Mathematical Methods for Physics (1版)

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本書所包的內容十分豐富，幾乎包含應用數學所有的重要課題，如Complex Variables, Partial Differential Equations, Special Functions, Fourier Transforms, Laplace Transforms etc。就如同作者在序中所言，本書適合研究生或優秀大學部學生研習，本書有些難度。作者寫書的方式是在每章每節開始時，先討論一個課題的基本概念及方法，而後舉出很多各式各樣不同的例子，其中有許多是來自古典力學、流体力學、量子力學、電磁學的重要例子，如果讀者能將本書全部念完並消化之，將受益不淺 目次 Chapter 1.COMPLEX VARIABLES. Chapter 2.CONFORMAL MAPPINGS. Chapter 3.ELLIPTICAL FUNCTIONS. Chapter 4.TENSOR CALCULUS. Chapter 5.Sturm-Liouville Theory. Chapter 6.GAMMA FUNCTION. Chapter 7.BESSEL FUNCTION. Chapter 8.LEGENDRE FUNCTIONS. Chapter 9.OTHER SPECIAL FUNCTIONS Chapter 10.Fourier SeriesLAPLACE TRANSFORM. Chapter 11.LAPLACE TRANSFORM. Chapter 12.MELLIN AND HANKEL TRANSFORM.I Chapter 14.NTEGRAL EQUATIONS.

Problems and Solutions in Mathematical Olympiad

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【簡介】 The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China. The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level. In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team. 【目錄】 Ingenious Computation of Rational Numbers Absolute Value First-Degree Equation with One Variable System of First-Degree Equations Application of a System of First-Degree Equations Setting Up (Systems of) Equations to Solve Word Problems (System of) First-Degree Inequalities Multiplication and Division of Polynomials with Integer Coefficients Line Segments Angles Sum of the Interior Angles of a Triangle Parallel Lines Assigning Variables Unnecessary for Solution Undetermined Coefficients Synthetic Division and Polynomial Remainder Theorem Simplifying and Evaluating an Algebraic Formula Logical Inference I Logical Inference II Divisibility Odd Numbers and Even Numbers Prime Numbers and Composite Numbers The Rule of Sum and the Rule of Product Number of Divisors Positional Notation Modular Arithmetic First-Degree Diophantine Equation with Two Unknowns The Drawer Principle