Math 123 - Calculus III, Winter 2010

Instructor: Anatolii Grinshpan
Office hours:  MTW 11-12, Korman 247, or by appointment, Korman 253.

Jan 4. Introduction to the course.

Jan 5. First-order linear equation with constant coefficients. Integrating factors.

Reading: 9.1. Problems: 1, 2, 6-13, 20, 25, 27, 28 (page 593).

Jan 6. Integrating factors. Separation of variables.

Jan 7. Quiz 1 (9.1). Mixing problems.

Jan 11. Mixing.

Problems: 43-46 (page 594).

Jan 12. Population growth model: exponential and logistic.

Reading: 9.3. Problems: 5-19 odds (page 608).

Jan 13. Solution of the logistic equation.

Problems: 33, 34, 40.

Jan 14. Quiz 2 (mixing, 9.3).

Jan 19. Second-order linear equations (homogeneous and not).

Particular solution and general solution.

Jan 20. Second-order linear homogeneous equations with constant coefficients.

Distinct characteristic roots, purely imaginary characteristic roots.

Jan 21. Second-order linear homogeneous equations with constant coefficients.

Complex characteristic roots. Repeated characteristic roots.

Reading: 9.4. Problems: 1-25 (odds),  31-33 (pages 619-20).

Jan 25. Quiz 3 (9.4).

Jan 27. Convergence of sequences.

Problems: 1-29 (odds), 38 (pages 633-4).

Jan 28. Quiz 4 (10.1). Exponential limits.

Feb 1. Monotone sequences.

Reading:10.2. Problems: 1-25 (odds),  28, 30.

Feb 2. Review.

Feb 3. Midterm 1 (9.1, 9.3, 9.4, 10.1, 10.2). (answers)

Feb 4. Infinite series.

Feb 8. Harmonic series. Oresme’s proof of divergence (ca. 1350).

Feb 9. Growth of harmonic numbers (integral estimates). Divergence test.

Feb 10. No class. Blizzard.

Feb 11. No class.

Feb 15. Geometric series.

Problems: 1-19 (pages 649-50).

Feb 16. Telescoping sums. P-series.

Additional notes: series with positive terms.

Feb 17. P-series.

Feb 18. Quiz 5 (10.3). Integral test and comparison test.

Reading: 10.4. Problems: 1-23 (odds), 32 (pages 657-8).

Feb 22. Limit comparison.

Reading: 10.5. Problems 1-10 (page 664).

Feb 23. Root test and ratio test.

Problems: 11-20, 22, 25, 26, 28, 30, 34, 39, 43, 45 (pages 664-5).

Feb 24. Testing series for convergence. Examples.

Feb 25. Quiz 6 (10.4, 10.5). Absolute/conditional convergence.

Mar 1.  Alternating series.

Problems 1-29 (odds), 35, 36 (pages 673-4).

Mar 2.  Review. Midterm 2 (10.1-10.6). (answers)

Mar 3. Power series: center, coefficients, radius of convergence.

Mar 4. Taylor series and Taylor polynomials. Coefficients of Taylor polynomials.

Problems: 1-25 (odds, page 684).

Mar 8. Finding the radius and the interval of convergence.

Problems: 19-49 (odds, page 693).

Mar 9. Taylor polynomials (an applet). Convergence to the function.

Reading: 10.7, 10.9. Problems: Examples 1, 2, 3 (10.9).

Mar 10. Derivatives and integrals of power series.

Reading: 10.10. Problems: 1, 2, 5, 6, 21-25, 27, 34 (pages 712-3).

Mar 11. Applications of power series.

Mar 15. Review. Extra office hour: 5-6 (Korman 253).

Mar 16. Final Exam: 3:30-5:30 P.M., Lebow 134. (answers)