Rensselaer Polytechnic Institute
Department of Mathematical Sciences
Syllabus Math 4600 Advanced Calculus ( Fall 2011 )
Textbook:
by S.J. Colley, Third Edition , Prentice Hall, 2006
by G.B. Folland, 2001 ( recommended )
Week Dates Sections Topics
1 8/29 – 9/2 2.3 Introduction to R n
. Differentiation of functions F:R n
--R m
HW 2.3 # 2, 4, 6, 15, 19, 21, 22, 38, 39, 50, 51
2 9/6 - 9/9 2.4 Properties. HW 2.4 # 1, 3, 7, 9, 12, 14, 20, 21, 22c
3 9/12 –9/16 2.5, 2.6 Chain rule. Directional Derivative
HW 2.5 # 1, 4, 10, 11, 15, 22, 23, 24
2.6 # 1, 3, 7, 9ab, 17, 18, 25, 33, 35
4 9/19 - 9/23 3.4, 4.1 Gradient, divergence and curl. Taylor Formula
HW 3.4 # 2, 3, 5, 8, 11, 14, 15,18, 19, 21, 22, 28, 29, 33
HW 4.1 # 8, 10, 12, 15, 20, 23, 25
5 9/26-9/30 4.2 Extrema. HW 4.2 # 3, 6, 8, 11, 22, 32, 38
6 10/3-10/7 Inversion Theorem. HW 2.6 # 48, 49
Exam # 1 on Friday October 7
7 10/10 – 10/14 Implicit Function Theorem. HW 2.6 # 40, 43, 47
8 10/17-10/21 4.3 Lagrange Multipliers. HW 4.3 # 1, 3, 4, 9, 18, 21, 29
5.5
This section on multiple integration is recommended for personal reading
9 10/24-10/28 Integrals depending on a parameter.
Fundamental Lemma of the Calculus of Variations. Euler Equation
10
10/31-11/4
6.1, 6.2 Curves and line integrals. Green’s Theorem
HW 6.1 # 1b, 3, 4, 8, 11, 14, 16, 17
6.2 # 1, 3, 5, 8, 10, 12, 15, 19, 25
11 11/7-11/11 6.3 Independence of path
HW 6.3 # 2, 5, 6, 7, 8, 10, 13, 15, 25
Exam # 2 on Friday, Nov 11
12 11/14-11/18 7.1, 7.2
Surfaces and Surface Integrals
HW 7.1 # 1, 3, 7, 20, 23,26; 7.2 # 1, 3, 6, 11, 14, 17, 21
13 11/22 7.3 Stokes Theorem. HW 7.3 # 1, 2, 3, 4, 10, 11, 13, 17
14 11/28-12/2 7.3 Gauss Theorem and Applications
HW # 7.3 # 6, 7, 9, 14, 18, 19, 20
15 Exam # 3 on Tuesday Dec 6 Dec 9 is the last day of class
Grading system: Exam #1: 25%, Exam # 2: 25%, Exam # 3: 20%, Homework: 25%
Attendance and Participation: 5%. No Final.
Instructor: Dr. Mohamed T. Boudjelkha
Office: # 404 Amos Eaton Hall, Office Hours: M, W, TH from 10:10 to 11:10; Phone: 2725
E-Mail: boudjm@rpi.edu
Note: The homework problems to be handed in and graded will be posted on RPI Mathematical Sciences
Website. These problems are a subset of the problems on this syllabus.