Math 308-505, Fall 2012 Tentative Day by Day Schedule
08/27.
Solutions of some differential equations (first order linear equations
with constant coefficients, section 1.2)
08/29 Separable equations
(section 2.2); direction field (sections 1.1)
08/31 Direction field (continued), autonomous equations, and population dynamics (sections 1.1 and 2.5
combined);
09/03 Autonomous equations and population dynamics (section 2.5
continued). Linear equations: Method of integrating factors (section 2.1);
09/05 Linear equations: Method of integrating factors (section 2.1 continued).
09/07 Modelling with first order equations (section 2.3);
09/10 Differences between linear and non-linear equations (section 2.4). Exact equations (section 2.6);
09/12 Exact equations and integrating factors (section 2.6 continued). Solutions of linear homogeneous equations of second order (section 3.2);
09/14 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);
09/17 Review of complex numbers.
09/19 Linear homogeneous equations of second order with constant coefficients: the case of complex roots of the characteristic equation (section 3.3);
09/21 The case of repeated roots (section 3.4); The method of reduction of order (section 3.4)
09/24 Non-homogeneous equations; Method of undetermined coefficients (section 3.5);
09/26 Method of undetermined coefficients (section 3.5, continued).
09/28 Method of variation of parameters (section 3.6);
10/01 Mechanical and electrical vibrations (section 3.7);
10/03 Forced vibrations (section 3.8);
10/05 Definition of Laplace transform (section 6.1). Solution of initial value problems using Laplace transform (section 6.2);
10/08 Solution
of initial vale problems using Laplace transform (section 6.2 continued).
10/10 Step functions.
Differential equations with discontinuous forcing functions (sections
6.3 and 6.4);
10/17 Introduction and review of matrices (section 7.1 and 7.2);
10/19 Linear algebraic equations: linear independence, eigenvalues, eigenvectors (section 7.3);
10/22 Basic theory of systems of first order linear equations (section 7.4);
10/24 Homogeneous linear systems with constant coefficients, the cae of distinct eigenvalues (section 7.5);
10/26 Complex eigenvalues (section 7.6);
10/29 Fundamental matrices (section 7.7);
10/31. Repeated eigenvalues (section 7.8);
11/02 Nonhomogeneous linear systems: variation of parameter (section 7.9);
11/05 The Phase Plane; Linear Systems (section 9.1);
11/07 Autonomous Systems and Stability (section 9.2);
11/09 Locally Linear Systems (section 9.3);
11/12 Review of power series (section 5.1);
11/14 Series solutions near an ordinary point, part I (section 5.2); 11/16 Series solutions near an ordinary point, part II (section 5.3);