Lecture Notes Fall 2024

• Lecture 1 August 29, 2024 Intro: classification of DFQ and separation of variables
• Lecture September 6, 2024 Integrating Factor. Beginning of Modeling.

• Lecture September 10, 2024 Modeling: population growth, logistic equation, mixing and Newton's law of cooling

• Lecture September 13, 2024 Modelling: Newton's law of cooling examples, nonlinear cooling, Second Newton Law

• Lecture September 17, 2024 Modeling, Phase Plane Technique, Second Order ODE

• Lecture September 20, 2024 General Second order ODE. Linear ODE. Constant Coefficients.

• Lecture September 24, 2024 Double and complex roots in second order ODE with constant coefficients

• Lecture September 27, 2024 Midterm Review. Linear second order ODE with constant coefficients.

• Lecture October 1, 2024 Midterm

• Lecture October 4, 2024 Review of linear homogeneos second order with constant ceofficients. Complex roots.

• Lecture October 8, 2024 Homogeneous, Constant coefficients, linear second order. Inhomogeneous second order and Method of constant coefficients

• Lecture October 11, 2024 Method of undetermined Coefficients

• Lecture October 15, 2024 Variation of a parameter method to find a particular solution to the linear second order non-homogeneous ODE

• Lecture October 18, 2024 Harmonic Oscillator

• Lecture October 22, 2024 Harmonic Oscillator - forced and damped

• Lecture October 25, 2024 Harmonic Oscillator and the Euler Equation

• Lecture October 29, 2024 Euler Equations and Midterm Review

• Lecture November 1, 2024 Linear System of Equations $\dot{\bf {x}} = A {\bf {x}}.$ Eigenvalues and Eigenvectors

• Lecture November 5, 2024 Linear system of Equations (cont). Complex eigenvalues and deffective matrices.

• Lecture November 8, 2024 ?

• Lecture November 12, 2024 Solution of lienar systems $\dot x(t) = A x(t).$

• Lecture November 15, 2024 Phase Plane Technique

• Lecture November 19, 2024 Phase Plane Technique for Linear Systems

• Lecture November 20 (make up), 2024 Nonlinear system of equations. Linearization.

• Lecture November 22, 2024 Nonlinear System Example

• Lecture November 26, 2024 Linear and Nonlinear Systems Midterm Review

• Lecture December 3, 2024 ?

• Lecture December 6, 2024 no lecture

• Lecture December 10, 2024 Review