Instructor: Anatolii Grinshpan
Office hours: MT 6-7, Korman 253, or by appointment.
Mar 28. Introduction to the course. First order equations. Slope fields.
Mar 29. Examples of integrating factors. Separation of variables. Radiocarbon dating.
Homework 1: due April 5.
Apr 4. More examples: exponential model, separation, integrating factors, domain of the solution, change of variables.
Homework 2: due April 12.
Apr 11. A formula for integrating factors. Existence and uniqueness. Isoclines. Phase line.
Homework 3: due April 19.
Apr 18. First-order linear equations: one-dimensional space of solutions.
Population modeling. Mixture problems.
Apr 19. Euler’s method.
Homework 4: due April 25.
Apr 25. Discussion.
Apr 26. Midterm 1 (lectures of March 28 – April 19).
Homework 5: none.
May 2. Second-order differential equations. Differential operators.
Linear homogeneous equations: two-dimensional space of solutions. Reduction of order.
May 3. Case of constant coefficients: characteristic roots (3 scenarios).
Linear independence of functions.
Homework 6: due May 10.
May 9. Fundamental pairs. Wronskian determinant. Abel’s theorem.
May 10. Nonreal characteristic roots. Simple harmonic oscillator.
Homework 7: due May 17.
May 16. Harmonic oscillator. The method of undetermined coefficients. Resonance.
May 17. The general solution of a nonhomogeneous equation. Superposition of forcing terms.
May 23. Discussion.
May 24. Midterm 2 (lectures of May 2 – May 17).
Homework 9: none.
May 30. Memorial day.
May 31. Systems of linear equations with constant coefficients. Phase portrait. Eigenvalues and eigenvectors.
Homework 10: due June 6 .
June 6. Systems of linear equations: classification of phase portraits. Examples.
June 7. Final exam 7-9 PM, Korman 247.