Lecture and Exam Schedule
Jan 4: Introduction to modeling with differential equations.
Jan 9: Separable and linear homogeneous equations.
Jan 11: Linear inhomogeneous equations. Phase lines.
Jan 16: MLK Holiday.
Jan 18: Modeling. Phase lines. Direction fields (using dfield).
Jan 23: Second order equations. Intro to harmonic motion.
Jan 25: Linear second order equations (inhomogeneous, homogeneous, and homogeneous with constant coefficients).
Jan 30: Harmonic motion revisited. Undetermined coefficients.
Feb 1: Undetermined coefficients.
Feb 6: Undetermined coefficients. Plotting in Matlab. Variation of parameters.
Feb 8: Variation of parameters.
Feb 13: Laplace Transforms
Feb 15: Laplace Transforms
Feb 20: Laplace Transforms
Feb 22: Review for Exam 1
Feb 27: Exam 1 - Cheat sheet that will be provided with exam
Feb 29: A crash course on linear algebra in two dimensions.
March 12: Linear planar systems.
March 14: Linear planar systems.
March 19: Linear planar systems: phase plane analysis and classification of solutions.
March 21: Linear planar systems. Intro to nonlinear planar systems.
March 26: Trace-determinant plane. Generic solution types. Linearization and classification of fixed points for nonlinear planar systems.
March 28: Global analysis of nonlinear planar systems: nullclines.
April 2: Global analysis of nonlinear planar systems: invariant sets and separatrices.
April 4: Limit cycles and the Poincare-Bendixson theorem. I will also give a list of topics to be covered on Exam 2.
April 9: Review for Exam 2. Mechanics, Conservative systems.
April 11: Exam 2
April 16: Brief review for final exam. Brief introduction to 3D systems and chaos.
April 18: Final Exam