MAT 127
Calculus C - Fall 2005

Textbook:

Calculus - Concepts and Contexts (Single Variable), 2nd Edition, by James Stewart.
Available from the university bookstore or check prices at AddAll

MAT 127 is the final course of the three-semester calculus sequence MAT 125, 126 and 127. We will cover this semester differential equations, sequences and series, power series, as well as some of their applications to sciences, engineering, and beyond.

The course is heavily dependent on the material you studied in MAT 125 and MAT 126. You are therefore specifically encouraged to review the following material from your textbook:

Chapter	1	2	3	4	5	Appendices
Sections	5,6	2-8	1,2,4-7	2,3,5,9	3-7,10	A,B,C,F

Course description & Homework assignments:

New material will be presented every week during the lectures. You should read the corresponding section of the text before coming to class, according to the following week-by-week list of reading and homework assignments:

Week	Topic	Notes	Homework assignments
8/29-9/4	Modeling with differential equations		7.1: 2,5,6,14 web homework
9/5-9/11	Direction fields/Euler's method	No classes 9/5 (Labour day)	7.2: 9,11,18,22 web homework
9/12-9/18	Separable equations		7.3: 6,24,34,35 web homework
9/19-9/25	Exponential growth and decay		7.4: 1,2,9,10,14,18 web homework
9/26-10/2	The logistic equation		7.5: 3,6,7,9 web homework
10/3-10/9	Predator-prey systems	No classes 10/3-10/5 (Rosh Hashanah) Midterm I, Th 10/6, 8:30-10:00 pm	7.6: 1,3,4 web homework
10/10-10/16	Sequences	No classes 10/12 after 5pm, No classes 10/13 (Yom Kippur)	8.1:5,6,9,14,24,40 web homework
10/17-10/23	Sequences cont, Series		8.2:4,9,11,13,19,20,43 web homework
10/24-10/30	Convergence tests		8.3: 1,2,11,15,18 web homework
10/31-11/6	More convergence tests; Power series		8.4:3,8,13,23,24,29 web homework
11/7-11/13	Power series; Representing functions as power series	Midterm II, Tue 11/8, 8:30-10:00 pm	8.5:3,5,8, 8.6: 7,9,14 web homework
11/14-11/20	Taylor and Maclaurin series		8.7:10,11,17,20 web homework
11/21-11/27	Taylor and Maclaurin series cont, Binomial series	No classes 11/24-11/26 (Thanksgiving)	8.7:35,39,40 web homework
11/28-12/4	Power series and ODEs		8.8:4, 8.10:1,2,5 web homework
12/5-12/11	Power series and ODE cont, Review
12/12-12/18	Review	Classes end 12/13
12/21		Final Exam Wed, 11:00am-1:30 pm

Grading

20% Homework and web-based homework
20% Midterm 1
20% Midterm 2
40% Final Exam

Links

The following is a (growing) list of web sites and java applets devoted to topics relevant for your class:

• A java applet for experimenting with the Malthus/Verhulst models of population growth.
• A Slope Field Calculator java applet.
• A ODE Solution Verifier (java applet).
• A simple java demonstration of Euler's method.
• A java applet implementing Euler's method (it displays also the slope field)
• Java tutorial on Exponential Growth and Decay
• A Predator Prey (Lotka-Volterra) Model Java Simulation
• Another Lotka-Volterra Predator-Prey mini tutorial (java).
• Two Power series java applets. They plot the graph of a function resulting from adding up the first 11 terms of a power series (coefficients can be adjusted by means of scroll bars or just typed in - second applet only).