Notes By Date

16-January: Here are your In-Class Notes covering the Intro to ODEs.

18-January:

Please complete the following Pre-Work Assignments and upload them to Gradescope here. Use this video as a guide.
- Pre-Work (Review): Integration by Parts here.
- Pre-Work Solving Separable ODEs Pt. 1 here.
Here are your In-Class Notes
- Solving Separable ODEs Pt. 2 here.
- Numerical Solutions: Euler's Method here.

23-January:

Please complete Pre-Work
- On-Your-Own: Matrices as Objects here.
- On-Your-Own: Matrix Operations here
- Overview of Partial Derivatives available here.
Here are your In-Class Notes:
- Matrix Properties here.
- Picard's Existence Theorem here.

25-January:

Please complete Pre-Work:
- Gaussian Elimination Part 1 here.
Here are your In-Class Notes:
- Gaussian Elimination Part 2 here.
- Numerical Solutions: Runge-Kutta here.

30-January:

Please complete Pre-Work:
- Pre-Work: Solving Exact Equations Part 1 here.
- Pre-Work: Matrix Inversion here.
- Pre-Work: Introduction to Superposition here.
Here are your In-Class Notes:
- Solving Exact Equations Part 2 here.
- Solving by Euler/Lagrange method here.

1-February

Please complete Pre-Work:
- Pre-Work: Solve Equations with Matrix Inversion here.
- Pre-Work: Solving by Integrating Factor Pt. 1 available here.
Here are your In-Class Notes:
- Solving by Integrating Factor Pt. 2 here.
- Solutions to Bernouli ODEs and Reduction of Order here.

6-February:

Please complete Pre-Work:
- Pre-Work: Partial Fraction Decomposition review here.
- Pre-Work: Solving Equations by Substitution Part 1 here.
- Pre-Work: Review of Sequences, Series and Convergence here.
Here are your In-Class Notes:
- Solving Equations by Substitution Part 2 here.
- The Inverse Matrix Theorem Part 1 here.

8-Febraury:

Please complete Pre-Work:
- Pre-Work: Review of Taylor Series here.
- Pre-Work: Qualitative Solutions to Autonomous ODEs Pt. 1 here.
Here are your In-Class Notes:
- Introduction to Power Series Solutions here.
- Qualitative Solutions to Autonomous ODEs Pt. 2 here.

13-Febrary:

Please complete Pre-Work:
- Pre-Work: Determinants Part 1 here.

Here are the In-Class Notes:
- Determinants Part 2 here.
- Exam I Review here.

15-February:

No Pre-Work.
We will take Exam I

20-Febraury

Please complete this Pre-Work:
- Pre-Work: Determinants Part 1 here. (FUTURE CHARLES, MOVE THIS BACK A DAY FOR SP25)
Here are the In-Class Notes:
- Determinants Part 2 here. (FUTURE CHARLES, MOVE THIS BACK TWO DAYS FOR SP25)
- Linear Independence here.

22-February

Please complete this Pre-Work:
- The Characteristic Equation Part 1 here.
- Intro to Vector Spaces here. (FUTURE CHARLES, MOVE THIS BACK A DAY FOR SP25)
- Cramer's Rule here. (FUTURE CHARLES, MOVE THIS BACK A DAY FOR SP25)
Here are the In-Class Notes:
- The Characteristic Equation Part 2 here.
- Examples of Vector Spaces and Subspaces here.

27-February

Please complete this Pre-Work:
- Review: Superposition here.
- Matrices as Linear Transformations here.
Here are the In-Class Notes
- The Characteristic Equation Pt. 3 (Complex/Repeated Roots) here.

29-Feb

Please complete this Pre-Work:
- Method of Undetermined Coefficients Pt. 1 here.
- Basis and Dimension Part 1 here. (FUTURE CHARLES, MOVE THIS BACK TWO DAYS FOR SP25)
Here are the In-Class Notes
- Method of Undetermined Coefficients Pt. 2 here.
- Basis and Dimension Part 2 here. (FUTURE CHARLES, MOVE THIS BACK ONE DAYFOR SP25)
- The Harmonic Oscillator Pt. 1 here.

5-March

Please complete this Pre-Work:
- The Harmonic Oscillator Pt. 2 here.
- Bases and the General Solution here. (FUTURE CHARLES, MOVE THIS BACK ONE DAYFOR SP25)
Here are the In-Class Notes:
- Power Series for Second Order here.
- Basis and Dimension Pt. 3. (FUTURE CHARLES, MOVE THIS BACK TWO DAYS FOR SP25)

7-March

Please complete this Pre-Work:
- Variation of Parameters Pt. 1 here.
- Eigenstuff Pt. 1 here.
Here are the In-Class Notes:
- Variation of Parameters Pt. 2 here.
- Eigenstuff Pt. 2 here.

Spring Break: No classes March 12th nor March 14th

19-March

Here is our In-Class Work:
- Preparation for Exam II here.

21-March

We will take Exam II. Info here.

26-March

Please complete this Pre-Work:
- Overview of Systems and Laplace here.
Here are the In-Class Notes:
- Finish Eigenstuff Pt. 2 here.
- Solving Homogeneous Systems, Pt. 1 here.
- Laplace Transforms, Pt. 1 here.

28-March

Please complete this Pre-Work:
- Laplace and Systems (Continued) here.
Here are the In-Class Notes:
- Solving Homogeneous Systems, Pt. 2 here.
- Catch up old Laplace Notes.

2-April

Please complete this Pre-Work:
- Overview of Systems and Laplace (Cont.)^2 here.
We will work:
- Solving Homogeneous Systems, Pt. 3 here.

4-April

Please complete this Pre-Work:
- The Unit Step Function here.
We will work:
- Laplace Transforms with Step Functions here.

9-April:

There is no Pre-Work. Instead, prepare for Exam III here.
In-Class we will review for Exam III

11-April: Exam III. See Exam III materials here.

16-April

Please complete this Pre-Work:
- The delaying theorems and additional Laplace Transforms here.
- Course Review #1 here.

We will work:
- Laplace Transforms of Discontinuous Functions here.
- (Not SP 24) Matrix Diagonalization here.

18-April

Please complete this Pre-Work:
- Course Review #2 here.
We will work:
- Laplace Transforms of Discontinuous Functions here.
- (Not SP 24) Intro to non-linear systems Pt. 1 here.

23-April

Please complete this Pre-Work:
- Course Review #3 here.
- Course Review #4 here.
We will work:
- The Unit Impulse Function here.
- (Not SP 24) Intro to non-linear systems Pt. 2 here.

25-April

Please complete this Pre-Work:
- Course Review #5 here.
We will work:
- Applications of Systems of Equations here.
- Catch-Up

30-April

Please Complete this Pre-Work:
- Course Review #6 here.
- We will work:
  - Q&A based on reviewing final exam materials found here.

2-May

Pre-Work: none. Study for Final
We will work:
- Final Exam
Post-Work:
- Enroll in another math course.
- Do something fun that you didn't have time to do during the semester.
- Crack open a favorite beverage, like sarsaparilla.