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Office hours: Friday from 9am- noon in Skye 259

Email: nchie005@ucr.edu

Please feel free to contact me with any questions via email. If the office hours times do not work for you and you would like to meet, don't hesitate to reach out!

*All material is supplementary and is not to be used as the primary material for the course.

Color coding of notes:

• Black - Theorems, Lemmas, Context, Writing in General

• Grey - Reserved for proofs 

• Green - Definitions

• Red - Examples, Exercises

• Blue - Remarks, Clarification, Justification

Week 0 - Review of product and chain rule

Key takeaways:

1. Recall the derivative rules. Most notably product and chain rule.

2. Recall how to apply product and chain rule.

Week 1 - Review of implicit differentiation and solutions for linear ODE

Key takeaways:

1. Can take implicit derivatives when variables are all functions of another. See examples in notes.

2. Can identify if the ODE is linear and requires integrating factor method.

3. Knows how to find the general solution when applying integrating factor method.

Week 2 - Review of Bernoulli and separable equations

Key takeaways:

1. Understands the relationship between Bernoulli and linear equations.

2. Can identify and find solutions to Bernoulli equations.

3. Can identify and find solutions to separable equations.

Week 3 - Review of homogenous and exact equations

Key takeaways:

1. Understands the relation between homogenous and separable equations.

2. Can identify and find solutions to homogenous equations.

3. Can identify and find solutions to exact equations.

Week 4 - Exam review 

Key takeaways:

1. Can identify and solve the 5 different ODEs: linear, Bernoulli, separable, homogeneous, and exact.

2. Can setup and solve the three application problems: Newton's law of cooling, falling body problem, and mixing problems.

3. Can sketch a direction field when given an ODE.

4. Can approximate solutions of an IVP problem using Euler's method.

Week 5  - Review of second order constant coefficient homogeneous case.

Key takeaways:

1. Understands how a characteristic polynomial relates to the problem.

2. Knows the three cases that arise depending on the characterstic polynomial.

3. Knows the corresponding general solution depending on each case from the characteristic polynomial.

4. Can solve IVP problems for second order constant coefficient homogeneous case.

No office hours this week. For any questions or help please feel free to email me.

Week 6 - Review of reduction of order

Key takeaways:

1. Understands how to search for a general solution y=y_1u and find an ODE in terms of u.

2. Understands how to reduce the order of the ODE of u to a first order linear.

3. Can solve first order linear equations and move the solution back through the substitutions defined to find the general solution y=y_1u.

Week 7 - Review of undetermined coefficients

Key takeaways:

1. Understands how to solve particular solutions of non-homogenous equations (polynomial, exponential, sine, cosine) using undetermined coefficients.

2. Understands the exception cases that can arise when trying to attempt to use undetermined coefficients. When particular coincides with homogenous solution.

3. Understands how to solve when sums or products of basic functions.

Week 8 - No office hours due to Mathematical Pathways conference.  Review of variation of parameters and some additional details about spring problems. 

Key takeaways:

1. Can apply variation of paremeters to solve second order ODE provided two solutions.

2. Understands that spring problems are just second order ODE's that we have learned to solve already. 

Week 9  -