Math 262 – Differential Equations, Spring 2011

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Instructor: Anatolii Grinshpan
Office hours:  MT 6-7, Korman 253, or by appointment.

Syllabus   Errata   Academic calendar    Math resource center   MIT video lectures

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.

 

Apr 5.  Homework discussion. Lab: MATLAB tutorial, numerical derivative.

            Homework 2: due April 12.

 

Apr 11. A formula for integrating factors. Existence and uniqueness. Isoclines. Phase line.

 

Apr 12. Lab: isoclines and slope fields. John Polking’s dfield: MATLAB, JAVA.

             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.

              Example. Homework 8: due May 23.

 

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.

             Purely imaginary eigenvalues. Phase portrait generator. John Polking’s pplane: MATLAB, JAVA.

 

June 7. Final exam 7-9 PM, Korman 247.