# Math 2410 Outline

## Tentative Outline for Math 1132 – Spring 2016

 Week Date Section Topic Suggested homework 1 1/19 1.1 Modeling via Differential Equations 2,5,7,14,17,22 1.2 Analytic Technique: Separation of Variables 8,11,19,23,30,34,38 2 1/25 1.3 Qualitative Technique: Slope Fields 1,7,8,11,12,14,16 1.4 Numerical Technique: Euler’s Methods 2,4,7,11 3 2/1 1.5 Existence and Uniqueness of Solutions 4,9,12,14,17 1.6 Equilibria and the Phase Line 6,10,23,28,30,34,37, 38,39 4 2/8 1.7 Bifurcations 4,6,10,11,13,18,20 1.8 Linear Equations 7,9,11,21,24 5 2/15 1.9 Integrating Factors for Linear Equations 1,4,12,13,21,25 2/18 In class Midterm 1 6 2/22 2.1 Modeling via Systems 9,11,13,15,16a,20,23 2.2 The Geometry of Systems 7a,b,9,11,13a,19a,b,21,27 7 2/29 2.3 The Damped Harmonic Oscillator 1b,4b,5b,7,8 2.4 Additional Analytical Methods for Special Systems 1,7,9,13a-c 2.5 Euler’s Method for Systems 1,4,5 2.6, 2.7* Existence and Uniqueness for Systems; SIR model of an Epidemic 2.6:1a,5,7,10,11 2.7: 3,4,6a-c 8 3/7 3.1 Properties of Linear Systems and the Linearity Principle 6,8,15,16,21,25,27 3.2 Straight-Line Solutions 3,6,8,11,13,19,20,22 9 3/14 No Classes Spring Break 10 3/21 3.3 Phase Portrait for Linear Systems with Real Eigenvalues 3,5,7,9,11,13,19,21 3.4 Complex Eigenvalues 3,5,7,9,11,13,15,19,21 11 3/28 3.5 Special Cases: Repeated and Zero Eigenvalues 2,3,6,7,11,18,20,21a,22a,24 3/31 In class Midterm 2 12 4/4 3.6 Second-Order Linear Equations 1,3,5,7,9,11,17-20,25-28 3.7 The Trace-Determinant Plane 3,5,7,9,11 13 4/11 4.1 Forced Harmonic Oscillator 1,7,11,13,15,17,19,21,23,25,27 32,39 4.2 Sinusoidal Forcing 7,9,13,17,20 4.3 Undamped Forcing and Resonance 1,5,9,13,15,19,21 14 4/18 5.1 Equilibrium Point Analysis 1,3,5,6,7a.b,17,21,23 6.1 Laplace Transform 7,11,13,15,19,23 15 4/25 6.2 Discontinuous Functions 1,3,5,9,11,14 6.3 Second-Order Equations 7,9,15,17,29,30,33 Review 17 5/2 Finals Week