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xiicontents9.7.1 Friction: Model and Implementation 2099.7.2 Resonances and Beats: Model and Implementation 2109.8 Implementation: Inclusion of Time-DependentForce 2119.9 Unit II. Binding A Quantum Particle 2129.10 The Quantum Eigenvalue Problem (Theory) 2129.10.1 Nucleon in a Box (Model) 2139.11 Combined Algorithms: Eigenvalues via ODESolver Plus Search 2149.11.1 Numerov Algorithm for the Schrödinger ODE ⊙ 2169.11.2 Implementation: Eigenvalues via an ODE Solver PlusBisection Algorithm 2189.12 Explorations 2219.13 Unit III. Scattering, Projectiles, and PlanetaryOrbits 2229.14 Problem 1: Classical Chaotic Scattering 2229.14.1 Model and Theory 2229.14.2 Implementation 2249.14.3 Assessment 2259.15 Problem 2: Balls Falling Out of the Sky 2259.16 Theory: Projectile Motion with Drag 2269.16.1 Simultaneous Second-Order ODEs 2279.16.2 Assessment 2289.17 Problem 3: Planetary Motion 2289.17.1 Implementation: Planetary Motion 22910 Fourier Analysis: Signals and Filters 23110.1 Unit I. Fourier Analysis of Nonlinear Oscillations 23110.2 Fourier Series (Math) 23210.2.1 Example 1: Sawtooth Function 23410.2.2 Example 2: Half-wave Function 23510.3 Summation of Fourier Series (Exercise) 23510.4 Fourier Transforms (Theory) 23610.4.1 Discrete Fourier Transform Algorithm 23710.4.2 Aliasing and Anti-aliasing ⊙ 24110.4.3 DFT for Fourier Series (Algorithm) 24310.4.4 Assessments 24410.4.5 DFT of Nonperiodic Functions (Exploration) 246−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.34811_fm — 2008/2/13 — Page xii