Differential Equations and Linear Algebra

ISBN-10: 013011118X

ISBN-13: 9780130111180

Edition: 2001

List price: $124.80
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Description: Written by a mathematician/engineer/scientist author who brings all three perspectives to the book. This volume offers an extremely easy-to-read and easy-to-comprehend exploration of both ordinary differential equations and linear algebra--motivated throughout by high-quality applications to science and engineering. Features many optional sections and subsections that allow topics to be covered comprehensively, moderately, or minimally, and includes supplemental coverage of Maple at the end of most sections. For anyone interested in Differential Equations and Linear Algebra.

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Book details

List price: $124.80
Copyright year: 2001
Publisher: Prentice Hall PTR
Publication date: 12/5/2000
Binding: Hardcover
Pages: 611
Size: 8.50" wide x 9.25" long x 1.25" tall
Weight: 2.794
Language: English

Preface
Introduction to Differential Equations
Definitions and Terminology
Linear First-Order Equations
Homogeneous Case
Solution by Separation of Variables
Nonhomogeneous Case
Applications of Linear First-Order Equations
General First-Order Equations
Separable Equations
Existence and Uniqueness
Exact Equations and Ones That Can Be Made Exact
Additional Applications
Linear and Nonlinear Equations Contrasted
Vectors and n-Space
Geometrical Representation of Arrow Vectors n-Space
Dot Product, Norm, and Angle for n-Space
Gauss Elimination
Span
Linear Dependence and Independence
Vector Space
Bases and Expansions
Matrices and Linear Algebraic Equations
Matrices and Matrix Algebra
The Transpose Matrix
Determinants
The Rank of a Matrix
Inverse Matrix, Cramer's Rule, and Factorization
Existence and Uniqueness for the System Ax= c
Vector Transformation (Optional)
Linear Differential Equations of Second Order and Higher
The Complex Plane and the Exponential, Trigonometric, and Hyperbolic Functions
Linear Dependence and Linear Independence of Functions
Homogeneous Equation
General Solution
Homogeneous Equations with Constant Coefficients
Homogeneous Equations with Nonconstant Coefficients
Cauchy-Euler Equation
Solution of Nonhomogeneous Equation
Applications of Linear Constant-Coefficient Equations
Linear Harmonic Oscillator
Free Oscillation
Linear Harmonic Oscillator
Phase Plane
Linear Harmonic Oscillator
Forced Oscillation
Additional Applications
Power Series Solution
Power Series
Power Series Solutions
Introduction to the Singular Case
The Eigenvalue Problem
Solution of the Eigenvalue Problem
The Special Case of Symmetric Matrices
Differential Equation Boundary Value Problems as Eigenvalue Problems
Systems of Linear Differential Equations
Existence, Uniqueness, and General Solution
Solution by Elimination
Constant-Coefficient Equations
Solution of Homogeneous Systems as Eigenvalue Problems
Diagonalization (Optional)
Triangularization (Optional)
Explicit Solution of x' = Ax and the Matrix Exponential Function (Optional)
Quantitative Methods: The Phase Plane
The Phase Plane
Singular Point Analysis
Additional Applications
Qualitative Methods: Numerical Solution
Euler's Method
Improvements: Runge-Kutta Methods
Application to Systems and Boundary Value Problems
Laplace Transform
Definitions and Calculation of the Transform
Properties of the Transform
Application to the Solution of Differential Equations
Discontinuous Forcing Functions
Heaviside Step Function
Additional Properties
Appendix
Answers to Selected Exercises
Index
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