Elementary Differential Equations and Boundary Value Problems 12th Edition by William E. Boyce, Richard C. DiPrima, Douglas B. Meade – Ebook PDF Instant Download/DeliveryISBN: 1119777670, 9781119777670
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ISBN-10 : 1119777670
ISBN-13 : 9781119777670
Author : William E. Boyce, Richard C. DiPrima, Douglas B. Meade
Elementary Differential Equations and Boundary Value Problems, 12th Edition 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. In this revision, new author Douglas Meade focuses on developing students conceptual understanding with new concept questions and worksheets for each chapter. Meade builds upon Boyce and DiPrima’s work 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. 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.
Elementary Differential Equations and Boundary Value Problems 12th 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 First-Order Differential Equations
2.1 Linear Differential Equations; Method of Integrating Factors
2.2 Separable Differential Equations
2.3 Modeling with First-Order Differential Equations
2.4 Differences Between Linear and Nonlinear Differential Equations
2.5 Autonomous Differential Equations and Population Dynamics
2.6 Exact Differential Equations and Integrating Factors
2.7 Numerical Approximations: Euler’s Method
2.8 The Existence and Uniqueness Theorem
2.9 First-Order Difference Equations
3 Second-Order 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 Higher-Order Linear Differential Equations
4.1 General Theory of nth 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 Second-Order 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 First-Order 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 First-Order Linear Equations
7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 Complex-Valued 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 Runge-Kutta Method
8.4 Multistep Methods
8.5 Systems of First-Order 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 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
10 Partial Differential Equations and Fourier Series
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
11 Boundary Value Problems and Sturm-Liouville Theory
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
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Tags: Elementary Differential, Equations, Boundary Value Problems, William Boyce, Richard DiPrima, Douglas Meade