COURSE CALENDAR 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:
 
 
  1. Taylor Approximation
  2. Infinite Series and Power Series
  3. Intrioductory Topics in Ordinary Differential Equation
  4. 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 arer Calculus,  by Salas, Hille and Etgen, Ninth Edition, for the single variable topics. This part of the course covers selected parts of Chapters 8 and 10, and all of 11 with some additional material covered on the web notes. In the remainder of the course we will work with the text Linear Algebra from the Beginning by Carlen and Carvalho. We will cover the first five chapters of the book.  (Detailed solutions for the odd numbered problems in Linear Algebra from the Beginning are available online.

 

The material consists of five blocks:

Block 1: Taylor Approximation and Infinite Series. Sections 10.5-10.7,  and 11.5-11.6  in Salas, Hille and Etgen (9 lectures)

Block 2:  Power Series and  and elementary differential equations.  Sections 11.1-11.4, 11.7-11.8  and  8.8-8.9 in Salas, Hille and Etgen (6 lectures)

Block 3: Introduction to Matrices, Row Reduction and Solution of Linear Systems.   Through Section 2.3 in Linear Algebra (10 lectures)  

Block 4: Linear Independence, Kernel  Range and Least Squares.   Section 2.4 through the end of Chapter 3 in Linear Algebra (10 lectures)

Block 5: Determinants, Eigenvectors, Eigenvalues and Geometric Topics.  Chapters 4 and 5 in Linear Algebra (10 lectures)

(3.) TEST DATES: In each case, there will be at least one recitation section (for review) between the time I  finish lecturing on the material and when you take the test.

Block 1:  Wednesday, Jan 24

Block 2:  Monday, Feb 12

Block 3:  Wednesday, Mar 14

Block 4:  Wednesday, Apr 11

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:

First Meeting: Monday, Aug 22

week 1: Jan 9, 11 

Reading: 11.5-11.6 in Salas Hille and Etgen

week 2: Jan 16, 18

Reading:  10.5-10.7 in Salas Hille and Etgen. Also, here are some  notes on Taylor polynomials and limits, and here is a Maple worksheet on Taylor approximation illustating some simple commands for computing and graphing Taylor approximations.  You will need the Maple program (which is not free) installed on the machine you are using to view the worksheet. If you do not have Maple on your own computer, you can use comuters in th various campus clusters. 

week 3: Jan 23, 25

Reading: 11.1--11.4   in Salas Hille and Etgen.  


Here is a practice test for Test One, which is
this Wednesday in recitation.  I will go over this practie test in the review session Tuesday evening.  The actual test will be the same length, and same format, but with different problems, of course.

week 4: Jan 30, Feb 1

Reading: 11.7  and 11.8  in Salas Hille and Etgen    

Week 5: Feb 6, 8

Reading: 8.8-8.9 in Salas Hille and Etgen.  Here is a Maple Worksheet on graphing the solutions to differential equations.


Here is a practice test for Test Two, which is Monday in the 12th in recitation.  I will go over this practice test in the review session Sundday evening. This review session starts at 6 and is in L1.  The actual test will be the same length, and same format, but with different problems, of course.

Week 6:  Feb 13, 15 (Progress grades turned in Feb 16)

Reading:  Sects. 1.1-1.3 in  Linear Algebra

Week 7: Feb 20, 22

Reading: Sects. 1.4-1.5 in  Linear Algebra  

Week 8: Feb 27, Mar 1 (March 2 is drop day for individual courses)

Reading: Sects. 2.1-2.3  in  Linear Algebra

Week 9: Mar 6, 8 

Reading: Sects. 2.4-2.5 in  Linear Algebra. Also,
 see the Maple worksheet on row reduction and the LU decomposition.

Week 10: Mar 13, 15

Reading: Sects.   3.1 - 3.3  in  Linear Algebra  Here is a practice test for the test this week. I will go over this in the review session a 7:30 Tuesday evening in IC 130.

Week 11: Mar 27, 29 (Mar 19-23 is Spring Break)

Here is a Maple worksheet to help with the current graded homework project: sample Maple worksheet with comands for using Maple to work with the normal equations.

Reading: Sects.  3.4-3.6 in  Linear Algebra

Week 12: Apr 3, 5

Reading: Sects.  3.7, 4.1- 4.2 in  Linear Algebra

Week 13: Apr 10, 12

Reading: Sects.    4.3 - 4.4 in  Linear Algebra
 Here is a practice test for the test this week. I will go over this in the review session a 7:30 Tuesday evening in the usual lecture hall.


Week 14: Apr 17, 19

Reading: Sects.  5.1 - 5.3 in  Linear Algebra

Week 15:  Apr 24, 26

Reading: Sects. 5.4 - 5.6 in  Linear Algebra   Here is a sample Maple worksheet with comands for using Maple to work with eigenvectors.

Here is an interesting not very technical article on eigenvectors, and how Google's search engine works. Thanks to  David Wu for bringing this link to my attention.

Exam Week:  The final exam is scheduled for  May 1, 11:30 to 2:20.  Here is a practice Final Exam.

I will  hold a review session  Monday evening in the lecture hall, 6 to 7.