David Aristoff
Associate Professor
Department of Mathematics
Colorado State University
Course outline (rough schedule, excluding Spring Break week)
Jan 16 -- Feb 22:
Week 1 Chapter 1: modeling (falling object, SIR system, etc.), direction fields, solutions and classification of ODEs
Weeks 2-3 Chapter 2, sections 1-3,5,6: 1st order linear ODEs and integrating factors,
separable ODEs; exact ODEs and integrating factors, modeling with first order ODEs (population dynamics, etc.), plotting direction fields (sketching and/or Matlab)
Weeks 4-5 Chapter 3, sections 1-8:
solutions of 2nd linear homogeneous ODEs w/ constant
coefficients, solutions of 2nd linear non homogeneous ODsE w/ constant coefficients,
method of undetermined coefficients, mechanical vibrations (undamped/damped free vibrations),
forced periodic vibrations (beat, resonance),
Wronskians, linear combinations and superposition, variation of parameters
Week 6 Chapter 4, sections 2-3: higher order linear ODEs, review, midterm 1
Feb 23 -- Apr 4:
Week 7 Chapter 7: linear algebra, eigenvalues, eigenvectors
Week 8 Chapter 7, section 5,6: linear algebra, systems of first order ODEs
Spring Break
Week 9 Chapter 7, section 8: systems of first order ODEs
Week 10 Chapter 7, section 1,4,7: systems of first order ODEs
Week 11 Chapter 7, section 9: systems of first order ODEs, review, midterm 2
Apr 5 -- May 3:
Weeks 12-13 Chapter 6, sections 1-2: Laplace transforms: review of improper integrals, definition & examples of Laplace transforms, properties of Laplace transform, inverse Laplace transforms, solving 1st and second order ODEs with Laplace transforms
Weeks 14-15 Chapter 9, sections 1-3: planar linear systems and classification, autonomous systems and stability, locally linear systems, review for final exam