Chapter 1: Models, differentiation, and integration basics.
Section 2.2: Solving separable equations, exponential equations, direct integration to solve initial value problems.
Section 2.3: Models of motion.
Section 2.4: (Pencast & .pdf) 1st Order Linear Equations: Integrating Factors & Variation of Parameters.
Section 2.5: Exact Differential Equations.
Section 2.7: Existence & Uniqueness.
Section 2.9: Autonomous Equations & Stability.
Section 3.1: Population Models. [.pdf]
Section 4.1: Second Order Equations.
Section 4.2: Second Order Equations & Systems & Harmonic Motion
Section 4.7: Forced Harmonic Motion
Section 7.1: Matrix Algebra & Systems of Linear Equations
Section 7.2: Linear Systems with Two or Three Variables
Section 7.3: Solving Systems of Equations
Section 7.4: Inhomogeneous & Homogeneous Solutions & Subspaces & Nullpaces
Exam 1 - Practice Exam and solutions!
Section 7.5: Bases and Spans
Section 7.6: Square Matrices
Section 7.6: Determinants
Section 8.1: Introduction to Systems
Sections 8.2 and 8.3: Systems: Geometry & Qualitative Analysis
Sections 8.4 and 8.5: Linear Systems
Sections 9.1 and 9.2: Solving Linear Systems
Sections 9.3 and 9.4: Phase Portraits
Sections 9.5: Homogenous Linear Systems
Sections 9.6: Generalized Eigen Vectors
Sections 9.7: Qualitative Analysis
Sections 6.1: Euler's Method
Sections 6.2: Runge-Kutta Methods
Sections 5.1-5.4: Laplace Transforms
Sections 5.5-5.7: More Laplace Transforms