Section

Topic

Page

Chapter 25

Electrostatic Potentials

343

25.1

Introduction: Types of PDE'S

343

25.2

Problem: Determining An Electrostatic Potential

344

25.3

Theory: Laplace's Equation (Elliptic PDE)

344

25.4

Method, Numerical: Finite Difference

345

25.5

Method, Analytic: Polynomial Expansions

347

25.6

Implementation: Solution on Lattice, laplace.f

350

25.7

Assessment And Visualization

351

25.8

Exploration

351

25.9

Exploration: ParallelPlate Capacitor

352

25.10

Exploration: Field Between Square Conductors

352

Chapter 26

Heat Flow

355

26.1

Problem: Heat Flow In A Metal Bar

355

26.2

Model: The Heat (Parabolic) PDE

355

26.3

Method, Analytic: Polynomial Expansions

356

26.4

Method, Numerical: Finite Difference

358

26.5

Analytic Assessment: Algorithm

359

26.6

Implementation, Heat Equation, eqheat.f
(.c)

360

26.7

Assessment: Continuity, Numeric vs Analytic

361

26.8

Assessment: Visualization

362

26.9

Exploration

362

Chapter 27

Waves on a String

365

27.1

Problem: A Vibrating String

365

27.2

Model: The Wave Equation (Hyperbolic PDE)

365

27.3

Method, Numerical: Time Stepping

367

27.4

Method, Analytic: Normal Modes

369

27.5

Implementation, Wave Equation, eqstring.f
(.c)

371

27.6

Assessment: Visualization

371

27.7

Exploration

372
