Textbook
Elementary Differential Equations and Boundary Value Problems, Enhanced eText, 11th EditionISBN: 9781119381648
704 pages
May 2017, ©2017

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Description
Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11^{th} edition includes new problems, updated figures and examples to help motivate students.
The program is primarily intended 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 engaging with the program 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.
The program is primarily intended 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 engaging with the program 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.
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Table of Contents
1. Introduction
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
2. FirstOrder Differential Equations
2.1 Linear Differential Equations; Method of Integrating Factors
2.2 Separable Differential Equations
2.3 Modeling with FirstOrder Differential Equations
2.4 Differences Between Linear and Nonlinear Differential Equations
2.5 Autonomous Differential Equations and Integrating Factors
2.6 Exact Differential Equations and Integrating Factors
2.7 Numerical Approximations: Euler's Method
2.8 The Existence and Uniqueness Theorem
2.9 FirstOrder Difference Equations
3. SecondOrder Linear Differential Equations
3.1 Homogeneous Differential Equations with Constant Coefficients
3.2 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 Periodic Vibrations
4. HigherOrder Linear Differential Equations
4.1 General Theory of n^{th} Order Linear Differential Equations
4.2 Homogeneous Differential Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters
5. Series Solutions of SecondOrder Linear Equations
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
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
7. Systems of FirstOrder Linear Equations
7.1 Introduction
7.2 Matrices
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
7.4 Basic Theory of Systems of FirstOrder Linear Equations
7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 ComplexValued Eigenvalues
7.7 Fundamental Matrices
7.8 Repeated Eigenvalues
7.9 Nonhomogeneous Linear Systems
8. Numerical Methods
8.1 The Euler or Tangent Line Method
8.2 Improvements on the Euler Method
8.3 The RungeKutta Method
8.4 Multistep Methods
8.5 Systems of FirstOrder Equations
8.6 More on Errors; Stability
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 PredatorPrey Equations
9.6 Liapunov's Second Method
9.7 Periodic Solutions and Limit Cycles
9.8 Chaos and Strange Attractors: The Lorenz Equations
10. Partial Differential Equations and Fourier Series
10.1 TwoPoint 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
11. Boundary Value Problems and SturmLiouville Theory
11.1 The Occurrence of TwoPoint Boundary Value Problems
11.2 SturmLiouville Boundary Value Problems
11.3 Nonhomogeneous Boundary Value Problems
11.4 Singular SturmLiouville Problems
11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
11.6 Series of Orthogonal Functions: Mean Convergence
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
2. FirstOrder Differential Equations
2.1 Linear Differential Equations; Method of Integrating Factors
2.2 Separable Differential Equations
2.3 Modeling with FirstOrder Differential Equations
2.4 Differences Between Linear and Nonlinear Differential Equations
2.5 Autonomous Differential Equations and Integrating Factors
2.6 Exact Differential Equations and Integrating Factors
2.7 Numerical Approximations: Euler's Method
2.8 The Existence and Uniqueness Theorem
2.9 FirstOrder Difference Equations
3. SecondOrder Linear Differential Equations
3.1 Homogeneous Differential Equations with Constant Coefficients
3.2 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 Periodic Vibrations
4. HigherOrder Linear Differential Equations
4.1 General Theory of n^{th} Order Linear Differential Equations
4.2 Homogeneous Differential Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters
5. Series Solutions of SecondOrder Linear Equations
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
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
7. Systems of FirstOrder Linear Equations
7.1 Introduction
7.2 Matrices
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
7.4 Basic Theory of Systems of FirstOrder Linear Equations
7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 ComplexValued Eigenvalues
7.7 Fundamental Matrices
7.8 Repeated Eigenvalues
7.9 Nonhomogeneous Linear Systems
8. Numerical Methods
8.1 The Euler or Tangent Line Method
8.2 Improvements on the Euler Method
8.3 The RungeKutta Method
8.4 Multistep Methods
8.5 Systems of FirstOrder Equations
8.6 More on Errors; Stability
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 PredatorPrey Equations
9.6 Liapunov's Second Method
9.7 Periodic Solutions and Limit Cycles
9.8 Chaos and Strange Attractors: The Lorenz Equations
10. Partial Differential Equations and Fourier Series
10.1 TwoPoint 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
11. Boundary Value Problems and SturmLiouville Theory
11.1 The Occurrence of TwoPoint Boundary Value Problems
11.2 SturmLiouville Boundary Value Problems
11.3 Nonhomogeneous Boundary Value Problems
11.4 Singular SturmLiouville Problems
11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
11.6 Series of Orthogonal Functions: Mean Convergence
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 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 havingvarious levels of computer involvement, ranging from little or none to intensive. Morethan 450 problems are marked with a technology icon to indicate those that areconsidered 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.
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