Math 308:102-103
Tentative Weekly Schedule
Summer 2014
Week 1
(06/02-06/06)
Introduction.
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)
Autonomous equations, and population dynamics (sections 1.1 and 2.5)
Modelling with first order equations (section 2.3)
Differences between linear and non-linear equations (section 2.4).
Exact equations and integrating factors (section 2.6).
Week 2
(06/09-06/13)
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).
Exam 1
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).
Non-homogeneous equations; Method of undetermined coefficients (section 3.5).
Week 3
(06/16-06/20)
Method of variation of parameters (section 3.6)
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).
Exam 2
Week 4
(06/23-06/27)
Step functions. Differential equations with discontinuous forcing functions (sections 6.3 and 6.4).
Impulse functions (section 6.5).
The convolution integral (section 6.6).
Introduction and review of matrices (section 7.1-7.2).
Basic theory of systems of first order linear equations (section 7.4).
Week 5
(06/30-07/03)
Linear algebraic equations: eigenvalues, eigenvectors (section 7.3).
Homogeneous linear systems with constant coefficients, the case of distinct eigenvalues (section 7.5).
Complex eigenvalues (section 7.6).
Fundamental matrices (section 7.7).
Repeated eigenvalues (section 7.8).
Nonhomogeneous linear systems: variation of parameter (section 7.9).
The Phase Plane. Linear Systems (section 9.1).
Autonomous Systems and Stability (section 9.2).
Final Exam