Mathematical Methods: For Students of Physics and Related Fields

Description

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previous edition: "The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities." --Physics Today "Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done." --Zentralblatt MATH Front Matter....Pages I-XXIII Front Matter....Pages 1-1 Coordinate Systems and Vectors....Pages 3-42 Differentiation....Pages 43-75 Integration: Formalism....Pages 77-100 Integration: Applications....Pages 101-137 Dirac Delta Function....Pages 139-170 Front Matter....Pages 171-171 Planar and Spatial Vectors....Pages 173-214 Finite-Dimensional Vector Spaces....Pages 215-236 Vectors in Relativity....Pages 237-255 Front Matter....Pages 256-256 Infinite Series....Pages 259-281 Application of Common Series....Pages 283-316 Integrals and Series as Functions....Pages 317-339 Front Matter....Pages 340-340 Vectors and Derivatives....Pages 343-363 Flux and Divergence....Pages 365-385 Line Integral and Curl....Pages 387-406 Applied Vector Analysis....Pages 407-421 Curvilinear Vector Analysis....Pages 423-438 Tensor Analysis....Pages 439-474 Front Matter....Pages 475-475 Complex Arithmetic....Pages 477-496 Complex Derivative and Integral....Pages 497-514 Complex Series....Pages 515-523 Front Matter....Pages 475-475 Calculus of Residues....Pages 525-537 Front Matter....Pages 539-539 From PDEs to ODEs....Pages 541-550 First-Order Differential Equations....Pages 551-562 Second-Order Linear Differential Equations....Pages 563-590 Laplace’s Equation: Cartesian Coordinates....Pages 591-605 Laplace’s Equation: Spherical Coordinates....Pages 607-637 Laplace’s Equation: Cylindrical Coordinates....Pages 639-659 Other PDEs of Mathematical Physics....Pages 661-689 Front Matter....Pages 690-690 Integral Transforms....Pages 693-726 Calculus of Variations....Pages 727-751 Nonlinear Dynamics and Chaos....Pages 753-779 Probability Theory....Pages 781-813 Back Matter....Pages 815-831