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1 FIRST-ORDER DIFFERENTIAL EQUATIONS |
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1 | (148) |
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1.1 Modeling via Differential Equations |
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2 | (19) |
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1.2 Analytic Technique: Separation of Variables |
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21 | (15) |
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1.3 Qualitative Technique: Slope Fields |
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36 | (16) |
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1.4 Numerical Technique: Euler's Method |
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52 | (11) |
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1.5 Existence and Uniqueness of Solutions |
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63 | (11) |
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1.6 Equilibria and the Phase Line |
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74 | (20) |
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94 | (16) |
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110 | (14) |
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1.9 Integrating Factors for Linear Equations |
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124 | (25) |
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Review Exercises for
Chapter 1 |
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136 | (6) |
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142 | (7) |
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149 | (90) |
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150 | (16) |
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2.2 The Geometry of Systems |
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166 | (17) |
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2.3 The Damped Harmonic Oscillator |
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183 | (6) |
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2.4 Additional Analytic Methods for Special Systems |
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189 | (7) |
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2.5 Euler's Method for Systems |
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196 | (8) |
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2.6 Existence and Uniqueness for Systems |
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204 | (5) |
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2.7 The SIR Model of an Epidemic |
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209 | (8) |
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217 | (22) |
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Review Exercises for
Chapter 2 |
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224 | (5) |
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229 | (10) |
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239 | (148) |
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3.1 Properties of Linear Systems and the Linearity Principle |
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240 | (24) |
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3.2 Straight-Line Solutions |
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264 | (16) |
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3.3 Phase Portraits for Linear Systems with Real Eigenvalues |
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280 | (16) |
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296 | (19) |
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3.5 Special Cases: Repeated and Zero Eigenvalues |
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315 | (15) |
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3.6 Second-Order Linear Equations |
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330 | (17) |
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3.7 The Trace-Determinant Plane |
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347 | (13) |
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3.8 Linear Systems in Three Dimensions |
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360 | (27) |
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Review Exercises for
Chapter 3 |
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376 | (5) |
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381 | (6) |
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387 | (70) |
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4.1 Forced Harmonic Oscillators |
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388 | (15) |
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403 | (12) |
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4.3 Undamped Forcing and Resonance |
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415 | (12) |
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4.4 Amplitude and Phase of the Steady State |
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427 | (12) |
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4.5 The Tacoma Narrows Bridge |
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439 | (18) |
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Review Exercises for
Chapter 4 |
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449 | (3) |
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452 | (5) |
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457 | (108) |
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5.1 Equilibrium Point Analysis |
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458 | (19) |
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477 | (13) |
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490 | (18) |
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508 | (22) |
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5.5 Nonlinear Systems in Three Dimensions |
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530 | (8) |
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5.6 Periodic Forcing of Nonlinear Systems and Chaos |
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538 | (27) |
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Review Exercises for
Chapter 5 |
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555 | (3) |
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558 | (7) |
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565 | (68) |
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566 | (12) |
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6.2 Discontinuous Functions |
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578 | (9) |
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6.3 Second-Order Equations |
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587 | (14) |
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6.4 Delta Functions and Impulse Forcing |
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601 | (8) |
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609 | (9) |
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6.6 The Qualitative Theory of Laplace Transforms |
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618 | (15) |
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Table of Laplace Transforms |
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626 | (1) |
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Review Exercises for
Chapter 6 |
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627 | (3) |
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630 | (3) |
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633 | (42) |
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7.1 Numerical Error in Euler's Method |
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634 | (13) |
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7.2 Improving Euler's Method |
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647 | (8) |
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7.3 The Runge-Kutta Method |
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655 | (10) |
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7.4 The Effects of Finite Arithmetic |
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665 | (10) |
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Review Exercises for
Chapter 7 |
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670 | (1) |
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671 | (4) |
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8 DISCRETE DYNAMICAL SYSTEMS |
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675 | (54) |
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8.1 The Discrete Logistic Equation |
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676 | (13) |
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8.2 Fixed Points and Periodic Points |
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689 | (9) |
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698 | (9) |
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707 | (8) |
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8.5 Chaos in the Lorenz System |
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715 | (14) |
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Review Exercises for
Chapter 8 |
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721 | (2) |
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723 | (6) |
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729 | (26) |
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730 | (12) |
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B Power Series: The Ultimate Guess |
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742 | (8) |
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C Complex Numbers and Euler's Formula |
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750 | (5) |
| Hints And Answers |
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755 | (70) |
| Index |
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825 | |
