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Below is a list of pre-recorded lectures for MATH:2560 Engineer Math IV: Differential Equations. These lectures are available to everyone. Logging into ICON is not required.

Recordings of class lectures are only available to students registered in MATH:2560. They are available by logging into ICON, click on UICapture (near bottom of column). The in class videos are in the folder titled "In Class videos." Note recordings of class lectures may not be available, and if available, the camera will not capture the entire chalkboard.

### Pre-req material

Integration by parts (12:44 min video),    slides pptx,   annotated slides:
View anytime before the end of week 1
This is a quick review of integration by parts. Note integration by parts comes from the product rule for differention (slide 1). We cover doing repeated integration by parts in a single step (slide 8) as well as solving for an integral to calculate $\int e^{2x} sin(3x)dx$ (slides 9 - 15). Consider stopping the video to do the examples on your own. Or take a look at slides 1, 8, 15 if you are already comfortable with integration by parts. See Paul's online notes for some interesting integration by parts examples.

Linear algebra + partial fractions review (25:45 min video),    slides,   annotated slides:
View anytime before the end of week 1
We will use several concepts that you have seen before in linear algebra. While you do not need an abstract understanding of these concepts for this course, it can be helpful (especially for future courses and out in the real world) to see how concepts that seem different can be very similar (for example, working with vectors, polynomials, or solutions to linear differential equations).

We will use the language of linear algebra in a very concrete setting: existence and uniqueness of solutions to linear differential equations.

### Week 1

Slope fields (45:18 min video)   slides annotated slides

1. A quick review of a standard slope field example: $y' = (y - 3)(y +1)$
2. A more complicated example that might help with HW 1: sect 1.1 # 23 (not assigned this year, but note software graphing errors).
3. Briefly introduce a standard counter-example $y' = y^\frac{1}{3}$. We will discuss this example more thoroughly later in this course.

### Week 2

Review of solving first order LINEAR differential equation using an integrating factor (15:46 min video)   slides annotated slides :
View anytime after in class 2.1 lecture and before 2.1 HW.

### Week 3

Theorem 2.4.2/domain (28:41 min video)   slides,   annotated slides:
View after 2.4 in class lecture and before doing 2.4 HW
Thm 2.4.2 can sometimes be used to determine if an IVP has a unique solution, but it cannot be used to determine the domain of that solution. In this video, we first use Thm 2.4.2 to determine when $y' = 1/[(1-t)(2-y)$, $y(t_0) = y_0$ is guaranteed to have a uniqe solution. We then use a lot of algebra and a little bit of calculus to solve this DE and determine the domain of this solution when the initial value is the point (0, 1).

### Week 4

2.7: Euler's method for approximating a function using tangent lines (27:00 min video)   slides,   annotated slides:
View before doing 2.7 HW.