This new edition has been made more user-friendly through organization into more concise chapters. It addresses the mathematical needs of sophomores and juniors in physics, engineering and other related fields. An entirely new section covers Probability.

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.

Includes many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts Broad scope will be useful for students across a wide range of fields such as physics, engineering, and mathematics Substantially revised edition features new sections on Tensors, Integral Transforms, Calculus of Variations, and Probability Theory

Autorentext

Sadri Hassani is Professor Emeritus of physics at Illinois State University and Adjunct Professor at the University of Illinois at Urbana-Champaign. He received his PhD in theoretical physics from Princeton University and is currently on the editorial board of Springer-Nature's Graduate Texts in Physics series. His first publication, Mathematical Physics, a graduate-level textbook now in its third edition, has become an authoritative text on the subject. His current area of interest is using physics as a venue for the dissemination of critical thinking. He lives with his wife in Champaign, IL.

Inhalt
Coordinates and Calculus.- Coordinate Systems and Vectors.- Differentiation.- Integration: Formalism.- Integration: Applications.- Dirac Delta Function.- Algebra of Vectors.- Planar and Spatial Vectors.- Finite-Dimensional Vector Spaces.- Vectors in Relativity.- Infinite Series.- Infinite Series.- Application of Common Series.- Integrals and Series as Functions.- Analysis of Vectors.- Vectors and Derivatives.- Flux and Divergence.- Line Integral and Curl.- Applied Vector Analysis.- Curvilinear Vector Analysis.- Tensor Analysis.- Complex Analysis.- Complex Arithmetic.- Complex Derivative and Integral.- Complex Series.- Calculus of Residues.- Differential Equations.- From PDEs to ODEs.- First-Order Differential Equations.- Second-Order Linear Differential Equations.- Laplace's Equation: Cartesian Coordinates.- Laplace's Equation: Spherical Coordinates.- Laplace's Equation: Cylindrical Coordinates.- Other PDEs of Mathematical Physics.- Special Topics.- Integral Transforms.- Calculus of Variations.- Nonlinear Dynamics and Chaos.- Probability Theory.