Math 308-505, 506, Spring 2015, Tentative Day by Day Schedule
01/21.
Solutions of some differential equations (first order linear equations
with constant coefficients, section 1.2)
01/23 Separable equations
(section 2.2); direction field (sections 1.1)
01/26 Direction field (continued), autonomous equations, and population dynamics (sections 1.1 and 2.5
combined);
01/28 Autonomous equations and population dynamics (section 2.5
continued). Linear equations: Method of integrating factors (section 2.1);
01/30 Linear equations: Method of integrating factors (section 2.1 continued).
02/02 Modelling with first order equations (section 2.3);
02/04 Differences between linear and non-linear equations (section 2.4). Exact equations (section 2.6);
02/06 Exact equations and integrating factors (section 2.6 continued). Solutions of linear homogeneous equations of second order (section 3.2);
02/09 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);
02/11 Review of complex numbers.
02/13 Linear homogeneous equations of second order with constant coefficients: the case of complex roots of the characteristic equation (section 3.3);
02/16 The case of repeated roots (section 3.4); The method of reduction of order (section 3.4)
02/18 Non-homogeneous equations; Method of undetermined coefficients (section 3.5);
02/20 Method of undetermined coefficients (section 3.5, continued).
02/23 Method of variation of parameters (section 3.6);
02/25 Mechanical and electrical vibrations (section 3.7);
02/27 Forced vibrations (section 3.8);
03/02 Definition of Laplace transform (section 6.1). Solution of initial value problems using Laplace transform (section 6.2);
03/04 Solution
of initial value problems using Laplace transform (section 6.2 continued).
03/06 Step functions.
Differential equations with discontinuous forcing functions (sections
6.3 and 6.4);
03/13 Introduction and review of matrices (section 7.1 and 7.2);
03/23 Linear algebraic equations: linear independence, eigenvalues, eigenvectors (section 7.3);
03/25 Basic theory of systems of first order linear equations (section 7.4);
03/27 Homogeneous linear systems with constant coefficients, the case of distinct eigenvalues (section 7.5);
03/30 Complex eigenvalues (section 7.6);
04/01 Fundamental matrices (section 7.7);