All Topic Notes in One File (PDF)
Linear DE’s
Topic 1: Introduction to DE’s, Modeling, Separable Equations (PDF)
Topic 2: Linear Systems: Input-Response Models (PDF)
Topic 3: Input-Response Models (cont.) (PDF)
Topic 4: Complex Numbers and Exponentials (PDF)
Topic 5: Linear DE’s, CC Homogeneous Case (PDF)
Topic 6: Operators, Inhomogeneous DE’s, Exponential Input Theorem (PDF)
Topic 7: Inhomogeneous DE’s: UC Methods, Theory (PDF)
Topic 8: Applications, Stability, Variation of Parameters (PDF)
Topic 9: Applications: Frequency Response (PDF)
Complexification vs. Inverse Euler’s Formula (PDF) (explanatory note)
Complex Impedance (PDF) (for enrichment)
First Order DE’s
Topic 10: Direction Fields, Integral Curves, Existence of Solutions (PDF)
Topic 11: Numerical Methods for First Order ODE’s (PDF)
Topic 12: Autonomous DE’s; Introduction to Stability (PDF)
Proof of Existence and Uniqueness (PDF) (for enrichment)
Substitution Methods (PDF) (for enrichment)
Power Series Techniques
Brief Note on Power Series (PDF) (for enrichment)
Linear Algebra and Linear Systems
Topic 13: Linearity, Vector Spaces, Matrix Multiplication, Systems of DE’s (PDF)
Topic 15: Transpose, Inverse, Determinant, Inner Product (PDF)
Topic 16: Eigenvalues, Diagonalization, Decoupling (PDF)
Topic 17: Linear Systems: Solution by Matrix Methods (PDF)
Symmetric Matrices (PDF) (for enrichment)
Topic 18: Matrix Exponential; Exponential and Sinusoidal Input (PDF) (for enrichment)
Topic 19: Fundamental Matrix, Variation of Param., Euler’s Method (PDF) (for enrichment)
Note: Topics 18 and 19 are not included in this course. The notes are for the enrichment of anyone who is interested.
Step and Delta Functions
Topic 20: Step and Delta Functions (PDF)
Fourier Series
Topic 21: Fourier Series (basics) (PDF)
Topic 22: Fourier Series (continuation) (PDF)
Topic 23: Sine and Cosine Series; Calculation Tricks (PDF)
Topic 24: More Calculation Tricks; Linear ODE’s with Periodic Input (PDF)
Topic 25: PDE’s, Separation of Variables (PDF)
Topic 26: Continuation; Applications to Sound (PDF)
Analysis of Gibbs’ Phenomenon (PDF) (for enrichment)
Completeness of Fourier Series (PDF) (for enrichment)
Using Complex Exponentials for Fourier Series (PDF) (for enrichment)
Heat Equation: Discrete and Continuous (PDF) (for enrichment)
Qualitative Description of Linear and Nonlinear Systems of Differential Equations
Topic 27: Qualitative Behavior of Linear Systems: Phase-Plane (PDF)
Topic 28: Qualitative Behavior of Non-Linear Systems, Linearization (PDF)
Topic 29: Structural Stability (PDF)
Topic 30: Applications to Population Biology: Volterra’s Principle (PDF)
Topic 31: Application to Physics: the Pendulum (PDF) (for enrichment)
