MAT 22B Summer Session II 2022



Syllabus


Lecture Notes

  1. Introduction to Differential Equations
  2. Classification of Differential Equations and the Method of Integrating Factors
  3. Separable Differential Equations and Modeling
  4. Linear vs Nonlinear Equations, Autonomous Differential Equations, and Population Dynamics
  5. Euler's Method and 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, and Variation of Parameters
  10. Mechanical and Electrical Vibrations
  11. The Laplace Transform and Solving the Initial Value Problem
  12. Inverting the Laplace Transform, Introduction to Systems of ODEs and Linear Algebra Review
  13. Basic Theory and Solving Systems of First-Order Linear Equations: Distinct Real and Complex Eigenvalues
  14. The Fundamental Matrix and the Matrix Exponential

Lecture Recordings


Problem Sets


Application Assignments


Exams