Preface |
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xi | |
Chapter 1 Background Material |
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1 | (38) |
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1.1 Multivariable Calculus |
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1 | (4) |
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1.2 Ordinary Differential Equations |
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5 | (10) |
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15 | (13) |
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28 | (11) |
Chapter 2 Conservation- Learning How to Count |
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39 | (8) |
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39 | (2) |
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2.2 Examples of Flux-How Things Move |
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41 | (3) |
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44 | (3) |
Chapter 3 The Diffusion Equation- Derivations |
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47 | (12) |
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47 | (1) |
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48 | (4) |
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52 | (4) |
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56 | (3) |
Chapter 4 Realizations of a Diffusion Process |
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59 | (16) |
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4.1 Following Individual Particles |
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59 | (2) |
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4.2 Other Features of Brownian Particle Motion |
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61 | (4) |
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4.3 Following Several Particles |
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65 | (1) |
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66 | (3) |
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4.5 An Agent-Based Approach |
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69 | (2) |
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71 | (4) |
Chapter 5 Solutions of the Diffusion Equation |
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75 | (20) |
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5.1 On an Infinite Domain |
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75 | (2) |
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5.2 On the Semi-infinite Line |
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77 | (2) |
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5.3 With Boundary Conditions |
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79 | (2) |
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5.4 Separation of Variables |
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81 | (3) |
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84 | (3) |
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87 | (1) |
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88 | (3) |
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91 | (4) |
Chapter 6 Diffusion and Reaction |
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95 | (36) |
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6.1 Birth-Death with Diffusion |
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95 | (6) |
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6.2 Growth with a Carrying Capacity-Fisher's Equation |
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101 | (12) |
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113 | (3) |
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6.4 Spread of Rabies-SIR with Diffusion |
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116 | (3) |
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6.5 Extras: Facilitated Diffusion |
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119 | (6) |
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125 | (6) |
Chapter 7 The Bistable Equation-Part I: Derivations |
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131 | (10) |
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131 | (3) |
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134 | (1) |
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135 | (2) |
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137 | (2) |
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139 | (2) |
Chapter 8 The Bistable Equation-Part II: Analysis |
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141 | (26) |
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141 | (5) |
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146 | (4) |
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150 | (13) |
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163 | (4) |
Chapter 9 Advection and Reaction |
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167 | (40) |
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167 | (1) |
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167 | (2) |
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9.3 Structured Populations |
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169 | (8) |
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177 | (4) |
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9.5 Nonlinear Advection; Burgers' Equation |
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181 | (8) |
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9.6 Extras: More Advection-Reaction Models |
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189 | (11) |
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200 | (7) |
Chapter 10 Advection with Diffusion |
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207 | (10) |
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10.1 A Biased Random Walk |
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207 | (1) |
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10.2 Transport with Switching |
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207 | (2) |
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10.3 Ornstein-Uhlenbeck Process |
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209 | (3) |
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10.4 Spread of an Ornstein-Uhlenbeck Epidemic |
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212 | (2) |
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214 | (3) |
Chapter 11 Chemotaxis |
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217 | (10) |
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219 | (5) |
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224 | (3) |
Chapter 12 Spatial Patterns |
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227 | (20) |
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12.1 The Turing Mechanism |
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228 | (4) |
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232 | (6) |
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238 | (6) |
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244 | (3) |
Chapter 13 Dispersal-Renewal Theory |
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247 | (6) |
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247 | (4) |
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251 | (2) |
Chapter 14 Collective Behavior |
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253 | (22) |
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253 | (9) |
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262 | (10) |
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272 | (3) |
Appendix A. Introduction to Matlab |
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275 | (10) |
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275 | (4) |
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A2 List of Available Matlab Codes |
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279 | (6) |
Appendix B. Constants, Units, and Functions |
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285 | (4) |
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285 | (2) |
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B2 Functions Used in this Book |
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287 | (2) |
Appendix C. Selected Answers to Exercises |
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289 | (10) |
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C1 Selected Answers for Chapter 1 |
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289 | (2) |
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C2 Selected Answers for Chapter 2 |
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291 | (1) |
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C3 Selected Answers for Chapter 3 |
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291 | (1) |
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C4 Selected Answers for Chapter 4 |
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291 | (1) |
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C5 Selected Answers for Chapter 5 |
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292 | (1) |
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C6 Selected Answers for Chapter 6 |
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293 | (1) |
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C7 Selected Answers for Chapter 7 |
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293 | (1) |
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C8 Selected Answers for Chapter 8 |
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294 | (1) |
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C9 Selected Answers for Chapter 9 |
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295 | (1) |
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C10 Selected Answers for Chapter 10 |
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296 | (1) |
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C11 Selected Answers for Chapter 11 |
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297 | (1) |
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C12 Selected Answers for Chapter 12 |
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297 | (1) |
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C13 Selected Answers for Chapter 13 |
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297 | (1) |
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C14 Selected Answers for Chapter 14 |
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297 | (2) |
Bibliography |
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299 | (6) |
Index |
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305 | |