Mathematical Methods in Engineering and Physics [Paperback]

This text is intended for the undergraduate course in math methods, with an audience of physics and engineering majors. As a required course in most departments, the text relies heavily on explained examples, real-world applications and student engagement. Supporting the use of active learning, a strong focus is placed upon physical motivation combined with a versatile coverage of topics that can be used as a reference after students complete the course. Each chapter begins with an overview that includes a list of prerequisite knowledge, a list of skills that will be covered in the chapter, and an outline of the sections. Next comes the motivating exercise, which steps the students through a real-world physical problem that requires the techniques taught in each chapter.

PREFACE xi

1 Introduction to Ordinary Differential Equations 1

1.1 Motivating Exercise: The Simple Harmonic Oscillator 2

1.2 Overview of Differential Equations 3

1.3 Arbitrary Constants 15

1.4 Slope Fields and Equilibrium 25

1.5 Separation of Variables 34

1.6 Guess and Check, and Linear Superposition 39

1.7 Coupled Equations (see felderbooks.com)

1.8 Differential Equations on a Computer (see felderbooks.com)

1.9 Additional Problems (see felderbooks.com)

2 Taylor Series and Series Convergence 50

2.1 Motivating Exercise: Vibrations in a Crystal 51

2.2 Linear Approximations 52

2.3 Maclaurin Series 60

2.4 Taylor Series 70

2.5 Finding One Taylor Series from Another 76

2.6 Sequences and Series 80

2.7 Tests for Series Convergence 92

2.8 Asymptotic Expansions (see felderbooks.com)

2.9 Addil³«