Week

Sections

Material

1

1.1, 1.2, 1.3

Introduction to differential equations – what do they mean and how do they show up in applications.  Slope fields, qualitative solutions, applications (falling objects, population models, Newton’s Law of Cooling), checking a solution, terminology

2.1, 2.2

Solving using separation of variables, linear equations and integrating factors

2

2.3, 2.4

Assorted applications including tank/mixture problems, approximating loans (cont.); Linear vs. nonlinear equations, existence and uniqueness , 

2.5

Autonomous equations and population models

3

2.6

Exact equations

2.7

More substitutions methods: Homogeneous and Bernoulli equations

4

8.1, 8.2

Numerical methods – Euler’s method, Runge-Kutta method, errors and efficiency

Test 1

5

3.1, 3.2, 6.2

Introduction to systems of differential equations, checking solutions, review of matrix notation and linear systems of algebraic equations, linear independence and the theory of solutions to linear systems 

3.3, 6.3

Solving a homogeneous system of differential equations with constant coefficients in 2 dimensions, Phase portraits, considering higher dimensions

6

3.4, 6.4

Systems with complex eigenvalues

3.5 (6.7)

Systems with repeated eigenvalues, 

7

6.6

Non-homogeneous linear systems with constant coefficients and variation of parameters

7.1, 7.2

Introduction to analyzing non-linear systems On

8

7.3, 7.4

Population problems using nonlinear systems - predator/prey systems and competing species

Test 2

9

4.1, 4.2, 4.3

Second order DE’s for fun and profit – New equations with old methods, now with 50% less work; The Wronskian, existence and uniqueness, and phase portraits; solving homogeneous equations with constant coefficients, reduction of order

4.5, 4.7

Non-homogeneous equations with undetermined coefficients, operator notation, the Exponential Input Theorem

10

4.4

Mechanical applications and electrical circuits

10.3

Basic boundary value problems with eigenvalues

11

5.1, 5.2, 5.3

Laplace transforms and initial value problems, 

5.3, 5.4

The inverse Laplace transform, using Laplace transforms to solve initial value problems

12

5.5, 5.6

Piecewise functions and the unit step function

Review for Test 3 (or Test 3 in class)

13

5.7 or 5.8

The impulse function or convolutions

9.1, 9.2

Series solutions near an ordinary point

14

10.1, 10.2

Orthogonality and Fourier series

10.2

More Fourier series (Sine and Cosine series)

15

11.1

Solving the one-dimensional heat equation using separation of variables

11.1

Solving the one-dimensional heat equation using separation of variables (cont.)

16

Review for Final Exam

Final Exam