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1 | (5) |
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1.2 Solutions and Initial Value Problems |
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6 | (9) |
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15 | (8) |
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1.4 The Approximation Method of Euler |
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23 | (12) |
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29 | (1) |
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Technical Writing Exercises |
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29 | (1) |
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Group Projects for
Chapter 1 |
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30 | (1) |
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30 | (1) |
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31 | (1) |
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32 | (3) |
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Chapter 2 First-Order Differential Equations |
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2.1 Introduction: Motion of a Falling Body |
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35 | (3) |
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38 | (8) |
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46 | (9) |
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55 | (9) |
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2.5 Special Integrating Factors |
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64 | (4) |
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2.6 Substitutions and Transformations |
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68 | (21) |
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76 | (1) |
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77 | (1) |
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Technical Writing Exercises |
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78 | (1) |
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Group Projects for
Chapter 2 |
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79 | (1) |
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79 | (1) |
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B Differential Equations in Clinical Medicine |
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80 | (2) |
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C Torricelli's Law of Fluid Flow |
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82 | (1) |
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83 | (1) |
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83 | (1) |
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F Clairaut Equations and Singular Solutions |
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84 | (1) |
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G Multiple Solutions of a First-Order Initial Value Problem |
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85 | (1) |
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H Utility Functions and Risk Aversion |
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85 | (1) |
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I Designing a Solar Collector |
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86 | (1) |
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J Asymptotic Behavior of Solutions to Linear Equations |
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87 | (2) |
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Chapter 3 Mathematical Models and Numerical Methods Involving First-Order Equations |
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3.1 Mathematical Modeling |
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89 | (2) |
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3.2 Compartmental Analysis |
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91 | (10) |
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3.3 Heating and Cooling of Buildings |
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101 | (7) |
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108 | (9) |
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117 | (4) |
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3.6 Improved Euler's Method |
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121 | (11) |
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3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta |
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132 | (21) |
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Group Projects for
Chapter 3 |
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414 | |
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A Dynamics of HIV Infection |
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141 | (3) |
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144 | (1) |
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145 | (1) |
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D Aircraft Guidance in a Crosswind |
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146 | (1) |
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E Feedback and the Op Amp |
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147 | (1) |
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148 | (1) |
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G Market Equilibrium: Stability and Time Paths |
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149 | (1) |
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H Stability of Numerical Methods |
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150 | (1) |
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I Period Doubling and Chaos |
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151 | (2) |
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Chapter 4 Linear Second-Order Equations |
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4.1 Introduction: The Mass-Spring Oscillator |
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153 | (5) |
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4.2 Homogeneous Linear Equations: The General Solution |
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158 | (9) |
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4.3 Auxiliary Equations with Complex Roots |
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167 | (8) |
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4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients |
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175 | (7) |
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4.5 The Superposition Principle and Undetermined Coefficients Revisited |
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182 | (7) |
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4.6 Variation of Parameters |
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189 | (4) |
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4.7 Variable-Coefficient Equations |
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193 | (10) |
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4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations |
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203 | (11) |
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4.9 A Closer Look at Free Mechanical Vibrations |
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214 | (9) |
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4.10 A Closer Look at Forced Mechanical Vibrations |
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223 | (19) |
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231 | (2) |
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233 | (1) |
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Technical Writing Exercises |
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234 | (1) |
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Group Projects for
Chapter 4 |
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235 | (1) |
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A Nonlinear Equations Solvable by First-Order Techniques |
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235 | (1) |
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236 | (1) |
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237 | (1) |
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D Linearization of Nonlinear Problems |
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238 | (1) |
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239 | (1) |
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F Undetermined Coefficients Using Complex Arithmetic |
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239 | (2) |
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G Asymptotic Behavior of Solutions |
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241 | (1) |
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Chapter 5 Introduction to Systems and Phase Plane Analysis |
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5.1 Interconnected Fluid Tanks |
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242 | (2) |
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5.2 Differential Operators and the Elimination Method for Systems |
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244 | (9) |
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5.3 Solving Systems and Higher-Order Equations Numerically |
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253 | (10) |
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5.4 Introduction to the Phase Plane |
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263 | (13) |
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5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models |
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276 | (9) |
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5.6 Coupled Mass-Spring Systems |
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285 | (6) |
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291 | (6) |
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5.8 Dynamical Systems, Poincare Maps, and Chaos |
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297 | (21) |
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307 | (1) |
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308 | (1) |
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Group Projects for
Chapter 5 |
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309 | (1) |
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A Designing a Landing System for Interplanetary Travel |
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309 | (1) |
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B Spread of Staph Infections in Hospitals---Part I |
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310 | (2) |
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312 | (1) |
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313 | (2) |
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E Cleaning Up the Great Lakes |
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315 | (1) |
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F A Growth Model for Phytoplankton---Part I |
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316 | (2) |
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Chapter 6 Theory of Higher-Order Linear Differential Equations |
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6.1 Basic Theory of Linear Differential Equations |
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318 | (9) |
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6.2 Homogeneous Linear Equations with Constant Coefficients |
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327 | (6) |
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6.3 Undetermined Coefficients and the Annihilator Method |
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333 | (5) |
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6.4 Method of Variation of Parameters |
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338 | (12) |
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342 | (1) |
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343 | (1) |
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Technical Writing Exercises |
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344 | (1) |
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Group Projects for
Chapter 6 |
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345 | (1) |
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A Computer Algebra Systems and Exponential Shift |
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345 | (1) |
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B Justifying the Method of Undetermined Coefficients |
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346 | (1) |
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C Transverse Vibrations of a Beam |
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347 | (1) |
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D Higher-Order Difference Equations |
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347 | (3) |
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Chapter 7 LaplaceTransforms |
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7.1 Introduction; A Mixing Problem |
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350 | (3) |
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7.2 Definition of the Laplace Transform |
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353 | (8) |
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7.3 Properties of the Laplace Transform |
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361 | (5) |
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7.4 Inverse Laplace Transform |
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366 | (10) |
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7.5 Solving Initial Value Problems |
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376 | (7) |
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7.6 Transforms of Discontinuous and Periodic Functions |
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383 | (14) |
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397 | (7) |
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7.8 Impulses and the Dirac Delta Function |
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404 | (8) |
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7.9 Solving Linear Systems with Laplace Transforms |
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412 | (10) |
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414 | (2) |
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416 | (1) |
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Technical Writing Exercises |
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417 | (1) |
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Group Projects for
Chapter 7 |
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418 | (1) |
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418 | (1) |
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B Frequency Response Modeling |
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419 | (2) |
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C Determining System Parameters |
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421 | (1) |
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Chapter 8 Series Solutions of Differential Equations |
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8.1 Introduction: The Taylor Polynomial Approximation |
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422 | (5) |
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8.2 Power Series and Analytic Functions |
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427 | (9) |
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8.3 Power Series Solutions to Linear Differential Equations |
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436 | (10) |
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8.4 Equations with Analytic Coefficients |
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446 | (6) |
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8.5 Cauchy-Euler (Equidimensional) Equations |
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452 | (3) |
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455 | (12) |
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8.7 Finding a Second Linearly Independent Solution |
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467 | (9) |
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476 | (22) |
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489 | (2) |
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491 | (1) |
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Technical Writing Exercises |
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492 | (1) |
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Group Projects for
Chapter 8 |
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493 | (1) |
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A Alphabetization Algorithms |
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493 | (1) |
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B Spherically Symmetric Solutions to Shrodinger's Equation for the Hydrogen Atom |
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494 | (1) |
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495 | (1) |
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495 | (2) |
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E Aging Spring and Bessel Functions |
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497 | (1) |
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Chapter 9 Matrix Methods for Linear Systems |
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498 | (4) |
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9.2 Review 1: Linear Algebraic Equations |
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502 | (5) |
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9.3 Review 2: Matrices and Vectors |
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507 | (10) |
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9.4 Linear Systems in Normal Form |
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517 | (9) |
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9.5 Homogeneous Linear Systems with Constant Coefficients |
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526 | (12) |
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538 | (5) |
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9.7 Nonhomogeneous Linear Systems |
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543 | (7) |
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9.8 The Matrix Exponential Function |
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550 | (16) |
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558 | (3) |
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561 | (1) |
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Technical Writing Exercises |
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562 | (1) |
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Group Projects for
Chapter 9 |
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563 | (1) |
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A Uncoupling Normal Systems |
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563 | (1) |
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B Matrix Laplace Transform Method |
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564 | (1) |
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C Undamped Second-Order Systems |
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565 | (1) |
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Chapter 10 Partial Differential Equations |
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10.1 Introduction: A Model for Heat Flow |
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566 | (3) |
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10.2 Method of Separation of Variables |
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569 | (9) |
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578 | (16) |
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10.4 Fourier Cosine and Sine Series |
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594 | (5) |
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599 | (12) |
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611 | (12) |
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623 | |
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636 | (1) |
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Technical Writing Exercises |
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637 | (1) |
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Group Projects for
Chapter 10 |
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638 | (1) |
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A Steady-State Temperature Distribution in a Circular Cylinder |
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638 | (2) |
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B Laplace Transform Solution of the Wave Equation |
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640 | (1) |
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641 | (1) |
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D Numerical Method for Δu = f on a Rectangle |
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642 | |
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A Review of Integration Techniques |
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1 | (7) |
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8 | (2) |
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10 | (1) |
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11 | (2) |
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E Method of Least Squares |
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13 | (2) |
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F Runge-Kutta Procedure for n Equations |
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15 | |
| Answers to Odd-Numbered Problems |
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1 | (1) |
| Index |
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1 | |
