| Description |
xxiv, 705 pages : illustrations ; 26 cm |
| Contents |
Machine derived contents note: Contents -- 1 First-Order Differential Equations -- 1.1 Dynamical Systems: Modeling 1 -- 1.2 Solutions and Direction Fields: Qualitative Analysis 11 -- 1.3 Separation of Variables: Quantitative Analysis 25 -- 1.4 Approximation Methods: Numerical Analysis 33 -- 1.5 Picard¿s Theorem: Theoretical Analysis 46 -- 2 Linearity and Nonlinearity -- 2.1 Linear Equations: The Nature of Their Solutions 55 -- 2.2 Solving the First-Order Linear Differential Equation 63 -- 2.3 Growth and Decay Phenomena 73 -- 2.4 Linear Models: Mixing and Cooling 80 -- 2.5 Nonlinear Models: Logistic Equation 87 -- 2.6 Systems of Differential Equations: A First Look 100 -- 3 Linear Algebra -- 3.1 Matrices: Sums and Products 115 -- 3.2 Systems of Linear Equations 130 -- 3.3 The Inverse of a Matrix 146 -- 3.4 Determinants and Cramer¿s Rule 156 -- 3.5 Vector Spaces and Subspaces 167 -- 3.6 Basis and Dimension 177 -- 4 Higher-Order Linear Differential Equations -- 4.1 The Harmonic Oscillator 195 -- 4.2 Real Characteristic Roots 210 -- 4.3 Complex Characteristic Roots 229 -- 4.4 Undetermined Coefficients 244 -- 4.5 Variation of Parameters 255 -- 4.6 Forced Oscillations 261 -- 4.7 Conservation and Conversion 274 -- 5 Linear Transformations -- 5.1 Linear Transformations 285 -- 5.2 Properties of Linear Transformations 300 -- 5.3 Eigenvalues and Eigenvectors 311 -- 5.4 Coordinates and Diagonalization 327 -- 6 Linear Systems of Differential Equations -- 6.1 Theory of Linear DE Systems 343 -- 6.2 Linear Systems with Real Eigenvalues 357 -- 6.3 Linear Systems with Nonreal Eigenvalues 372 -- 6.4 Stability and Linear Classification 384 -- 6.5 Decoupling a Linear DE System 394 -- 6.6 Matrix Exponential 400 -- 6.7 Nonhomogeneous Linear Systems 410 -- 7 Nonlinear Systems of Differential Equations -- 7.1 Nonlinear Systems 421 -- 7.2 Linearization 431 -- 7.3 Numerical Solutions 441 -- 7.4 Chaos, Strange Attractors, and Period Doubling 449 -- 7.5 Chaos in Forced Nonlinear Systems 456 -- 8 Laplace Transforms -- 8.1 The Laplace Transform and Its Inverse 467 -- 8.2 Solving DEs and IVPs with Laplace Transforms 475 -- 8.3 The Step Function and the Delta Function 485 -- 8.4 The Convolution Integral and the Transfer Function 499 -- 8.5 Laplace Transform Solution of Linear Systems 509 -- 9 Discrete Dynamical Systems -- 9.1 Iterative Equations 517 -- 9.2 Linear Iterative Systems 530 -- 9.3 Nonlinear Iterative Equations: Chaos Again 542 -- 10 Control Theory -- 10.1 Feedback Controls 557 -- 10.2 Introduction to Optimal Control 567 -- 10.3 Pontryagin Maximum Principle 579 |
| Notes |
Previous ed., 2001 |
|
Formerly CIP. Uk |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Differential equations.
|
|
Algebras, Linear.
|
| Author |
Farlow, Jerry.
|
| LC no. |
2006034955 |
| ISBN |
0131860615 hardback |
|
