COURSE OUTLINE FOR MATH 1502

(1.) COURSE OBJECTIVES AND TOPICS OF STUDY:

This course is aimed at developing proficiency, with an understanding of the ideas behind the methods, in the following specific subjects:

 

Taylor Approximation
Infinite Series and Power Series
Numerical Integration
Linear Algebra, the theory of linear functions and Equations in several variables
The first three topics complete the coverage of single variable calculus, and the fourth, on which we shall spend roughly two thirds of the course is the basis of the calculus of functions of several variables, as well as a fundamental subject in its own right.

 
 

(2.) TEXTS:

The textbooks is Calculus , by Salas, Hille and Etgen (SH&E), Tenth edition,  for the single variable calculus topics, section 8, 10,11.
For the topics on linear algebra we use the book Linear Algebra from the beginning by Carlen, Carvalho (CC), Chapters 1-5.

The readings can be broken into five blocks:

Block 1: Taylor Approximation and Infinite Series. Sections 12.1 - 12.7,  and 11.1-11.6  in Salas, Hille and Etgen (10 lectures)

Block 2:  Power Series and Numerical Integration, and elementary differential equations.  Sections 12.7-12.8  and  8.7, 9.1-9.3 in Salas, Hille and Etgen (6 lectures)

Block 3: Introduction to Matrices, Row Reduction and Solution of Linear Systems.  Sections 1.1-1.6 and 2.1-2.3 in Carlen-Carvalho,   (9 lectures)

Block 4:  Inverses, Linear Independence, Kernel and Range.  2.4, 2.5, 3.1-3.8 (10 lectures)

Block 5: Eigenvectors, Eigenvalues and Geometric Topics.  4.1-4.3, 5.1-5.6 (10 lectures)

(3.) TEST DATES:

Block 1:  Tuesday September 14; . (Lecturing on this material finishes on Wednesday, September 8). Review: Monday September 13, 6-8 pm.

Block 2:  Tuesday October 5; . (Lecturing on this material finishes on Wednesday, September 29 ). Review: Monday October 4, 6-8 pm.

Block 3:  . Tuesday, October 26 (Lecturing on this material finishes on Wednesday Oct 20 ). Review: Monday October 25, 6-8 pm.

Block 4:  . Tuesday, November 16  (Lecturing on this material finishes on Wednesday, November 10 ). Review: Monday November 15, 6-8 pm.

Block 5:  This material will be tested only on the final exam -- which does not mean that the final exam will be only on this material. The final exam will be comprehensive.


(4.) COURSE CALENDAR:

Week 1: August 23, 25, 27.

Reading: Section 12.1, 12.6, 12.7 in SH&E. Homework problems: 1, 2, 8, 10, 13, 17, 20, 29, 28, 43, 45, 46 on p.611/612 in SH&E.


Week 2: August 30, September 1, 3.

Reading: Section 11.5 -11.7 in SH&E. Homework problems: 2, 8, 11, 43 on page 558 in SH&E,  8, 9, 26, 31, 53 on page 563/564
                                                                                                 in SH&E,  17, 38, 55, 56 on page 571/572  in SH&E.

Week 3: September 8, 10. (September 6 is official school holiday)

Reading: 12.2 -12.3 in SH&E. Homework problems: 7, 10, 21, 29, on page 584/585 in SH&E, 12, 16, 25, 40, on page 592/593 in
                                                                                     SH&E.

Week 4: September 13, 15, 17. Test 1 on September 14.

Reading: 12.4, 12.5, 12.8 in SH&E,  Homework Problems: 9, 27, 32, 33 on page 596/597 in SH&E, 9,11, 33, 41, on page 601 of SH&E, 3, 30, 31, 44, on page 622/623 of SH&E.

Week 5: September 20, 22, 24.

Reading: 12.9, 9.1, 9.2 in SH&E, 1,3, 8, 39, on page 632/633 of SH&E, 3, 4, 8, 18, 37 on page 449/450 in SH&E, 1-4 and 21 on page 457 of SH&E.

Week 6: September 27, 29, October 1. (Progress Report Grades due on October 1).

Reading: 9.3 in SH&E, Chapter 1.1, 1.2 in CC. Homework problems: 1,3, 19, 20 on page 465 in SH&E. 1.1, 1.3, 1.5, 1.8 on page 13/14 in CC,
2.3, 2.8, 2.10, 2.11 on page 29/30 in CC.

Week 7: October 4, 6, 8. Test 2 on October 5.

Reading:  Chapter 1.3-1.5 in CC. Homework problems: 3.1, 3.3, 3.7, 3.12 on page 45/46 in CC., 4.1, 4.5, 4.14, 4.17 on pages 58-61 in CC., 5.3, 5.11, 5.22, 5.23 on pages 70-73 in CC.

Week 8: October 11, 13, 15. (October 15 last day to drop an individual class with grade `W' by 4:00 pm ET)

Reading: 1.6, 2.1, 2.2 in CC. Homework problems: 6.1, 6.3, 6.6 on pages 83/84 in CC., 1.1, 1.5, 1.10, 1.21, 1.25 on pages 95-98 in CC, 2.1, 2.2 on pages 104/105 in CC.

Week 9: October 20, 22. (October 16 - 19 Fall recess.)

Reading: 2.3, 2.4 in CC. Homework problems: 3.3, 3.7, 3.9, 3.11, 3.14, on pages 116-118 in CC.,
4.1, 4.4, 4.12, 4.14, 4.10. on pages 135-137 in CC.

Week 10: October 25, 27, 29. (October 31 last day to withdraw from school with `W' in all courses). Test 3 on October 26.

Reading: 2.5, 3.1, 3.2 in CC. Homework problems: 5.1, 5.5, 5.7, 5.14, on pages 151-153 in CC., 1.1, 1.3, 1.7, 1.12,  on page 167 in CC.,
2.1, 2.5, 2.6, 2.7 on pages 184/185 in CC.

Week 11: November 1, 3, 5. 

Reading: 3.3-3.5 in CC. Homework problems: 3.1, 3.9, 3.12, 3.15 on pages 195-197 in CC, 4.3, 4.7, 4.12,  4.19, on pages 206-208 in CC, 5.4, 5.6, 5.7 on page 218 in CC.

Week 12: November 8, 10, 12.

Reading:  3.6- 3.8in CC. Homework problems: 6.1, 6.3, 6.5 on pages 230/231 in CC,  7.1, 7.2, 7.5, 7.6, on pages 242/243 in CC, 8.1, 8.2, 8.7 on page 254 in CC.

Week 13: November 15, 17, 19. Test 4 on November 16.

Reading: 4.1 - 4.3 in CC. Homework problems: 1.1, 1.3, 1.5, on page 271 in CC,  2.1-2.3 on page 283 in CC, 3.1, 3.9, 3.13 on pages 293-295 in CC.

Week 14: November 22, 24. (November 25-26 Thanksgiving, official school holiday)

Reading: 5.1- 5.2 in CC. Homework problems: 1.1, 1.3, 1.6, 1.8, on page 321-323 in CC, 2.1, 2.4, 2.6, 2.7 on page329/330 in CC.

Week 15: November 29,  December 1, 3.

Reading:   5.3-5.5 in CC. Homework problems: 3.1, 3.3, 3.4, 3.9 on page 342/343 in CC 4.1, 4.2, 4.7, 4.8 on page 353/354 in CC, 5.1, 5.3, 5.4, 5.6 on page 371/372 in CC.

Week 16: December 6, 8, 10.  (December 10, last day of classes).

Reading: 5..6 in CC and review. Homework problems: 6.1, 6.2,  6.4, 6.5 on pages 383-385 in CC.

Final exams: December 13-17.