Elementary Differential Equations and Boundary Value Problems, 9th Edition
October 2008, ©2009
The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two- or three-semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Chapter 1 Introduction 1
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
1.4 Historical Remarks
Chapter 2 First Order Differential Equations
2.1 Linear Equations; Method of Integrating Factors
2.2 Separable Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factors
2.7 Numerical Approximations: Euler's Method
2.8 The Existence and Uniqueness Theorem
2.9 First Order Difference Equations
Chapter 3 Second Order Linear Equations 135
3.1 Homogeneous Equations with Constant Coefficients
3.2 Fundamental Solutions of Linear Homogeneous Equations; The Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
3.6 Variation of Parameters
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations
Chapter 4 Higher Order Linear Equations
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters
Chapter 5 Series Solutions of Second Order Linear
5.1 Review of Power Series
5.2 Series Solutions Near an Ordinary Point, Part I
5.3 Series Solutions Near an Ordinary Point, Part II
5.4 Euler Equations; Regular Singular Points
5.5 Series Solutions Near a Regular Singular Point, Part I
5.6 Series Solutions Near a Regular Singular Point, Part II
5.7 Bessel's Equation
Chapter 6 The Laplace Transform
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions
6.4 Differential Equations with Discontinuous Forcing Functions
6.5 Impulse Functions
6.6 The Convolution Integral
Chapter 7 Systems of First Order Linear Equations
7.2 Review of Matrices
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
7.4 Basic Theory of Systems of First Order Linear Equations
7.5 Homogeneous Linear Systems with Constant Coefficients?
7.6 Complex Eigenvalues
7.7 Fundamental Matrices
7.8 Repeated Eigenvalues
7.9 Nonhomogeneous Linear Systems
Chapter 8 Numerical Methods
8.1 The Euler or Tangent Line Method
8.2 Improvements on the Euler Method
8.3 The Runge-Kutta Method
8.4 Multistep Methods
8.5 More on Errors; Stability
8.6 Systems of First Order Equations
Chapter 9 Nonlinear Differential Equations and Stability
9.1 The Phase Plane: Linear Systems
9.2 Autonomous Systems and Stability
9.3 Locally Linear Systems
9.4 Competing Species
9.5 Predator-Prey Equations
9.6 Liapunov's Second Method
9.7 Periodic Solutions and Limit Cycles
9.8 Chaos and Strange Attractors: The Lorenz Equations
Chapter10 Partial Differential Equations and Fourier
10.1 Two-Point Boundary Value Problems
10.2 Fourier Series
10.3 The Fourier Convergence Theorem
10.4 Even and Odd Functions
10.5 Separation of Variables; Heat Conduction in a Rod
10.6 Other Heat Conduction Problems
10.7 The Wave Equation: Vibrations of an Elastic String
10.8 Laplace's Equation
Appendix A Derivation of the Heat Conduction Equation
Appendix B Derivation of the Wave Equation
Chapter 11 Boundary Value Problems and Sturm-Liouville
11.1 The Occurrence of Two-Point Boundary Value Problems
11.2 Sturm-Liouville Boundary Value Problems
11.3 Nonhomogeneous Boundary Value Problems
11.4 Singular Sturm-Liouville Problems
11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
11.6 Series of Orthogonal Functions: Mean Convergence
Answers to Problems
Additional examples have been added and some existing examples expanded
New end of chapter problems for added practice
Expanded sections for clarity and motivation (Chapters 2, 3, 5)
Discussion of linear dependence and independence moved from Chapter 3 to Chapter 4
More explanation of integrals of piecewise continuous functions and how Laplace transforms are used to solve initial value problems (Chapter 6)
Abel's formula explicitly stated, with itemized summary (Chapter 7)
New subsection on the importance of critical points (Chapter 9)
More emphasis on the Jacobian matrix
- A Flexible approach to content. Self-contained chapters allow instructors to customize the selection, order, and depth of chapters.
- A Flexible approach to technology. Boyce/DiPrima is adaptable to courses having various levels of computer involvement, ranging from little or none to intensive. More than 450 problems are marked with a technology icon to indicate those that are considered to be technology intensive.
- Sound and accurate exposition of theory. Special attention is made to methods of solution, analysis, and approximation.
- Outstanding exercise sets. Boyce/DiPrima remains unrivaled in quantity, variety, and range providing great flexibility in homework assignments.
- Applied Problems. Many problems ask the student not only to solve a differential equation but also to draw conclusions from the solution, reflecting the usual situation in scientific or engineering applications.
- Historical footnotes. The footnotes allow the student to
trace the development of the discipline and identify outstanding
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