046 (Section 011, 012, 13)

Office Hours: Wednesday 1-4pm at Skye 281 or https://ucr.zoom.us/j/94325777751 (In person preferred)

Week 1 (Jan 12) - Worksheet Solns

Key Takeaways: 

1. Integration by Parts

2. Partial Fraction Decomposition

3. Integral and properties of ln

Week 2 (Jan 19) - Notes

Keywords: (Ordinary) Differential Equations (ODE, DE), Order, Solution, General and Particular Solution, Initial Value Problem (IVP), Direction Field, Linear, Nonlinear, Homogenous, Non-homogenous, Integrating Factor, Standard and Differential Form

Key Questions to Understand:

1. What is a differential equation and ordinary differential equation?

2. What is the general solution of a linear first order differential equation?

3. What is the integrating factor method?

Week 3 (Jan 26) - Classwork 1 and Notes

Keywords: Separable, Bernoulli Equations, Non-homogenous linear

Key Questions to Understand:

1. What are separable differential equations? How to solve separable differential equations?

2. What are bernoulli differential equations? How to solve such equations?

3. What are homogenous non-linear differential equations? How to solve such equations?

**There is a typo in the notes. Where I write nonhomogeneous linear it should really say homogenous non-linear.

Week 4 (Feb 2) - Notes

Keywords: Implicit differentiation, differential form, exact

Key Questions to Understand:

1. How calculate the implicit differentiation?

2. What is an exact equation?

3. What are solutions to an exact equation?

Week 5 (Feb 9) - Classwork 2 and Notes

Keywords: Non-exact equations

Key Questions to Understand

1.  Relations of exact equations to other equations?

2.  How to move (some) equations to an exact equation?

Week 6 (Feb 16) - Discussion cancelled

Week 7 (Feb 23) - Notes

Keywords: Second order differential equations,  Proportional, Linear Independence, Wronskian, Abel's formula, Characteristic equation

Key Questions:

1. How to find wronskian?

2. How to check linear independence of solutions?

3. How to find solutions of second order homogenous constant coefficient when there exists two unique real roots?

Week 8 (Mar 1) - Classwork 3 and Notes

Keywords: Undetermined coefficients

Key Questions: 

1.  How to solve constant coefficient case?

2. Three cases of undetermined coefficients?

Week 9 (Mar 8)  - Notes

Keywords: Undetermined coefficients, reduction of order, linearly independents, linearly dependent, wronskian

Key Question

1. Given a particular solution of the homogenous second order equation, can we derive a general solution for the non-homogenous question?

2. How to apply reduction of order?

3. How to determine if a list of functions are linearly dependent or independent using the wronskian?

Week 10 (Mar 15) - Classwork 4 and Notes

Keywords: n-th order linear, principle of superposition, multiplicity of roots

Key Questions:

1. How to solve n-th order constant coefficient homogenous linear equations?

Supplementary Material:

Extra Notes on Section 1.3

Keywords: Equilibrium points, stable, unstable, semi-stable points

Final Review

Key Concepts:

1. First order linear equations

2. Separable equations

3. Bernoulli equations

4. Homogeneous nonlinear equations

5. Exact Equations

6. Exact problems that are not in exact form

7. Second order constant coefficient homogeneous

8. Particular solutions of second order constant coefficient non-homogeneous depending on exponential and polynomials

9. Particular solutions of second order constant coefficient non-homogeneous depending on exponential and sin/cos functions

10. n-th order linear homogeneous constant coefficients