涉及到星形线的一个运动轨迹问题
前几天在群里被问到一个定长木棍在竖直墙边上运动的轨迹问题,还是挺有趣的,涉及到星形线,解决起来也不简单.
十大坑爹高数题(转自哆嗒数学网)
一系列类似积分相等的证明
前阵子四叶群里有人问道下面这题,虽感觉此题结论优美但无从下手.
一个很火的积分题
求解\[\displaystyle \int_0^1 \frac{\log^2(1-x)\log(x)}{x}dx=-\frac{\pi^4}{180}.\]
解.$For $|z|<1$ we have that
绘制一个船舶图案
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一个与多项式分拆有关的级数题
国立台湾大学大學部必修課教科書及參考書籍
線性代數
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Principles of Mathematical Analysis | Rudin |
Introduction to calculus and analysis | Richard Courant, Fritz John |
A first course in real analysis | Murray H. Protter, Charles B. Morrey |
Elementary classical analysis | Jerrold E. Marsden, Michael J. Hoffman |
Modern Algebra | John R.Durbin |
Abstract Algebra
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John B.Fraleigh |
Algebra
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Michael Artin |
Topics in Algebra
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I. N. Herstein |
Basic Algebra
|
Nathan Jacobson |
Algebra | Vander Waerden |
Algebra | Serge Lang |
Ordinary differential equations | V. I. Arnold. |
Differential equations, dynamical systems, and linear algebra | Morris W. Hirsch, Stephen Smale |
Differential equations | Paul Blanchard, Robert L. Devaney, Glen R. Hall |
Ordinary differential equations | E.L. Ince |
An introduction to partial differential equations | Walter A. Strauss |
Complex analysis : an introduction to the theory of analytic functions of one complex variable | Lars V. Ahlfors |
The theory of functions | E. C. Titchmarsh |
Introduction to complex analysis | Nevanlinna |
Real and complex analysis | Rudin |
Functions of one complex variable | Conway |
A First Course in Probability | Sheldon Ross |
Elementary Probability Theory with Stochastic Processes | Kai Lai Chung ( 鍾開萊 ) |
An Introduction to Probability and Its Applications | W. Feller |
Probability : Theory and Examples | Richard Durret |
Probability with Martingales | David Williams |
A Course in Probability Theory | Kai Lai Chung ( 鍾開萊 ) |
Probability Theory | S.R.S. Varadhan |
Stochastic Processes | Sheldon Ross |
幾何 (曲線、曲面論)
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Differential geometry of curves and surfaces | Manfredo P. do Carmo |
Lectures on classical differential geometry | Dirk Jan Struik |
Differential geometry in the large | Heinz Hopf ; with a preface by S.S. Chern |
Elementary differential geometry | B. O'Neill |
初等微分幾何講稿 | 黃武雄 |
Topology; a first course | James R. Munkres |
Basic topology | M.A. Armstrong |
Algebraic topology | Allen Hatcher |
Topology from the differentiable viewpoint | John W. Milnor |
Differential topology | Morris W. Hirsch |
Morse Theory | J﹒Milnor |
Differential Forms in Algebraic Topology | Raoul Bott, Loring W. Tu |
Topology of Fiber Bundles | Norman Steenrod |
Real analysis | H.L. Royden |
Measure and integral : an introduction to real analysis | Richard L. Wheeden and Antoni Zygmund |
Real analysis : modern techniques and their applications | Gerald B. Folland |
Functional analysis | Peter D. Lax |
Topics in nonlinear functional analysis | L. Nirenberg |
Methods of mathematical physics | R. Courant and D. Hilbert |
Partial Differential Equations | Lawrence C. Evans |
Partial Differential Equations | F. John |
Elliptic partial differential equations of second order | David Gilbarg, Neil S. Trudinger |
Second order parabolic differential equations | Gary M. Lieberman |
Lectures on elliptic and parabolic equations in Holder spaces | N.V. Krylov |
Riemannian Geometry | Manfredo P. do Carmo |
A Comprehensive Introduction to Differential Geometry | Michael Spivak |
Riemannian geometry and geometric analysis | Jurgen Jost |
Notes on Differential Geometry | Noel J. Hicks |
Riemannian Geometry | S. Gallot, D. Hulin, J. Lafontaine |
Modern Geometry--Methods and Applications | B.A. Dubrovin, A.T. Fomenko, S.P. Novikov |
Comparison Theorems in Riemannian Geometry | Jeff Cheeger, David G. Ebin |
Nonlinear Analysis on Manifolds, Monge Ampere Equations | Thierry Aubin |
Foundations of differential manifolds and Lie groups | F.Warner |
Differential Geometry, Lie Groups, and Symmetric Spaces | Sigurdur Helgason |
Geometric Measure Theory | L. Simon |
Introductions to Riemann surfaces | Springer |
緊黎曼曲面引論 | 伍鴻熙 |
Lectures on Riemann Surfaces | Gunning |
Complax Manifolds | Kunihiko Kodaira ( 小平邦彥) , James Morrow |
Principles of Algebraic Geometry | Phillip Griffith, Joseph Harris |
The Red Book of Varieties and Schemes | David Munford |
Algebraic Geometry | Robin Hartshorne |
Introduction to Grothendieck Duality Theory | Allen Altman, Steven Kleiman |
Compact Complex Surfaces | W. Barth, C. Peters, A. Van de Ven |
Birational Geometry of Algebraic Varieties | Janos Kollar, Shigefumi Mori |
Elements of Discrete Mathematics 2nd Edition | 劉炯朗 Liu, C.-L. (Chung Laung) |
Invitation to Discrete Mathematics | Jiri Matousek, Jaroslav Nesetril |
Combinatorics : topics, techniques, algorithms | Cameron, Peter J. (Peter Jephson), 1947- |
A Course in Combinatorics 2nd Edition | J.H. van Lint, R.M. Wilson |
Introduction to Graph Theory 2nd Edition | Douglas B. West |
Combinatorial Optimization:Algorithms and Complexity | Christos H. Papadimitriou, Kenneth Steiglitz |
Introduction to Algorithms 2nd Edition | Thomas H. Cormen |
Introduction to algorithms: a creative approach | Udi Manber |
The design and analysis of computer algorithms | Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman |
Elementary Statistics – a step by step approach | Bluman |
Mathematical Statistics and Data Analysis | John A. Rice |
Statistics for Experimenters | George E. P. Box, William G. Hunter, J. Stuart Hunter |
Statistics | David Freedman, Robert Pisani, Roger Durves |
Linear Statistical Inference and its Applications (Second Edition) | C. Radhakrishna Rao |
Statistical Inference. 2nd edition | Casella, G. and Berger, R. L. |
A First Course In Multivariate Statistics | Bernard Flury, Springe 2 |
Mathematical Statistics and Data Analysis, 2nd Edition | Rice, John A |
Mathematical Statistics with applications, 6th edition |
Dennis D. Wackerly, William Mendenhall Ⅲ, Richard L. Scheaffer |
高等微積分參考書目及評論
代數參考書目及評論
微分方程參考書目及其評論
偏微分方程式參考書目及其評論
複變參考書目及其評論
幾何(曲線、曲面論)參考書目及其評論
拓樸參考書目及其評論
分析參考書目及其評論
偏微分方程式參考書目及其評論
多複變及黎曼面參考書目及其評論
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西西爆难积分题求解
在这里,主要展示西西12年7月在百度贴吧数学吧中贴出的30个积分题的求解,本文中主要参考的是自己以前的摘录,不知何故,与西哥的版本有些出入,但基本包含了西哥的所有问题,来源于网友的解答均会注明出处。
参阅:[1]http://tieba.baidu.com/p/2114477017
[2]http://tieba.baidu.com/p/3148596990
[3]http://tieba.baidu.com/p/2121721064