Reading Assignments 2250 Spring 2009 ======================================================================= All Reading is approximately one week ahead of the lectures. Please read the text in the week assigned! Then read it again after the lectures on the topics. ======================================================================= Week 1, Jan 12-16 Read sections 1.1,1.2,1.3,1.4. Method of Quadrature, Direction fields, Picard theory, Separable DE Week 2, Jan 19-23 Read sections 1.5,2.1,2.2,2.3. linear DE, populations, stability, Verhulst DE, phase analysis, Newton kinematic models. Week 3, Jan 26-30 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 Simpon rules in calculus. Week 4, Feb 2-6 Read sections 3.1,3.2,3.3. Intro linear algebra. Read the online notes for linear algebraic equations. Week 5, Feb 9-13 Read sections 3.4,3.5,3.6. Matrices, rref, matrix operations, inverses, determinants Week 6, Feb 16-20 Read sections 4.1,4.2,4.3. Vector space, subspace, independence Week 7, Feb 23-27 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, Mar 2-6 Read sections 5.1,5.2,5.3,5.4. Linear constant DE, superposition, atoms, vibrations, steady-states, observables Week 9, Mar 9-13 Read sections 10,1,10.2,10.3,10.4. Laplace intro, history, Laplace tables, Laplace's method, Laplace rules. Week 10, Mar 23-27 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, Mar 30,31 Apr 1,2,3 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, Apr 6-10 Read sections 7.1,7.2,7.3,7.4. First order systems, eigenanalysis method, Putzer's algorithm, resolvent method, Cayley-Hamilton method. Second order systems, railway cars, earthquakes, sliding plates, oscillation control of an elevator. Week 13, Apr 13-17 Read sections 7.5 /w Laplace, 8.1, 8.2. Jordan form, Putzer's formulas, generalized eigenanalysis, Caley-Hamilton theorem, matrix exponential, spectral methods, variation of parameters for systems. Week 14, Apr 20-24 Read sections 9.1,9.2,9.3. Stability, phase plane, linear systems, almost linear systems, predator-prey models. Week 15, Apr 27-29 Read sections 9.3,9.4. More detail predator-prey, nonlinear mechanical systems. Pendulum. Soft and hard springs. =======================================================================