Math 123 – Calculus III, Spring 2019

Instructor: Anatolii Grinshpan
Office hours: Tue and Thu 11-2, Korman 207.

Apr 1.  Introduction to the course. Differential equations and their solutions. Problems 1-14, page 486.

Apr 2.  Separation of variables. Problems 1-16, page 494.

Apr 3.  Examples and practice.  Example.

Apr 4.  Quiz 1 (8.1, 8.2).

Apr 8.   Euler’s numerical method. Problems 7, 9, 11 pages 502-503.

Apr 9.   Approximation of square roots. Integrating factors. Problems 1-10, page 509.

Apr 10. Examples and practice.

Apr 11. Quiz 2 (8.3, 8.4).

Apr 15. Sequences: definitions and examples. Problems 1-4, page 522.

Apr 16. Convergence of sequences. Problems 5-30, page 522.

Apr 17. Examples and practice.

Apr 18. Quiz 3 (9.1).

Apr 22. Monotone sequences. Problems 1-28, page 530.

Apr 23. Examples and practice.

Apr 24. Quiz 4 (9.2).

Apr 25. Midterm 1: 8.1-8.4, 9.1, 9.2.

Apr 29. Series: definitions and examples. Problems 1,2, page 537.

Apr 30. Geometric series. Problems 3-16, page 537.

May 1.  Telescoping series. Series with positive terms. Harmonic series.

May 2.  Quiz 5 (9.3). Growth of harmonic numbers.

May 6. Test for divergence. Comparison, limit comparison, and integral tests.

May 7. The p-series. Ratio and root tests. Problems 1-30, page 545.

May 8.  Examples and practice. More practice problems.

May 9.  Quiz 6 (9.4, 9.5).

May 14. Root and ratio tests. Problems 1-32, page 561.

May 15. Power series.

May 16. Quiz 7 (9.6).

May 20. Taylor polynomials. Problems 1-16, page 572.

May 21. Examples and practice.

May 22. Quiz 8 (9.7).

May 23. Midterm 2: 9.3-9.7.

May 28. Lagrange remainder estimate. Problems 31-36, page 572.

May 29. Taylor polynomials and series. Example.

May 30. Quiz 9 (9.7).

June 3.  Power series: interval of convergence. Problems 19-40, page 581.

June 4. Operations with power series.

June 5. Examples and practice. Problems 7, 13 (a), 15 (a), 24, 27, 29, 31, pages 600-601.

June 6. Quiz 10 (9.8, 9.10).