SYLLABUS

Honors Calculus III (Math 2411)
Spring 2006, Georgia Tech

Lecture Section
T Th 12:05-13:25 Skiles 169 M W 12:05-12:55 Skiles 243
Instructor
Professor Mohammad Ghomi
Teaching Assistant
Craig Sloan

Course Description
We study calculus of vector valued functions. Main topics include Taylor's theorems, Lagrange multipliers and constrained optimization, parametrized curves and surfaces, change of variables formula and Jacobians, line and path integrals, surface integrals, theorems of Green, Gauss, Stokes, differential forms, and various applications to problems in Physics, Engineering, and Geometry.

Textbook
Vector Calculus, by Susan Colley, third edition.

Homeworks
There will be homework assignments due every Monday. Late homeworks will not be accepted.

Lecture and Reading Schedule
Dates Lectures
Jan 10
12		 T
Th		 1.1
1.2,1.3		 Intro to vectors
Dot products
17
19		 T
Th		 1.4, 1.5
1.7		 Cross Products, Distance problems
Cylindrical and Spherical coordinates
24
26		 T
Th		 2.1, 2.2
2.3, 2.4		 Functions of several variables, Limits, Continuity
Derivatives
31 T 2.5 The Chain Rule, Gradient
Feb 2 Th 2.6 Directional derivatives
7
9		 T
Th		 3.1
3.2		 Parametrized curves and Kepler's laws
Arclength
14
16		 T
Th		 3.2
3.3		 Frenet-Serret formulas
Flow lines in vector fields
21
23		 T
Th		 3.4, 4.1
4.2		 Divergence and Curl,Taylor's Theorem
Extrema of functions
28 T 4.3 Lagrange Multipliers
Mar 2 Th 5.1, 5.2 Areas and Volumes; Intro to Double Integrals
7
9		 T
Th		 5.3, 5.4, 5.5
5.6		 Triple Integrals, Change of variables
Averages and Centers of Mass
14
16		 T
Th		 6.1
6.2		 Line Integrals
Green's Theorem
28
30		 T
Th		 6.3
7.1		 Conservative vector fields
Parametrized surfaces
Apr 4
6		 T
Th		 7.2
7.3		 Surface integrals
Stokes and Gauss's Theorems
11
13		 T
Th		 7.4
8.1		 Maxwell's Equations
Intro to Differential forms
18
20		 T
Th		 8.2
8.3		 Integrals of k-forms
General Stokes theorem
25
27		 T
Th

Assignments
# Due Date Problems
1 Jan 17 1.2) 14, 18, 24, 25, 28, 29, 37, 38;
1.3) 8, 10, 14, 16, 21, 24, 25, 26.
2 Jan 23 1.4) 10, 12, 16, 18, 20, 24, 25, 26, 27, 30, 32;
1.5) 5, 29, 33, 34, 35;
1.7) 6, 8, 12, 16, 18, 26, 32.
3 Jan 30 2.1) 12, 20, 35, 36, 46;
2.2) 14, 23, 28, 32, 46;
2.3) 8, 14, 20, 22, 24, 30, 36, 48;
2.4) 10, 20.
4 Feb 6 2.5) 3, 16, 20, 22, 26, 27, 30;
2.6) 6, 12, 16, 20, 22, 34, 36, 42.
5 Feb 13 3.1) 4, 6, 8, 16, 22, 25, 27, 29, 30, 32;
3.2) 4, 8, 9, 10, 12.
6 Feb 20 3.2) 16, 17, 18, 24, 29, 30, 32;
3.3) 18, 20, 24, 25.
7 Feb 27 3.4) 2, 8, 12, 14, 18, 29;
4.1) 10, 14, 18;
4.2) 4, 6, 28, 32, 33.
8 Mar 6 4.3) 2, 17, 19, 24, 28, 36, 37;
4.6) 20, 23;
5.1) 2, 4, 10, 16;
5.2) 4, 10, 12, 20, 23.
9 Mar 13 5.3) 2, 12;
5.4) 6, 9, 12;
5.5) 8, 14, 18, 24;
5.6) 3, 11, 12, 18, 22;
5.8) 11.
10 Mar 27 6.1) 2, 8, 16, 23, 24, 25, 27, 29;
6.2) 5, 10, 14, 17, 22, 25.
11 Apr 3 6.3) 4, 10, 18, 25;
6.5) 2, 23, 25, 27;
7.1) 2, 10, 20, 22, 26, 28.
12 Apr 10 7.2) 6, 7, 10, 23;
7.3) 2, 6, 12, 16, 20.
13 Apr 17 7.4) 5, 11, 13, 16;
7.6) 6, 8, 21, 38;
8.1) 2, 6, 8, 10.
14 Apr 24 8.2) 6, 7, 9;
8.3) 2, 4, 8, 11, 12;
8.5) 3.

Tests and Exams
There will be 2 midterms on Wednesdays Feb 15 and Mar 15. The Final Exam is on Friday, May 5 , 8-10:50.

Grading
Your final grade is comprised of the homeworks (20%), midterms (20% each) and the final exam (40%).

Attendance Policy
You are required to attend all lectures and sections.