MAT 22B Summer Session I 2022



Syllabus


Lecture Notes

  1. Introduction to Differential Equations
  2. Integrating Factors and Separable Equations
  3. Modeling, Linear vs Nonlinear Equations, and Autonomous Differential Equations
  4. Autonomous Differential Equations, Population Dynamics, and Euler's method
  5. Elements of the Existence and Uniqueness Theorem
  6. First-Order Difference Equations and Introduction to Second-Order Differential Equations
  7. The Homogeneous Equation, Wronskian, and Complex Roots
  8. Repeated Roots and Reduction of Order
  9. Nonhomogeneous Equations, the Method of Undetermined Coefficients, Variation of Parameters, and Mechanical Vibrations
  10. The Laplace Transform and the Solution of the Initial Value Problem
  11. Inverting the Laplace Transform, Introduction to Systems of ODEs and Linear Algebra Review
  12. Basic Theory and Solving Systems of First-Order Linear Equations
  13. Complex eigenvalues and the Fundamental Matrix
  14. Repeated eigenvalues and nonhomogeneous systems
  15. Final Review Session

Lecture Recordings


Problem Sets


Application Assignments


Exams