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Elementary Differential Equations
Math 2410Q § 010 & § 015D Fall 2017

Schedule

Week
Sec.
Topic
Supplements
1
1.1
Modeling with differential equations

1.2
Separation of variables (analytical technique)

2
1.2
Separation of variables (analytical technique)
A Mixing Problem
1.3
Slope fields (qualitative technique)
Matching DEs with slope fields
1.4
Euler's method (numerical technique)

3
1.4
Euler's method (numerical technique)

1.5
Existence and Uniqueness of Solutions

1.6
Equilibria and the Phase Line

4
1.6
Equilibria and the Phase Line

1.7
Bifurcations

1.8
Linear Equations
Video: Undetermined Coefficients
5
1.9
Integrating Factors for Linear Equations


Exam 1
2/17: Covers all of chapter 1.
6
2.1
Modeling via systems

2.2
Qualitative analysis via vector fields

2.4
Decoupled systems

7
2.4
Decoupled systems

2.5
Euler's method for systems

2.6
Existence and uniqueness for systems
Will not be assessed.
2.3
Harmonic oscillators

8
3.1
Properties of linear systems

9

Spring break

10
3.1
Properties of linear systems

3.2
Straight-line solutions

11
3.3
Phase portraits for linear systems with:
Real eigenvalues


3.4


Complex eigenvalues

Finding the general solution
and solving an IVP:
an example

12
3.4
Complex eigenvalue



Exam 2

4/7: Covers sections 2.1 - 2.5, 3.1 - 3.4
"Study Guide"
13
3.5
Repeated and zero eigenvalues

3.6
Second-order linear equations

14
3.6
Second-order linear equations
Example: Solving an IVP
4.1
Forced harmonic oscillators

4.2
Sinusoidal forcing

15
6.1
The Laplace transform

6.3
Second-order equations

6.2
Discontinuous functions

16

Final exam
Wed. 5/3 3:30-5:30 in PB 38.
Comprehensive.
"Study Guide"