2250-4 JWB 335 12:25pm Reading Schedule Fall 2010 Week 1, Aug 23 to 27 Read sections 1.1,1.2,1.3,1.4. Method of Quadrature, Direction fields, Picard theory, Separable DE Week 2, Aug 30 to Sep 3 Read sections 1.5,2.1,2.2,2.3. linear DE, populations, stability, Verhulst DE, phase analysis, Newton kinematic models. Week 3, Sep 6 to 10 Read sections 2.3,2.4,2.5,2.6. Earth to the moon, numerical methods of Euler, Heun, Runge-Kutta, review of rectangular, trapezoidal and Simpson rules in calculus. Week 4, Sep 13 to 17 Read sections 3.1,3.2,3.3. Intro linear algebra. Read the online notes for linear algebraic equations. Week 5, Sep 20 to 24 Read sections 3.4,3.5,3.6. Matrices, rref, matrix operations, inverses, determinants Week 6, Sep 27 to Oct 1 Read sections 4.1,4.2,4.3. Vector space, subspace, independence Week 7, Oct 4 to 8 Read sections 4.4,4.5,4.6,4.7 Bases, dimension, row and column space, pivot theorem, orthogonality, abstract vectors spaces, function spaces Week 8, Oct 18 to 22 Read sections 5.1,5.2,5.3,5.4. Linear constant DE, superposition, atoms, vibrations, steady-states, observables Week 9, Oct 25 to 29 Read sections 10.1,10.2,10.3,10.4. Laplace intro, history, Laplace tables, Laplace's method, Laplace rules. Week 10, Nov 1 to 5 Read sections 10.5,EPbvp7.6,5.5 Periodic inputs, square wave, ramp, piecewise methods, Heaviside and Dirac inputs, engineering functions. Variation constants, undetermined coefficients. Week 11, Nov 8 to 12 Read 5.6,EPbvp3.7,6.1,6.2. Forced oscillations, beats, resonance, mechanical systems, electric circuits. Eigenanalysis, systems of DE, Fourier's model, diagonalization. Week 12, Nov 15 to 19 Read sections 7.1,7.2,7.3,7.4. First order systems, eigenanalysis method, Putzer's algorithm, resolvent method, Cayley-Hamilton-Ziebur method. Second order systems, railway cars, earthquakes, sliding plates, oscillation control of an elevator. Week 13, Nov 22 to 26 Read sections 7.5 /w Laplace, 8.1, 8.2. Jordan form, Putzer's formulas, generalized eigenanalysis, Cayley-Hamilton-Zeibur theorem, matrix exponential, spectral methods, variation of parameters for systems. Week 14, Nov 20 to Dec 3 Read sections 9.1,9.2,9.3. Stability, phase plane, linear systems, almost linear systems, predator-prey models. Week 15, Dec 6 to 10 Read section 9.4. More detail predator-prey, nonlinear mechanical systems. Pendulum. Soft and hard springs.