Differential Equations and Linear Algebra

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  • Edition: 2nd
  • Format: Paperback
  • Copyright: 12/26/2006
  • Publisher: Pearson

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For sophomore-level courses in Differential Equations and Linear Algebra. Extensively rewritten throughout, the Second Edition of this flexible text features a seamless integration of linear algebra into the discipline of differential equations. Abundant computer graphics, IDE interactive illustration software, and well-thought-out problem sets make it an excellent choice for either the combination DE/LA course or pure differential equations courses. The authorsrs" consistent, reader-friendly presentation encourages students to think both quantitatively and qualitatively when approaching differential equations - and reinforces concepts using similar methods to solve various systems (algebraic, differential, and iterative).

Table of Contents

First-Order Differential Equations
Dynamical Systems: Modelingp. 1
Solutions and Direction Fields: Qualitative Analysisp. 11
Separation of Variables: Quantitative Analysisp. 25
Approximation Methods: Numerical Analysisp. 33
Picards Theorem: Theoretical Analysisp. 46
Linearity and Nonlinearity
Linear Equations: The Nature of Their Solutionsp. 55
Solving the First-Order Linear Differential Equationp. 63
Growth and Decay Phenomenap. 73
Linear Models: Mixing and Coolingp. 80
Nonlinear Models: Logistic Equationp. 87
Systems of Differential Equations: A First Lookp. 100
Linear Algebra
Matrices: Sums and Productsp. 115
Systems of Linear Equationsp. 130
The Inverse of a Matrixp. 146
Determinants and Cramers Rulep. 156
Vector Spaces and Subspacesp. 167
Basis and Dimensionp. 177
Higher-Order Linear Differential Equations
The Harmonic Oscillatorp. 195
Real Characteristic Rootsp. 210
Complex Characteristic Rootsp. 229
Undetermined Coefficientsp. 244
Variation of Parametersp. 255
Forced Oscillationsp. 261
Conservation and Conversionp. 274
Linear Transformations
Linear Transformationsp. 285
Properties of Linear Transformationsp. 300
Eigenvalues and Eigenvectorsp. 311
Coordinates and Diagonalizationp. 327
Linear Systems of Differential Equations
Theory of Linear DE Systemsp. 343
Linear Systems with Real Eigenvaluesp. 357
Linear Systems with Nonreal Eigenvaluesp. 372
Stability and Linear Classificationp. 384
Decoupling a Linear DE Systemp. 394
Matrix Exponentialp. 400
Nonhomogeneous Linear Systemsp. 410
Nonlinear Systems of Differential Equations
Nonlinear Systemsp. 421
Linearizationp. 431
Numerical Solutionsp. 441
Chaos, Strange Attractors, and Period Doublingp. 449
Chaos in Forced Nonlinear Systemsp. 456
Laplace Transforms
The Laplace Transform and Its Inversep. 467
Solving DEs and IVPs with Laplace Transformsp. 475
The Step Function and the Delta Functionp. 485
The Convolution Integral and the Transfer Functionp. 499
Laplace Transform Solution of Linear Systemsp. 509
Discrete Dynamical Systems
Iterative Equationsp. 517
Linear Iterative Systemsp. 530
Nonlinear Iterative Equations: Chaos Againp. 542
Control Theory
Feedback Controlsp. 557
Introduction to Optimal Controlp. 567
Pontryagin Maximum Principlep. 579
Table of Contents provided by Publisher. All Rights Reserved.

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