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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.  ​

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15-February:

• No Pre-Work.

• We will take Exam I

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20-Febraury

• Please complete this Pre-Work:​

  • Pre-Work: Determinants Part 1 here. (FUTURE CHARLES, MOVE THIS BACK A DAY FOR SP25)

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• 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.

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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.​

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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.

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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.

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

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19-March

• Here is our In-Class Work:

  • Preparation for Exam II here.  

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21-March

• We will take Exam II.  Info here.

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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.

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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.

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2-April

• Please complete this Pre-Work:

  • Overview of Systems and Laplace (Cont.)^2 here.​

• We will work:

  • Solving Homogeneous Systems, Pt. 3 here.

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4-April

• Please complete this Pre-Work:

  • The Unit Step Function here.​ 

• We will work:

  • Laplace Transforms with Step Functions here.​

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9-April:

• There is no Pre-Work.  Instead, prepare for Exam III here.

• In-Class we will review for Exam III

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

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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.

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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.

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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.

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25-April

• Please complete this Pre-Work:​

  • Course Review #5 here.​

• We will work:

  • Applications of Systems of Equations here.​

  • Catch-Up

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30-April

• Please Complete this Pre-Work:​

  • Course Review #6 here.

  • We will work:

    • Q&A based on reviewing final exam materials found here.​

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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.

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