Math 308:501-505
Tentative Weekly Schedule
Spring 2013
Week 1
Solutions of some differential equations (first order linear equations with constant coefficients, section 1.2)
Separable equations (section 2.2)
Linear equations: Method of integrating factor (section 2.1 ).
Direction field (section 1.1)
Week 2
Autonomous equations, and population dynamics (sections 1.1 and 2.5 combined)
Modelling with first order equations (section 2.3)
Week 3
Differences between linear and non-linear equations (section 2.4).
Exact equations and integrating factors (section 2.6).
Solutions of linear homogeneous equations of second order (section 3.2).
The Wronskian (section 3.2).
Linear homogeneous equations of second order with constant coefficients: the case of distinct roots of characteristic equation (section 3.1)
Week 4
Review of complex numbers.
Linear homogeneous equations of second order with constant coefficients: the case of complex roots of the characteristic equation (section 3.3);
The case of repeated roots (section 3.4);
The method of reduction of order (section 3.4)
Week 5
Non-homogeneous equations; Method of undetermined coefficients (section 3.5);
Method of variation of parameters (section 3.6)
Week 6
Mechanical and electrical vibrations (section 3.7).
Forced vibrations (section 3.8).
Definition of Laplace transform (section 6.1).
Solution of initial value problems using Laplace transform (section 6.2).
Week 7
Solution of initial vale problems using Laplace transform (section 6.2 continued).
Step functions. Differential equations with discontinuous forcing functions (sections 6.3 and 6.4).
Week 8
Impulse functions (section 6.5 ); The convolution integral.(section 6.6)
Introduction and review of matrices (section 7.1 and 7.2).
Linear algebraic equations: linear independence, eigenvalues, eigenvectors (section 7.3).
Week 9
Basic theory of systems of first order linear equations (section 7.4).
Homogeneous linear systems with constant coefficients, the cae of distinct eigenvalues (section 7.5)
Complex eigenvalues (section 7.6)
Week 10
Fundamental matrices (section 7.7).
Repeated eigenvalues (section 7.8).
Nonhomogeneous linear systems: variation of parameter (section 7.9).
Week 11
The Phase Plane; Linear Systems (section 9.1).
Autonomous Systems and Stability (section 9.2).
Locally Linear Systems (section 9.3).
Week 12
Review of power series (section 5.1).
Series solutions near an ordinary point, part I (section 5.2).
Series solutions near an ordinary point, part II (section 5.3).
Week 13
Euler equations; Regular singular points (section 5.4);
Series solution near a regular singular point, part I (section 5.5)
Week 14
Series solution near a regular singular point, part II (section 5.6).
Competing Species, Predator-Prey Equations (section 5.4, 5.5).
Review before the final exam.