| 書名: | A Friendly Approach to Complex Analysis (2版) | |||
| 作者: | Sara Maad Sasane 、 Amol Sasane | |||
| 版次: | 2 | |||
| ISBN: | 9789811274107 | |||
| 出版社: | World Scientific | |||
| 出版日期: | 2023/07 | |||
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#數學與統計學
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The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text. The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained. Request Inspection Copy Sample Chapter(s) Overview Chapter 1: Complex numbers and their geometry Contents: Complex Numbers and Their Geometry Complex Differentiability Cauchy Integral Theorem Taylor and Laurent Series Harmonic Functions Solutions to All Exercises Readership: Undergraduate students in complex analysis.
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【原文書】 書名:Complex Analysis (Princeton Lectures in Analysis, No. 2) 作者:STEIN 出版社:PRINCETON 出版日期:2003/04/07 ISBN:9780691113852
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The knowledge of mechanics of materials is the very foundation for advanced topics in mechanical, civil, aerospace, chemical, ceramic engineering and materials science. This comprehensive book presents materials with a three-dimensional approach rather than two-dimensional analysis adopted by existing books. It develops the required background thoroughly before basic elements such as stress and strain tensors are formulated. The presentation is richly filled with anecdotes, illustrations and solved examples. Special care has been taken to carry out algebra and the derivations in small digestible steps. This useful reference text largely meets the requirements of computer-aided engineering (CAE) softwares which are widely used in industrial-sector and research & development laboratories to design structural members. Related Link(s) Press Release — A Friendly Approach to the Mechanics of Materials Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Getting into a New Ball Game Contents: Getting into a New Ball Game Forces, Moments, and Equilibrium Reactions and Free Body Diagrams Internal Forces in Slender Members Stress Tensor Transformation of Stress Components Deformation and Strain Tensor Material Behavior: Stress–Strain Relations Axial Members: Stresses, Thermal Strains, and Compatibility Bending Moments and Shear Forces Deflection due to Bending Torsion Combined Stresses and Yield Criteria Energy Methods Historical Perspective Readership: Researchers, professionals, academics, undergraduate and graduate students in mechanical engineering, civil engineering, aerospace engineering, materials science and chemical engineering.
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作(編/譯)者 : SILVERMAN 出版年份 : 2014 ISBN : 9781292027098 書號 : BX0145N 幾色 : 1 規格 : 平裝 發行公司 : PEARSON 英文書名中譯 : 數論學 版次 : 4E 頁數 : 480 Table of Contents: 1. What Is Number Theory? 2. Pythagorean Triples 3. Pythagorean Triples and the Unit Circle 4. Sums of Higher Powers and Fermat’s Last Theorem 5. Divisibility and the Greatest Common Divisor 6. Linear Equations and the Greatest Common Divisor 7. Factorization and the Fundamental Theorem of Arithmetic 8. Congruences 9. Congruences, Powers, and Fermat’s Little Theorem 10. Congruences, Powers, and Euler’s Formula 11. Euler’s Phi Function and the Chinese Remainder Theorem 12. Prime Numbers 13. Counting Primes 14. Mersenne Primes 15. Mersenne Primes and Perfect Numbers 16. Powers Modulo m and Successive Squaring 17. Computing kth Roots Modulo m 18. Powers, Roots, and “Unbreakable” Codes 19. Primality Testing and Carmichael Numbers 20. Squares Modulo p 21. Quadratic Reciprocity 22. Proof of Quadratic Reciprocity 23. Which Primes Are Sums of Two Squares? 24.Which Numbers Are Sums of Two Squares? 25. Euler’s Phi Function and Sums of Divisors 26. Powers Modulo p and Primitive Roots 27. Primitive Roots and Indices 28. The Equation X4 + Y4 = Z4 29. Square–Triangular Numbers Revisited 30. Pell’s Equation 31. Diophantine Approximation 32. Diophantine Approximation and Pell’s Equation 33. Number Theory and Imaginary Numbers 34. The Gaussian Integers and Unique Factorization 35. Irrational Numbers and Transcendental Numbers 36. Binomial Coefficients and Pascal’s Triangle 37. Fibonacci’s Rabbits and Linear Recurrence Sequences 38. Cubic Curves and Elliptic Curves 39. Elliptic Curves with Few Rational Points 40. Points on Elliptic Curves Modulo p 41. Torsion Collections Modulo p and Bad Primes 42. Defect Bounds and Modularity Patterns 43. Elliptic Curves and Fermat’s Last Theorem 44. The Topsy-Turvy World of Continud Fractions 45. Continued Fractions and Pell’s Equation 46. Generating Functions 47. Sums of Powers 48. Appendix: A List of Primes
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