Synopses & Reviews
Ledder's innovative, student-centered approach reflects recent research on successful learning by emphasizing connections between new and familiar concepts and by engaging students in a dialogue with the material. Though streamlined, the text is also flexible enough to support a variety of teaching goals, in part through optional topics that give instructors considerable freedom in customizing their courses. Linear algebra is presented in self-contained sections to accommodate both courses that have a linear algebra prerequisite and those that do not. Throughout the text, a wide variety of examples from the physical, life and social sciences, among other areas, are employed to enhance student learning. In-depth Model Problems drawn from everyday experience highlight the key concepts or methods in each section. Other innovative features of the text include Instant Exercises that allow students to quickly test new skills and Case Studies that further explore the powerful problem-solving capability of differential equations. Readers will learn not only how to solve differential equations, but also how to apply their knowledge to areas in mathematics and beyond.
Table of Contents
1 Introduction
1.1 Natural Decay and Natural Growth
1.2 Differential Equations and Solutions
1.3 Mathematical Models and Mathematical Modeling
Case Study 1 Scientific Detection of Art Forgery
2 Basic Concepts and Techniques
2.1 A Collection of Mathematical Models
2.2 Separable First-Order Equations
2.3 Slope Fields
2.4 Existence of Unique Solutions
2.5 Euler's Method
2.6 Runge-Kutta Methods
Case Study 2 A Successful Volleyball Serve
3 Homogeneous Linear Equations
3.1 Linear Oscillators
3.2 Systems of Linear Algebraic Equations
3.3 Theory of Homogeneous Linear Equations
3.4 Homogeneous Equations with Constant Coefficients
3.5 Real Solutions from Complex Characteristic Values
3.6 Multiple Solutions for Repeated Characteristic Values
3.7 Some Other Homogeneous Linear Equations
Case Study 3 How Long Should Jellyfish Hold their Food?
4 Nonhomogeneous Linear Equations
4.1 More on Linear Oscillator Models
4.2 General Solutions for Nonhomogeneous Equations
(and more...)