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Differential Equations
Differential Equations
43 lessons across 14 topics
1. Introduction to Differential Equations
1
Basic Terminology
2
Direction Fields And Solution Curves
3
Initial Value Problems
2. First-Order Equations I
4
Growth And Decay
5
Logistic Models
6
Separable Equations
3. First-Order Equations II
7
Integrating Factors
8
Linear First-order Equations
9
Mixing Problems
4. Exact Equations and Substitutions
10
Exact Equations
11
Existence And Uniqueness Overview
12
Homogeneous Substitutions
5. Second-Order Linear Equations
13
Characteristic Equations
14
Homogeneous Equations
15
Repeated And Complex Roots
6. Nonhomogeneous Linear Equations
16
Mechanical Applications
17
Undetermined Coefficients
18
Variation Of Parameters
7. Applications of Second-Order Equations
19
Damping
20
Forced Oscillations
21
Resonance
22
Spring-mass Systems
8. Midterm 1 and Laplace Transforms I
23
Definition And Properties Of Laplace Transforms
24
Key Themes In Midterm 1 And Laplace Transforms I
25
Midterm 1
9. Laplace Transforms II
26
Impulse Forcing
27
Solving Initial Value Problems
28
Step Functions
10. Systems of Differential Equations
29
Eigenvalues And Eigenvectors
30
Linear Systems
31
Matrix Form
11. Phase Plane Analysis
32
Equilibrium Points
33
Linearization Intuition
34
Stability
12. Numerical and Qualitative Methods
35
Error Interpretation
36
Euler’s Method
37
Qualitative Behavior Without Closed Forms
13. Advanced Modeling Topics
38
Coupled Systems
39
Population Interactions
40
Predator-prey Models
14. Review and Synthesis
41
Connections Among Analytic, Qualitative, And Applied Methods
42
Final Review
43
Key Themes In Review And Synthesis
