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Based on the author's junior-level undergraduate course, this classroom-tested textbook is designed for an introductory course in mathematical physics. Focusing on the physics of oscillations and waves, it helps students understand the mathematical techniques needed for their future studies in physics. The book introduces the methods while studying one underlying theme from physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics.
Inhaltsverzeichnis
Introduction and Review. Free Fall and Harmonic Oscillators. Linear Algebra. Nonlinear Dynamics. The Harmonics of Vibrating Strings. Non-sinusoidal Harmonics and Special Functions. Complex Representations of Functions. Transform Techniques in Physics. Vector Analysis and EM Waves. Extrema and Variational Calculus. Problems in Higher Dimensions. Review of Sequences and Infinite Series.
Über den Autor / die Autorin
Russell L. Herman
Zusammenfassung
Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics.
The book offers:
- A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra
- Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions
- Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems
- Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions
Zusatztext
"… a welcome and refreshing addition to a rich body of literature. … should fit into the sophomore or junior year of a typical physics undergraduate curriculum. … Engineers and chemistry majors, too, would benefit from taking such an intermediate-level course, perhaps even more so than from a higher-level one. Our own department at Howard University is considering a mid-level math methods course, and I would definitely recommend this textbook as well suited. A Course in Mathematical Methods for Physicists includes plenty of interesting worked-out examples, many of them quite realistic, and uses them to introduce concepts in a reasonable progression. …Although the subject of mathematical methods has inspired many valuable texts, Herman’s approach, motivated by the physics applications, is novel, seldom used by other authors. The myriad well-chosen worked-out examples and other strengths have earned my firm endorsement …"—Tristan Hübsch, Howard University, Washington, District of Columbia, USA, from Physics Today
