Intro: First-year physics problems in Maple
In1.1 Circular rocket motion ; In1.2 Maple Solution ; In1.3 Net acceleration vector .
In2.1 Rolling down an incline ; In2.2 Concepts ; In2.3 Solution .
In3.1 Velocity-dependent drag ; In3.2 Discussion ; In3.3 Ballistic motion .
0.2 A quick guide to MATLAB
0.1 Matrices and vectors ; 0.2 Mathematical operations ; 0.3 Programming elements ; 0.4 Input/Output .
1. Introduction to computational methods: trajectory calculations
1.1 Overview ; 1.2 Maple vs Matlab ; 1.3 Science Overview .
1.4 Newton's law: damped oscillator ; 1.5 Maple approach ; 1.6 maple follow-up ; 1.7 more follow-up .
1.8 Oscillator model: an ODE ; 1.9 Understand damped oscillations ; 1.10 x-v phase space plot ;
1.11 Energy consideration ; 1.12 Maple: scoping rules .
1.13 The Pendulum ; 1.14 Approximation ideas ; 1.15 Maple solution
1.16 Matlab vs Maple ; 1.17 Function plot in Matlab ; 1.18 First Matlab program ; 1.19 Solve pendulum ODE in Matlab ; 1.20 Discussion of results
1.21 The driven oscillator ; 1.22 Properties ; 1.23 Maple implementation ; 1.24 The driven pendulum in Maple ; 1.25 The driven pendulum in Matlab
1.26 Finite differences ; 1.27 Newton's law: recursion approach ; 1.28 Recursion for the Kepler problem; 1.29 The Maple code ; 1.30 The Matlab code
1.31 Kepler problem with drag force ; 1.32 Energy and angular momentum ; 1.33 Observations; page32.mws ; page32.m .
1.34 The notebook interface to MATLAB via MS-WORD; page32.doc ; page32.html
2. Simulations of continuous mass or charge distributions
2.1 Overview ; 2.2 Monte-Carlo integration ; 2.3 Pseudorandom numbers ; 2.4 Moment of inertia .
2.5 Potential energy of a massive sphere ; 2.6 Point-mass discretization ; 2.7 Monte-Carlo calculation ; 2.8 Gauss' law .
2.9 Gravitational attraction of two spheres ; 2.10 testing the hypothesis ; 2.11 Planet moving about an ellipsoid
2b. Notes on Probability and Measurement Error
Gaussian Distribution ; GD2 ; Standard Deviation ; Confidence Interval .
3. The Eigenvalue Problem in linear algebra and differential equations
3.1 Eigenvalue Problem; 3.2; 3.3 ; 3.4. 3.5 Solve Poisson eq.; 3.6; 3.7 ; 3.8.