Calculus with Applications (Math 11B)
Spring 1999, UCSC

Lecture Sections
Earth&Marine B206 M W F 12:30-1:40pm 11S: M W 8-9:50am Applied Sci 268.
12S: M W 4-5:50pm Applied Sci 268.
13S: M W 6-7:50pm Applied Sci 295.
14S: T TH 8-9:50am Applied Sci 295.
15S: T TH 4-5:50pm Applied Sci 295.
16S: M W 2-3:50pm Applied Sci 295.

Instructor
Professor Mohammad Ghomi Check instructor's web site periodically for revised versions of this syllabus, and to obtain copies of old tests and quizzes.

Teaching Assistants
Jamey Bass, Astatke Gizaw, and Craig Gordon Each TA will conduct two sections where their students take quizzes and turn in their homework assignments. Here are the section assignments for each TA: Jamey, Sections 11S and 16S; Astatke, Sections 12S and 13S; Craig, Sections 14S, and 15S.

Course Description
Continuation of Calculus 11A. We will study integration, infinite series, and differential equations. The main focus will be on integrals and their applications. For a list of topics see the Lecture and Reading Schedule below.

Prerequisites
Calculus 11A--a sound understanding of derivatives and their applications.

Textbook
Calculus, by Hughes-Hallet and Gleason et al., Second Edition.

Homework and Quizzes
There will be weekly homework assignments to be turned in to the teaching assistants. Students in M-W sections will turn in their homework on Wednesdays, and students in T-Th sections will turn in their homework on Thursdays. Late homeworks will not be accepted. Also, there will be weekly quizzes. Students in M-W sections will take their quizzes on Mondays, and students in T-Th sections will take their quizzes on Tuesdays.

Lecture and Reading Schedule
For the first six weeks we will concentrate on integrals and their applications. The remaining four weeks will be devoted to infinite series, and then to differential equations. The lecture schedule appears below. You should try to read the sections, or at least glance at them, before coming to class.
Dates Lectures
March
April		 31
2		 W
F		 3.1
3.2, 3.3		 Estimating integrals numerically
Integral as average and area
April 5
7
9		 M
W
F		 3.4
6.1
6.2		 Basic properties of integrals
Antiderivatives, graphically
Computing antiderivatives analytically
12
14
16		 M
W
F		 6.3
6.4
7.1		 Some differential equations
Antiderivatives and integrals
Integration by substitution
19
21
23		 M
W
F		 7.2
7.3
.		 More substitution techniques
Integration by parts
Review
26
27
30		 M
W
F		 .
7.7
8.1		 Midterm #1 (Covers up to 7.2)
Improper integrals
Applications of integrals to geometry
May 3
5
7		 M
W
F		 8.2
8.3
8.4		 More applications: center of mass
Applications to physics
Applications to economics
10
12
14		 M
W
F		 9.1
9.2
9.3		 Taylor series
Notion of convergence
Using Taylor series
17
19
21		 M
W
F		 9.4, 10.1
.
.		 Geometric series, Differential equations
Review
Midterm #2 (from 7.3 to 9.3)
24
26
28		 M
W
F		 10.2
10.3
10.4		 Solving DE's graphically
Solving DE's numerically
Solving DE's analytically
June 1
2
4		 T*
W
F		 10.5
10.6
.		 Applications of DE's: growth and decay
More applications: Modelling
Review
7 M . Final Exam (Comprehensive)

* Exchange day (Monday classes will meet on Tuesday).

Assignments
The following are the homework assignments for the entire quarter. You should plan to work on these problems over a period of several days. Getting a head start on each assignment is perhaps the most critical factor determining your success in this class.
Homework # Due Date Problems
1 Apr 7/8 3.1) 1, 4, 5;
3.2) 2, 9, 24, 28;
3.3) 7, 8, 11, 15, 17;
3.4) 1, 2, 8.
2 Apr 14/15 3.4) 18, 22, 24, 25;
6.1) 2, 6, 14;
6.2) 12, 15, 16, 17, 34, 39, 50, 58, 60;
6.3) 2, 6, 11.
3 Apr 21/22 6.3) 12, 14, 18, 20;
6.4) 4, 8, 12, 14;
7.1) 1, 2, 4, 8, 12, 18, 29, 42, 43, 44;
7.2) 1,4.
4 Apr 28/29 7.2) 8, 28, 30, 33, 39, 40;
7.3) 1, 2, 4, 6, 12, 20, 21, 37, 40, 48, 49, 52.
5 May 5/6 7.7) 2, 4, 12, 26, 30;
8.1) 3, 4, 5, 6, 12, 13, 16, 20, 21;
8.2) 3, 4, 7.
6 May 12/13 8.2) 10, 11, 13;
8.3) 2, 4, 8, 10, 11, 19, 20;
8.4) 2, 4, 5, 6;
9.1) 1, 4, 9, 12.
7 May 19/20 9.1) 15, 26, 28, 30;
9.2) 2, 4, 6, 10, 12, 16, 18, 21, 23;
9.3) 3, 4, 5, 13, 16, 27, 28.
8 May 26/27 9.4) 2, 4, 6, 12, 18, 23, 24, 26;
10.1) 3, 4, 7, 10, 11;
10.2) 2, 4, 8.
9 June 2/3 10.3) 1, 4, 7, 10;
10.4) 2, 8, 15, 18, 23, 28, 34;
10.5) 1, 3, 4, 8, 18, 19.
10 Not to be turned in 10.6) 4, 5, 13, 15, 18.

Tests and Exams
There will be two midterms, the first on Monday Apr 26, and the second on Friday May 21. The final exam will be on Monday, Jun 7, 8-11am.

Grading
The final grade is based on homeworks and quizzes, 20%, midterms, 20% each, and the final exam, 40%.

A Few Words to the Student
Come to the lecture and sections prepared. Keep up with the reading schedule, and start working on each assignment well in advance of the due date. A single problem may take hours to solve. Only you can convince yourself how clear a solution can be. And as much as your Professor and the TA's are commited to helping you along, you also have to work hard to make that possible.