Plan

 MondayWednesdayThursday
Week 1
11 jan		First day of class.
Def of ODE's, examples
T 1.2, Z 1.1		Examples cont'd, Existence and Uniqueness
T 2.3, Z 1.2		Existence and uniqueness, and separable ODE's, more examples
T2.2, 2.3, Z 1.2, 2.2
Week 2Existence and Uniqueness cont'd, more separable ODE's and equilibrium solutions
T 2.2, Z 2.2, 2.1		Exis and Uniq/separable cont'd, Direction Fields
T 1.3, Z 2.1.2, 3.2		Direction Fields, Autonomous systems, stability of equil solutions, applications
T 1.3, Z 2.1.2, 3.2
Week 3stability of equil solutions, applications, Linear 1st order ODE's
T 1.3, Z 2.1.2, 3.2 Z2.3, T2.1		Linear 1st order ODE's
Z2.3, T2.1		n-th order linear ODE's homogeneous
Z 4.1 T9.1, 5.1
Week 4Homogeneous n-th order ODE's, proof of thm on Wronskian, n-th order constant coefficient, 2nd order
Z 4.1, 4.3 T 5.1, 9.1, 5.2		Homogeneous 2nd order constant coefficient cont'd
Z 4.1, 4.2, 4.3 T 5.2, 9.2		Intro to Numerical analysis
Z Sec 2.6, T Sec 3.1
Week 5Test #1Homogeneous 2nd order constant coefficient, examples, case of repeated roots: Reduction of order, Exemple,
Non homogeneous linear: method of undetermined coefficients,
Z 4.1, 4.2, 4.3 T 5.2, 9.2		Reduction of order cont'd.
Non homogeneous linear: method of undetermined coefficients, exemple with exponentials and polynomials.
Z 4.2, 4.3, 4.4 T 5.2, 9.2, 5.3, 5.4
Reading Week!
Week 7Method of undetermined coefficients cont'd, examples,
Method of Variation of Parameters for linear non homogeneous 2nd order ODE's
Z 4.4, 4.6 T 5.4, 5.5, 5.7		Method of Variation of Parameters for linear non homogeneous 2nd order ODE's cont'd
Z 4.6; T 5.7
Spring-Mass systems-simple harmonic oscillator, undamped/damped cases
Z 5.1 T 6.1, 6.2
Week 8Spring-Mass systems cont'd
Damped case, forced
Z 5.1 T 6.1, 6.2		Spring-Mass systems cont'd:
undamped case with period forcing, Cauchy-Euler
Z 5.1 T 6.1, 6.2		Cauchy-Euler eqn Cont'd
Z 4.7
Week 9Power series solutions
Z 6.1, 6.2 T7.1, 7.2, 7.3		Power series solutions cont'd
ordinary points
Z 6.2, T 7.2, 7.3		Regular and irregular singular points, Frobenius method, Bessel's equation

Z 6.3, 6.4, T 7.2, 7.3, 7.4, 7.5
Week 10Regular and irregular singular points, Frobenius method cont'd, Bessel eqn

Z 6.3, 6.4, T 7.2, 7.3, 7.4, 7.5		Regular and irregular singular points, Frobenius method cont'd, Bessel eqn

Z 6.3, 6.4, T 7.2, 7.3, 7.4, 7.5		Frobenius method, cont'd, exemple: Bessel eqn
Z 6.3, 6.4, T 7.2, 7.3, 7.4, 7.5
Week 11Test #2Laplace Transform: def, examples, properties
Z 7.1 T 8.1		Laplace Transform cont'd: derivatives, inverse Laplace Transform
Z 7.1, 7.2, 7.4 T 8.1 8.2 8.3 8.4
Week 12Laplace Transform cont'd: translations
Z 7.3 T 8.1-5		Laplace Transform: translations and convolution
Z 7.4 T 8.4-6		Laplace Transform: convolution and Dirac delta
Z 7.4, 7.5 Z 8.6, 8.7
Week 13Laplace Transform cont'd: Dirac delta, periodic forcing
Z 7.4, 7.5 T8.5-7		Boundary Value problems
Z 5.2 T 11.1		Boundary Value problems cont'd
Z 5.2, 11.1 T 11.1
Week 14Last class!
I will finish the exemple of Laplace Transform I started last Monday and answer questions.		No class: Enjoy your summer!