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[[数学]]>解析学基礎
 
この本は [[:en:Calculus:Outline|Calculus]]を、翻訳することにより作成されますが、元の説明が分かりにくい場合などは適宜加筆・修正されます。また、元にしてる本自体が完成していないこともあり、新たに書かなければならない項目も多いです。
新しいページを作るときの、各項目名の最初には「解析学基礎/」を付けることが推奨されます。
 
==解析学基礎:目次==
===はじめに===
* [[Calculus:Introduction|Introduction]]
** [[Calculus:Introduction#What_is_calculus.3F|What is calculus?]]
** [[Calculus:Introduction#Why_learn_calculus.3F|What does learning calculus involve?]]
** [[Calculus:Introduction#What_is_involved_in_learning_calculus.3F|What do I need to know to learn calculus?]]
==準備==
===初歩の初歩===
*[[解析学基礎_関数|関数]]
===極限===
*[[/極限|極限]]
==解析学基礎1&2==
===微分法===
*[[/微分1|微分の導入]]
*[[/微分2|微分の公式]]
===微分の応用===
*[[/二階微分|二階微分]]
*[[/微分の応用1|微分の使い方1]]
*[[/微分の応用2|微分の使い方2]]
*[[/微分可能関数|微分可能関数]]
===積分法===
*[[/総和|総和]]
*[[/積分|積分]]
*[[/ベクトル|ベクトル]]
===対数、指数、超越関数など===
*[[/双曲線関数|双曲線関数]]
===基本的な積分、ロピタルの定理、広義積分===
*[[/基本的な積分|基本的な積分]]
*[[/広義積分|広義積分]]
===無限級数===
*[[/級数|級数]]
*[[/テイラー級数|テイラー級数]]
*[[/べき級数|べき級数]]
 
==解析学 3==
*[[Calculus:Multivariable calculus|Multivariable calculus]]
==常微分方程式==
*[[Calculus:Ordinary differential equations|Ordinary differential equations]]
==偏微分方程式==
*[[Calculus:Partial differential equations|Partial differential equations]]
==Beyond==
(Anything beyond 1st-year undergrad should go down here,
e.g
*Section 4/ <br>
**full theory of linear ODE's, green functions, special functions etc,
**solving nonlinear ODE's perturbation, stability, multi-time scales etc
**Integral transforms, fourier, laplace, etc
**PDE's, spherical harmonics, how to reduce to standard forms, ways of solving, etc.
**and more...
*Section 5/
**Postgrad stuff, Lie groups, nonlinear PDE's, etc
*Section 6/
**Post-doc stuff.)
 
==Futher analysis==
* [[Calculus:Systems of ordinary differential equations|Systems of ordinary differential equations]]
==Formal theory of calculus==
*[[Calculus:Formal limits|Formal limits]]
*[[Calculus:Real numbers|Real numbers]]
*[[Calculus:Sequences|Sequences]]
==Answers to Exercises==
*[[Calculus:Answers_to_introductory_concepts|Introductory Concepts]]
*[[Calculus:Answers_to_beginning_analysis|Beginning Analysis]]
*[[Calculus:Answers_to_futher_analysis|Further Analysis]]
*[[Calculus:Answers_to_formal_theory_of_calculus|Formal Theory of Calculus]]
==TODO==
*ADD MORE, ORGANIZE MORE.
*Provide answer for Differentation exercise on the absolute value function.
*Provide a more in-depth Precalculus section.
*Reorganise site to accomadate for a strict course for AP Calculus [http://www.collegeboard.com/student/testing/ap/calculus_bc/topic.html?calcbc] curriculum, but ''definitely'' not limited to that.
*Create problem sets (preferrably original, and realistic).
*Create answer sets.
== External links ==
*[http://www.math.wisc.edu/~keisler/calc.html Elementary Calculus: An Approach Using Infinitesimals] a free text
*[http://www.math.umn.edu/~garrett/calculus/ First-Year Calculus Notes] a GPL'd text
*[http://math.furman.edu/~dcs/book/ Difference Equations to Differential Equations: An Introduction to Calculus] another GPL'd text
 
[[Category:解析学|かいせきかくきそ]]
 
[[en:Calculus:Outline]]