9780201662122

Linear Algebra and Differential Equations

by ;
  • ISBN13:

    9780201662122

  • ISBN10:

    0201662124

  • Edition: 1st
  • Format: Paperback
  • Copyright: 7/24/2001
  • Publisher: Pearson

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Summary

This book has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including courses that cover differential equations first. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest. Matrices and Determinants; Vector Spaces; First Order Ordinary Differential Equations; Linear Differential Equations; Linear Transformations and Eigenvalues and Eigenvectors; Systems of Differential Equations; The Laplace Transform; Power Series Solutions to Linear Differential Equations; Inner Product Spaces For all readers interested in linear algebra and differential equations.

Table of Contents

Matrices and Determinants
1(64)
Systems of Linear Equations
2(15)
Matrices and Matrix Operations
17(11)
Inverses of Matrices
28(9)
Special Matrices and Additional Properties of Matrices
37(6)
Determinants
43(8)
Further Properties of Determinants
51(7)
Proofs of Theorems on Determinants
58(7)
Vector Spaces
65(46)
Vector Spaces
66(8)
Subspaces and Spanning Sets
74(9)
Linear Independence and Bases
83(12)
Dimension; Nullspace, Row Space, and Column Space
95(11)
Wronskians
106(5)
First Order Ordinary Differential Equations
111(68)
Introduction to Differential Equations
112(8)
Separable Differential Equations
120(4)
Exact Differential Equations
124(6)
Linear Differential Equations
130(6)
More Techniques for Solving First Order Differential Equations
136(8)
Modeling with Differential Equations
144(9)
Reduction of Order
153(4)
The Theory of First Order Differential Equations
157(11)
Numerical Solutions of Ordinary Differential Equations
168(11)
Linear Differential Equations
179(52)
The Theory of Higher Order Linear Differential Equations
179(10)
Homogeneous Constant Coefficient Linear Differential Equations
189(14)
The Method of Undetermined Coefficients
203(8)
The Method of Variation of Parameters
211(6)
Some Applications of Higher Order Differential Equations
217(14)
Linear Transformations and Eigenvalues and Eigenvectors
231(62)
Linear Transformations
231(14)
The Algebra of Linear Transformations; Differential Operators and Differential Equations
245(8)
Matrices for Linear Transformations
253(16)
Eigenvalues and Eigenvectors of Matrices
269(9)
Similar Matrices, Diagonalization, and Jordan Canonical Form
278(9)
Eigenvectors and Eigenvalues of Linear Transformations
287(6)
Systems of Differential Equations
293(52)
The Theory of Systems of Linear Differential Equations
295(7)
Homogeneous Systems with Constant Coefficients: The Diagonalizable Case
302(10)
Homogeneous Systems with Constant Coefficients: The Nondiagonalizable Case
312(3)
Nonhomogeneous Linear Systems
315(4)
Converting Differential Equations to First Order Systems
319(3)
Applications Involving Systems of Linear Differential Equations
322(12)
2 x 2 Systems of Nonlinear Differential Equations
334(11)
The Laplace Transform
345(30)
Definition and Properties of the Laplace Transform
345(7)
Solving Constant Coefficient Linear Initial Value Problems with Laplace Transforms
352(4)
Step Functions, Impulse Functions, and the Delta Function
356(10)
Convolution Integrals
366(4)
Systems of Linear Differential Equations
370(5)
Power Series Solutions to Linear Differential Equations
375(38)
Introduction to Power Series Solutions
376(8)
Series Solutions for Second Order Linear Differential Equations
384(9)
Euler Type Equations
393(4)
Series Solutions Near a Regular Singular Point
397(16)
Inner Product Spaces
413(28)
Inner Product Spaces
413(8)
Orthonormal Bases
421(9)
Schur's Theorem and Symmetric Matrices
430(11)
Answers to Odd-Numbered Exercises 441(18)
Index of Maple Commands 459(2)
Index 461

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