COURSE OUTLINE FOR MATH 1502

This page will change in the first few weeks. Please consult it often!

(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 and elementary Differential Equations
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 fundamental in virtually all of the sciences.

 
 

(2.) TEXTS:

The textbooks is Calculus , by Salas, Hille and Etgen (SH&E), tenth edition,  for the single variable calculus topics, section 9, 11, 12.
For the topics on linear algebra we use the book Linear Algebra and Its Applications by Lay (L), fourth edition.

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 elementary differential equations.  Sections 12.7-12.8  and  9.1-9.3 in Salas, Hille and Etgen (6 lectures)

Block 3: Introduction to Matrices, Row Reduction and Solution of Linear Systems.   (9 lectures)

Block 4:  Inverses, Linear Independence, Kernel and Range.   (10 lectures)

Block 5: Eigenvectors, Eigenvalues and Geometric Topics.   (10 lectures)

(3.) TEST DATES:

Block 1:  Tuesday September 11; . (Lecturing on this material finishes on Wednesday, September 5). Review: Monday September 10, 6-8 pm in Room Skiles 202.

Block 2:  Tuesday October 2; . (Lecturing on this material finishes on Wednesday, September 26 ). Review: Friday September 28, 6-8 pm in Room Skiles 202.

Block 3:  . Tuesday, October 23 (Lecturing on this material finishes on Wednesday Oct 17 ). Review: Monday October 22, 6-8 pm in Room Skiles 202.

Block 4:  . Tuesday, November 13  (Lecturing on this material finishes on Wednesday, November 7). Review: Monday November 12, 6-8 pm in Room Skiles 202.

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 20, 22, 24.

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 27, 29, 31.

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 5, 7. (September 3 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 10, 12, 14. Test 1 on September 11.

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 17, 19, 21.

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 24, 26, 28. (Progress Report Grades due on September 28, Noon).   

Reading: 9.3 in SH&E,  and Sections 1.1 and 1.2 in Lay.  Homework problems: 1,3, 19, 20 on page 465 in SH&E, 7, 8, 12, 15, 25 on p 10/11 in Lay, 2, 7, 11,15.

Week 7: October 1, 3, 5. Test 2 on October 2.

Reading: Sections 1.3 - 1.5 in Lay.  Homework problems: 1-4, 21, 22 on page 32 in Lay, 1-4, 13-15 on page 40 in Lay,  1, 2, 5, 6, 21,22 on page 47 in Lay.

Week 8: October 8, 10, 12. (October 12, last day to drop an individual class with grade `W' by 4:00 pm ET)

Reading: Sections 1.7 - 1.9, 2.1  in  Lay.  Homework problems: 1-4, 21, 23, 24, on pages 60/61 in Lay, 19, 20, 22,  on pages 68/69 in Lay, 1, 2, 10, 12 on page 78 in Lay. 1, 5, 17, 18  on pages 100/101 in Lay.

Week 9: October 17, 19. (October 13 - 16 Fall recess.)

Reading: Sections 2.2-2.3 in Lay.  Homework problems: 1, 2, 7, 21 on pages 109/110 in Lay, 1, 3, 5, 10, 20 on pages 114/115 in Lay.

Week 10: October 22, 24, 26. (October 28 last day to withdraw from school with `W' in all courses). Test 3 on October 23.

Reading: Sections 2.8, 2.9, 3.1 in Lay. Homework problems: 5, 6,7, 11, 12 on pp151/152 in Lay, 1, 2, 19, 20, 21 on pp 158/159 in Lay, 1, 2, 31, 32, 37 on pp 167/168 in Lay.

Week 11: October 29, 31, November 2.

Reading: Sections 3.2, 3.3, 5.1 in Lay. Homework problems: 1-3, 24, 25, 43 on pp 175/176 in Lay, 19-21, 23,24 on p. 184  in Lay, 1-3, 21-23 on pp 271/272 in Lay.

Week 12: November 5, 7, 9.

Reading:  Sections 5.2, 5.3 and 5.5 in Lay. Homework problems: 10-12, 15 and 16 on p. 280 in Lay, 3, 4, 9-12 on pp. 286/287 in Lay, 1-4 on p 300 in Lay.

Week 13: November 12, 14, 16. Test 4 on November 13.

Reading: Sections   6.1-6.3 in Lay. Homework problems: 14, 15-18, 25 on pp. 336/337 in Lay, 12, 16, 17, 18 on p 345 in Lay, 7, 11, 12, 13 on p 352 in Lay.

Week 14: November 19, 21. (November 22-23  Thanksgiving, official school holiday)

Reading: Sections 6.4, 6.5 in Lay. Homework problems: 3, 9, 10, 15, 16 on pp 358/359 in Lay, 1, 2, 5, 6 on p 366 in Lay.

Week 15: November 26, 28, 30.

Reading:  Sections  6.5, 7.1, 7.2 in Lay. Homework problems: 8, 10, 11, 17, 18, 20,   on page 399 in Lay, 7, 8, 9, 13 on p.407 in Lay.

Week 16: December 3, 5, 7.  (December 7, last day of classes).

Reading: Sections 7.4 and review. Homework: 2, 3, 8, 11, 23 on pp 423/424 in Lay.

Final Exam, Wednesday December 12 (Wed) 2012 8:00am - 10:50am in Room 16 CoC.