MATH168 - Introduction to Mathematical Modeling (2024 Winter): an undergraduate course with the main objective to expose students to classical differential equation modeling, including derivation and nondimensionalization, stability analysis, bifurcation, and the applications of modeling results.   

Lecture notes:

Lecture 1: Introduction to modeling with 1st order linear differential equations

Lecture 2: Introduction to modeling with 1st order nonlinear differential equations 

Lecture 3: Opinion dynamics: an example of modeling with a 1st order differential equation 

Lecture 4: Modeling with bifurcations in 1st order differential equations 

Lecture 5: Insect outbreak - I: derivation, nondimensionalization, steady states, & stability

Lecture 6: Insect outbreak - II: bifurcation and hysteresis

Lecture 7: Introduction to harmonic oscillations

Lecture 8: Forced vibrations: beating, resonance, & forced response

Lecture 9: Simple 1D materials: elasticity, viscoelasticity, Maxwell & Kelvin-Voight materials

Lecture 10: Mathematical Pendulum: derivation, nondimensionalization, & phase portrait

Lecture 11: Modeling with systems of linear differential equations

Lecture 12: An example of modeling with linear systems: Love affair (by S. Strogatz)

Lecture 13: Modeling with systems of nonlinear differential equations

Lecture 14: Examples of modeling with systems of nonlinear differential equations: Chemical kinetics and Power of true believers

Lecture 15: Model of competing species - I: derivation, nondimensionalization, steady states, & stability 

Lecture 16: Model of competing species - II: stability of coexistence

Lecture 17: Lotka-Volterra predator-prey model