one can factor $$c$$ out of the numerator, and then of the entire limit, in the definition. The details are left as an exercise.

Example

We already know that
 * $$\frac{d}{dx}\big[x^2\big]=2x$$

Suppose we want to find the derivative of $$3x^2$$

 * $$\frac{d}{dx}\big[3x^2\big]$$
 * $$=3\frac{d}{dx}\big[x^2\big]$$
 * $$=3\cdot2x$$
 * $$=6x$$
 * }
 * $$=3\cdot2x$$
 * $$=6x$$
 * }
 * $$=6x$$
 * }

Another simple rule for breaking up functions is the addition rule.

The Addition and Subtraction Rules
$\frac{d}{dx}\big[f(x)\pm g(x)\big]=\frac{d}{dx}\big[f(x)\big]\pm\frac{d}{dx}\big[g(x)\big]$

Proof

From the definition:

By definition then, this last term is $$ \frac{d}{dx} \left[f(x)\right] \pm \frac{d}{dx}\left[g(x)\right] $$
 * $$\lim_{\Delta x\to 0}\left[\frac{\big[f(x+\Delta x)\pm g(x+\Delta x)\big]-\big[f(x)\pm g(x)\big]}{\Delta x}\right]$$
 * $$=\lim_{\Delta x\to 0}\left[\frac{\big[f(x+\Delta x)-f(x)\big]\pm\big[g(x+\Delta x)-g(x)\big]}{\Delta x}\right]$$
 * $$=\lim_{\Delta x\to 0}\left[\frac{f(x+\Delta x)-f(x)}{\Delta x}\right]\pm\lim_{\Delta x\to 0}\left[\frac{g(x+\Delta x)-g(x)}{\Delta x}\right]$$
 * }
 * $$=\lim_{\Delta x\to 0}\left[\frac{f(x+\Delta x)-f(x)}{\Delta x}\right]\pm\lim_{\Delta x\to 0}\left[\frac{g(x+\Delta x)-g(x)}{\Delta x}\right]$$
 * }

Example

What is the derivative of $$3x^2+5x$$ ?

 * $$\frac{d}{dx}\big[3x^2+5x\big]$$
 * $$=\frac{d}{dx}\big[3x^2+5x\big]$$
 * $$=\frac{d}{dx}\big[3x^2\big]+\frac{d}{dx}\big[5x\big]$$
 * $$=6x+\frac{d}{dx}\big[5x\big]$$
 * $$=6x+5$$
 * }
 * $$=6x+\frac{d}{dx}\big[5x\big]$$
 * $$=6x+5$$
 * }
 * $$=6x+5$$
 * }
 * $$=6x+5$$
 * }

The fact that both of these rules work is extremely significant mathematically because it means that differentiation is linear. You can take an equation, break it up into terms, figure out the derivative individually and build the answer back up, and nothing odd will happen.

We now need only one more piece of information before we can take the derivatives of any polynomial.

The Power Rule
$\frac{d}{dx}\big[x^n\big]=nx^{n-1}$ This has been proved in an example in Derivatives of Exponential and Logarithm Functions where it can be best understood.

For example, in the case of $$x^2$$ the derivative is $$2x^1=2x$$ as was established earlier. A special case of this rule is that $$\frac{dx}{dx}=\frac{dx^1}{dx}=1x^0=1$$.

Since polynomials are sums of monomials, using this rule and the addition rule lets you differentiate any polynomial. A relatively simple proof for this can be derived from the binomial expansion theorem.

This rule also applies to fractional and negative powers. Therefore

 * $$\frac{d}{dx}\big[\sqrt x\big]$$
 * $$=\frac{d}{dx}\big[x^\frac12\big]$$
 * $$=\frac12x^{-\frac12}$$
 * $$=\frac{1}{2\sqrt x}$$
 * }
 * $$=\frac12x^{-\frac12}$$
 * $$=\frac{1}{2\sqrt x}$$
 * }
 * $$=\frac{1}{2\sqrt x}$$
 * }

Derivatives of polynomials
With these rules in hand, you can now find the derivative of any polynomial you come across. Rather than write the general formula, let's go step by step through the process.
 * $$\frac{d}{dx}\big[6x^5+3x^2+3x+1\big]$$

The first thing we can do is to use the addition rule to split the equation up into terms:
 * $$\frac{d}{dx}\big[6x^5\big]+\frac{d}{dx}\big[3x^2\big]+\frac{d}{dx}\big[3x\big]+\frac{d}{dx}[1]$$

We can immediately use the linear and constant rules to get rid of some terms:
 * $$\frac{d}{dx}\big[6x^5\big]+\frac{d}{dx}\big[3x^2\big]+3+0$$

Now you may use the constant multiplier rule to move the constants outside the derivatives:
 * $$6\frac{d}{dx}\big[x^5\big]+3\frac{d}{dx}\big[x^2\big]+3$$

Then use the power rule to work with the individual monomials:
 * $$6(5x^4)+3(2x)+3$$

And then do some algebra to get the final answer:
 * $$30x^4+6x+3$$

These are not the only differentiation rules. There are other, more advanced, differentiation rules, which will be described in a later chapter.

Exercises

 * Find the derivatives of the following equations:

Solutions


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Waves/Fourier Transforms

Fourier Transform
So far, you've learned how to superimpose a finite number of sinusoidal waves. However, a wave in general can't be expressed as the sum of a finite number of sines and cosines. Fortunately, we have a theorem called Fourier's theorem which basically states that under certain technical assumptions, any function, f(x) is equal to an integral over sines and cosines. In other words,

 * $$f(x)=\int_{-\infty}^{\infty}(c_1(k)\cos(kx)+c_2(k)\sin(kx)) dk$$.

Now, if we're given the wave function when t=0, φ(x,0) and the velocity of each sine wave as a function of its wave number, v(k), then we can compute φ(x,t) for any t by taking the inverse Fourier transform of φ(x,0) conducting a phase shift, and then taking the Fourier transform.

Fortunately, the inverse Fourier transform is very similar to the Fourier transform itself.

 * $$c_1(k)=\frac{1}{2\pi}\int_{-\infty}^{\infty} f(x)\cos (kx)\,dx \quad

c_2(k)=\frac{1}{2\pi}\int_{-\infty}^{\infty} f(x) \sin (kx)\,dx $$

This tells us that, since waves which are very spread out, like the sine wave, have a narrow range of wave numbers, wave functions whose wave numbers are very spread out will only be significant at a narrow range of positions.

title: Waves/Fourier Transforms


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Organic Chemistry/Introduction to reactions/How to write organic reactions

Organic chemistry > How to write organic reactions

<< Introduction to reactions | Overview of reactions >>

Writing General Chemistry Reactions
In organic chemistry, a reaction may be written precisely as it is for general chemistry if only a basic amount of information is needed. For example, when a haloalkane is turned into an alkene, the reaction may be written:

""

Unfortunately, this method of notation does not tell anyone very much about the reaction, and it takes expertise to know exactly what is going on. A new student to organic chemistry probably would not notice that the product molecule contains one site of unsaturation due to a double bond between carbon atoms number one and number two. Because it is so general, this notation is good for general chemistry, but organic chemistry requires more precision.

For most students, common practices in writing organic reactions will be different than used in general chemistry.

Differences in Organic Chemistry Notation
Organic chemistry reactions are often not written as balanced equations. This is because many organic chemists - who are just as lazy as anyone else - tend to be more interested in the organic product of a reaction than in anything else going on in the reaction. Side products are often ignored, and just as often catalysts and solution notation may be highly abbreviated or left out altogether. As you gain familiarity with organic chemistry you will come to understand just what may be abbreviated or left out, but in the beginning this can be a source of frustration.

Another difference is that modified Lewis drawings of molecules are often used instead of molecular formulas. This makes sense due to the fact that organic molecules are often rather large in size and complicated in structure, so that they can be more easily understood in the form of a drawing as opposed to a word-formula. A two-dimensional drawing reveals some of the three-dimensional shape of the molecule, but when necessary even three-dimensional drawings are used to depict reactants and products.

Working with the above drawing of a molecule may be difficult, but it is still far easier than using its name, or attempting to guess at the structure and functionality of a molecule using just its chemical formula of.

Examples of Organic Chemistry Notation
Typically organic chemistry molecules are drawn as modified Lewis structures. If you remember, a Lewis structure uses lines to connect chemical symbols together, illustrating a covalent bond, and also uses dots to represent non-bond electrons. This is shown in the diagram below of carbon dioxide. The drawing illustrates the four electrons of carbon participating in two double bonds with two oxygen atoms, and also the non-bonding electron pairs for each atom of oxygen.

In organic chemistry, there are a lot of carbons in every molecule, generally, so organic chemists by convention do not draw every single carbon in every molecule. The same is true of hydrogens attached to the carbons; it is twice the annoyance to draw thirty hydrogens in a fatty acid than it is to draw the fifteen carbons. Therefore, in organic chemistry, carbon atoms are assumed to be wherever a line or line segment begins or ends. Furthermore, enough hydrogen atoms are assumed to be attached to any carbon not marked with a + or - sign (indicating an ionic charge) to bring that carbon's total number of bonds to four. At first this notation may be confusing, but the shorthand method rapidly proves its worth.

<< Alkanes | << Introduction to reactions | How to write organic reactions | Overview of reactions >> | Introduction to functional groups >>


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User:LouI~enwikibooks/Sandbox

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