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.

Mathematical Methods and Physical Insights: An Integrated Approach (1版)

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Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension. Initial chapters review essential mathematical concepts and techniques that students need to know, helping students to fill gaps in their background knowledge and enabling instructors to focus on the main course material Each Part has sections designed to highlight and apply the techniques and concepts within, so that physics motivates the math, which deepens understanding of physics Boxed asides throughout the book called 'By the Ways' (BTWs) provide optional digressions into the math or physics, to help to lift motivated students to the next level Flexible paths through the text allow it to be used for both one- and two-semester courses, depending on the course goals and instructor's preference 本書目錄： Part I. Things You Just Gotta' Know: 1. Prelude: symbiosis 2. Coordinating coordinates 3. Complex numbers 4. Index algebra 5. Brandishing binomials 6. Infinite series 7. Interlude: orbits in a central potential 8. Ten integration techniques and tricks 9. The Dirac delta function 10. Coda: statistical mechanics Part II. The Calculus of Vector Fields: 11. Prelude: visualizing vector fields 12. grad, div & curl 13. Interlude: irrotational and incompressible 14. Integrating scalar & vector fields 15. The theorems of Gauss & Stokes 16. Mostly Maxwell 17. Coda: Simply connected regions Part III. Calculus in the Complex Plane: 18. Prelude: path independence in the complex plane 19. Series, singularities & branches 20. Interlude: conformal mapping 21. The calculus of residues 22. Coda: analyticity & causality Part IV. Linear Algebra: 23. Prelude: superposition 24. Vector space 25. The inner product 26. Interlude: rotations 27. The Eigenvalue problem 28. Coda: normal modes Entr'acte: Tensors 29. Cartesian tensors 30. Beyond cartesian Part V. Orthogonal Functions: 31. Prelude: 1 2 3 . . . infinity 32. Eponymous polynomials 33. Fourier series 34. Convergence and completeness 35. Interlude: beyond the straight & narrow 36. Fourier transforms 37. Coda: of time intervals and frequency bands Part VI. Differential Equations: 38. Prelude: first order first 39. Second-order ODEs 40. Interlude: the Sturm-Liouville Eigenvalue problem 41. Partial differential equations 42. Green's functions 43. Coda: quantum scattering Appendix A. Curvilinear coordinates Appendix B. Rotations in R3 Appendix C. The Bessel family of functions 會計 經濟 國際貿易 財務 企業管理 數學 機率與統計 資訊與資工 工業工程 社會與心理 醫務管理 物理 化學與化工 電子與電機 機械工程 航空工程 土木工程 環境工程 生命科學 護理 休閒觀光與餐飲 化妝品科學 其他 帳號 密碼 驗證碼

Mathematical Methods for Physics: An Introduction to Group Theory, Topology and Geometry

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This detailed yet accessible text provides an essential introduction to the advanced mathematical methods at the core of theoretical physics. The book steadily develops the key concepts required for an understanding of symmetry principles and topological structures, such as group theory, differentiable manifolds, Riemannian geometry, and Lie algebras. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering. The material has been subject to more than twenty years of feedback from students, ensuring that explanations and examples are lucid and considered, and numerous worked examples and exercises reinforce key concepts and further strengthen readers' understanding. This text unites a wide variety of important topics that are often scattered across different books, and provides a solid platform for more specialized study or research.

MATHEMATICAL METHODS OF THEORETICAL PHYSICS

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"This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas … The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students." CHOICE This book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics. Sample Chapter(s) 5: Brief review of complex analysis Request Inspection Copy Contents: Why Mathematics? Linear Vector Spaces: Finite-Dimensional Vector Spaces and Linear Algebra Multilinear Algebra and Tensors Groups as Permutations Projective and Incidence Geometry Functional Analysis: Brief Review of Complex Analysis Brief Review of Fourier Transforms Distributions as Generalized Functions Differential Equations: Green's Function Sturm–Liouville Theory Separation of Variables Special Functions of Mathematical Physics Divergent Series Bibliography Index Readership: Undergraduate students in Mathematical Physics and Computer Science.