Mathematics for Engineers

This third and last volume in our series on Mathematics for Engineers serves as a companion text to the third semester mathematics prelims for students and instructors of electrical engineering and other engineering disciplines. Ordinary and partially differential equations take a central role in graduate engineering courses. This topic is mainly on the focus of the third volume: The description of engineering problems either leads to ordinary differential equations as long as there is only one independent variable. In case that the problem is described by more than one variable the model equations are partially differential equations such as the wave equation, the heat transfer equation, the Laplace equation and many more. Differential equations are discussed in detail. Additionally to the description of engineering problems by means of differential equations we have to analyze signals produced by oscillations and vibrations. For that, we need the frequency analysis of the signals which leads to the topic of Fourier Series for periodic and Fourier Transform for non-periodic signals. Both techniques are also required when solving differential equations. This volume provides students at universities and applied universities with a largely accurate but always descriptive presentation of these topics to provide a practical aid to higher mathematics. A large number of examples and applications illustrate and deepen the material and the numerous exercises (with solutions on the homepage of the book) facilitate the preparation for the exam.