MATHEMATICS FOR ENGINEERS (V3)

Volume 3: Systems of Differential Equations, n-th Order Differential Equations, Fourier Series and Fourier Transform, Partial Differential Equations, Vector Analysis and Maxwell Equations, Splines

By: Thomas Westermann

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eText | 2 September 2025

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This third and final volume in our Mathematics for Engineers series serves as a companion text to the third-semester mathematics preliminaries for students and lecturers in electrical engineering and other engineering disciplines.

Ordinary and partially differential equations play a central role in graduate engineering courses. This topic is one of the main focus of the third volume. In addition to describing engineering problems using differential equations, we analyze signals produced by oscillations and vibrations. This requires frequency analysis of the signals, which leads to the topic of Fourier series for periodic signals and Fourier transform for non-periodic signals.

This volume provides students at universities and colleges with a vivid presentation of these topics as a practical aid to higher mathematics. Mathematical terms are clearly motivated, systematically equated and visualized in many animations. A large number of examples and applications illustrate and deepen the material, and the numerous exercises (with solutions on the book's homepage) make it easier to prepare for exams.

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