# Math 2410 Lectures

## First- Order Differential Equations

 Aug 25-29 1.1 Modeling via Diff Eqs # 2, 3, 5, 7, 8, 9, 15, 16, 17, 19, 20 1.2 Separation of Variables # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34 Sept 1-5 1.3 Slope Fields # 1, 3, 5, 7, 9, 11, 13, 15, 16, 17, 18, 24 1.4 Euler’ s Method # 1, 3, 5, 7, 8, 10, 11 Sept 8-12 1.5 Existence and Uniqueness # 1, 3, 5, 6, 7, 8, 13, 18 1.6 Equilibria and the Phase Line # 1, 3, 5, 7, 9, 11, 29, 31, 33, 35, 37, 38, 39, 45, 46, 47, 48 Sept 15-19 1.7 Bifurcations # 1, 3, 5, 7, 9, 11, 17, 22, 23 1.8 Linear Equations # 1, 3, 5, 7, 9, 11, 13, 21, 23, 25, 27, 32, 33, 34 Sept 22-26 1.9 Integrating Factors # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 21, 22, 25

## Hour Exam One: Friday, 26 September 2008

First- Order Systems

 Sept 29-3 2.1 Modelling via Systems # 1, 2, 3, 4, 5, 6, 7, 8, 9-14, 15, 17, 18, 20-24, 25-30 2.2 The Geometry of Systems # 1, 3, 5, 7, 11, 13, 15, 17, 20, 21, 23, 24, 25, 26, 27, 28, 29 Oct 6-10 2.3 Special Systems (Analytic) # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17 2.4 Euler’s Method for Systems # 1, 2, 3, 5, 7, 8, 9, 12, 13, 14, 15 Oct 13-17 2.5 Lorenz Equations # 1, 2, 3, 4, 5

Linear Systems

 3.1 Linear Systems # 1, 2, 3, 4, 5, 7, 9, 14, 15, 16, 17, 20, 21, 22, 23, 25, 26, 27, 34 Oct 20-24 3.2 Straight- Line Solutions # 1, 3, 5, 7, 11, 15, 16, 17, 18, 19, 20, 21, 23 3.3 Real Eigenvalues # 1, 3, 5, 9, 13, 15, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27 Oct 27-31 3.4 Complex Eigenvalues # 1, 2, 3, 5, 7, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24 3.5 Repeated and Zero Eigenvalues # 1, 3, 5, 7, 9, 10, 11, 12, 13, 15, 17, 20, 24 Nov 3-7 3.6 Second- Order Linear Equations # 1, 3, 5, 7, 9, 11, 30, 31, 32, 36

## Hour Exam Two : Friday, 7 November 2008

Forcing and Resonance

 Nov 10-14 4.1 Forced Harmonic Oscillators # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 25, 27, 29, 36, 37, 39, 41 4.2 Sinusoidal Forcings # 1, 3, 5, 7, 9, 11, 13, 15, 16, 17, 18, 19, 20

Nonlinear Systems

 Nov 17-21 5.1 Equilibrium Point Analysis # 1, 2, 3, 4, 5, 6, 27, 28, 29, 30

Laplace Transforms

 6.1 Laplace Transforms # 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19, 26, 27 Dec 1-5 6.2 Discontinuous Functions # 1, 2, 3, 5, 7, 9, 11, 13, 14, 15, 16, 17, 18

Final Exam: Wednesday, 10 December 2008, 10:30AM-12:30PM

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