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Notes By Date

21-January:  Here are your In-Class Notes covering the Intro to ODEs.  (Charles will bring printed off copies of the Pre-Work and In-Class Notes for the first two weeks of class.)

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23-January:

  • Please complete the following Pre-Work Assignments and upload them to Gradescope here.  Use this video as a guide. (Enrollment KEY: 6ZRDWV)

    • Pre-Work (Review): Integration by Parts here.​

    • Pre-Work Solving Separable ODEs Pt. 1 here.

  • Here are your In-Class Notes​

    • Some Quick Examples here.

    • Numerical Solutions: Euler's Method here.

    • Solving Separable ODEs Pt. 2 here.​

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28-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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30-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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4-February:

  • 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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6-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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11-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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13-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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18-Febrary:

  • Please complete Pre-Work:

    • Pre-Work: Determinants Part 1 here.

    • Complete at least one practice exam here.

  • Here are the In-Class Notes:​

    • Determinants Part 2 here.

    • Exam I Review here.  ​

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20-February:

  • No Pre-Work.

  • We will take Exam I

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25-Febraury

  • Please complete this Pre-Work:​

    • Intro to Vector Spaces here.​

    • Cramer's Rule here. 

  • Here are the In-Class Notes:​

    • Linear Independence here.

    • Further Applications of ODEs here.

 

27-February

  • Please complete this Pre-Work:  

    • The Characteristic Equation Part 1 here.

    • Basis and Dimension Part 1 here. ​

  • Here are the In-Class Notes:

    • The Characteristic Equation Part 2 here.​

    • Examples of Vector Spaces and Subspaces here.

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4-March

  • 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.​

    • Basis and Dimension Part 2 here.

6-March

  • Please complete this Pre-Work:

    • Method of Undetermined Coefficients Pt. 1​ here.

  • Here are the In-Class Notes

    • Method of Undetermined Coefficients Pt. 2 here.​

    • The Harmonic Oscillator Pt. 1 here.

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​11-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)

13-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 18th nor March 20th

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25-March

  • Here is our In-Class Work:

    • Preparation for Exam II here.  

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27-March

  • We will take Exam II.  Info here.

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​​​1-April

  • 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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3-April

  • 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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8-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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10-April

  • Please complete this Pre-Work:

    • The Unit Step Function here.​ 

  • We will work:

    • Laplace Transforms with Step Functions here.​

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​15-April:

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

  • In-Class we will review for Exam III

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

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22-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. ​

    • Matrix Diagonalization here.

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24-April

  • Please complete this Pre-Work:

    • Course Review #2 here.​

  • We will work:

    • Laplace Transforms of Discontinuous Functions here. ​

    • Intro to non-linear systems Pt. 1 here.

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29-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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1-May

  • Please complete this Pre-Work:​

    • Course Review #5 here.​

  • We will work:

    • Applications of Systems of Equations here.​

    • Catch-Up

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8-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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10-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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