A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equations and systems of differential equations; and systems of nonlinear equations.
Each chapter concludes with a summary of the important concepts in the chapter. Figures and tables are provided within sections to help students visualize or summarize concepts. The book also includes examples and exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering. This book is designed for undergraduate students majoring in mathematics, the natural sciences, and engineering. However, students in economics, business, and the social sciences with the necessary background will also find the text useful.
- student friendly readability- assessible to the average student
- early introduction of qualitative and numerical methods
- large number of exercises taken from biology, chemistry, economics, physics and engineering
- Exercises are labeled depending on difficulty/sophistication
- Full ancillary package including; Instructors guide, student solutions manual and course management system
- end of chapter summaries
- group projects
Undergraduate students studying differential equations.
Preface Acknowledgements Chapter 1 Introduction to Differential Equations Introduction 1.1 Basic Terminology 1.2 Solutions of Differential Equations 1.3 Initial-Value Problems and Boundary-Value Problems Summary Project 1-1 Chapter 2 First-Order Differential Equations Introduction 2.1 Separable Equations 2.2 Linear Equations 2.3 Compartment Problems 2.4 Slope Fields 2.5 Phase Lines and Phase Portraits 2.6 Equilibrium Points: Sinks, Sources, and Nodes 2.7 Bifurcations 2.8 Existence and Uniqueness of Solutions Summary Project 2-1 Project 2-2 Chapter 3 The Numerical Approximation of Solutions Introduction 3.1 Euler’s Method 3.2 The Improved Euler Method 3.3 More Sophisticated Numerical Methods: Runge-Kutta and Others Summary Project 3-1 Chapter 4 Second- and Higher-Order Equations Introduction 4.1 Homogeneous Second-Order Linear Equations with Constant Coefficients 4.2 Nonhomogeneous Second-Order Linear Equations with Constant Coefficients 4.3 The Method of Undetermined Coefficients 4.4 Variation of Parameters 4.5 Higher-Order Linear Equations with Constant Coefficients 4.6 Higher-Order Equations and Their Equivalent Systems 4.7 The Qualitative Analysis of Autonomous Systems 4.8 Spring-Mass Problems 4.9 Existence and Uniqueness 4.10 Numerical Solutions Summary Project 4-1 Chapter 5 Systems of Linear Differential Equations Introduction 5.1 Systems and Matrices 5.2 Two-Dimensional Systems of First-Order Linear Equations 5.3 The Stability of Homogeneous Linear Systems: Unequal Real Eigenvalues 5.4 The Stability of Homogeneous Linear Systems: Equal Real Eigenvalues 5.5 The Stability of Homogeneous Linear Systems: Complex Eigenvalues 5.6 Nonhomogene
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- © Academic Press 2009
- 12th March 2009
- Academic Press
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Medgar Evers College of the City University of New York, Brooklyn, USA