# Math 1451H

### Course objective

This is the second course of a two-semester sequence covering all major Calculus content. The main goals of this course are to

• master advanced differentiation and integration techniques in multivariate calculus and to apply them, and
• enhance your skills in thinking, formulating, and writing more clearly, critically, and logically, which is useful in general problem solving and in your future studies.

### Preparation, Homework, Quizzes and Exams

This is a fast paced course. You are required to read the sections covered each week during the weekend before and begin to familiarize yourself with the posted problems. Selected problems will then be worked out in the recitation sections. In addition, you may consult the solutions key at the end of the book to check your answers. At the end of each week, you are responsible for knowing how to solve all posted homework problems! On most Fridays, the material of the week will be tested with an 18-minute quiz. Groups of two chapters usually make up the material for each in-class exam. The final exam is comprehensive, with a slight emphasis of the material of the last two weeks.

Your total score is composed of exam and quiz scores

 2 x 200 pt. exams 400 points 10 x 30 pt. quizzes 270 (drop lowest score) Final exam 330 TOTAL 1000 points

Final grades will be based on the total of 1000 points. You are guaranteed a grade based on the standard scale, that is:  A >=9O% > B >=8O% > C >= 7O% > D >= 6O% > F. However, I will adjust the scale downward in case the distribution of scores indicates that I should.

### Getting help

Free tutoring is available at CASA. Tutors are usually available Mo-Th 9am-7pm, Fr 9am-2pm.

### Syllabus (numbering follows chapters in the textbook)

VECTORS AND THE GEOMETRY OF SPACE

12.1 Coordinate systems
12.2 Vectors
12.3 The dot product
12.4 The cross product
12.5 Equations of lines and planes

VECTOR FUNCTIONS

13.1 Vector functions and space curves
13.2 Derivatives and integrals of vector functions
13.3 Arc length and curvature

PARTIAL DERIVATIVES

14.1 Vector functions and space curves
14.2 Limits and continuity
14.3 Partial derivatives
14.4 Tangent planes and linear approximation
14.5 The chain rule
14.6 Directional derivatives
14.7 Maximum and minimum values
14.8 Lagrange multipliers

MULTIPLE INTEGRALS

15.1 Double integrals over rectangles
15.2 Iterated integrals
15.3 Double integrals over general regions
15.4 Double integrals in polar coordinates

15.5 Applications of double integrals
15.6 Triple integrals
15.7 Triple integrals in cylindrical coordinates
15.8 Triple integrals in spherical coordinates
15.9 Change of variables

VECTOR CALCULUS

16.1 Vector fields
16.2 Line integrals
16.3 The fundamental theorem for line integrals
16.4 Green's theorem
16.5 Curl and divergence
16.6 Parametric surfaces
16.7 Surface integrals
16.8 Stokes's theorem
16.9 Divergence integrals

### Tentative Course Calendar (check the course website for updates!)

Week Sections to be read, Exam dates Suggested homework problems

Jan 20-23

 No class on Jan 19
12.1-12.2 12.1 1-13 odd, 25, 29, 35
12.2
1-13 odd, 19, 23, 33
Jan 26-30  12.3-12.5 12.3 3-17 odd, 23, 25, 29, 43, 47, 49, 51
12.4
1, 3, 9, 23, 25, 29, 33, 35, 41, 45
12.5
1-19 odd, 23, 27, 31, 39, 47, 53, 67, 69
Feb 2-6  13.1-13.3 13.1 1-15 odd, 19-23 odd, 27, 35, 39
13.2
5, 9, 11, 17, 19, 23, 29, 31, 35
13.3 1, 3, 11, 17, 19, 43, 45, 49, 59
Feb 9-13  14.1, 14.2, 14.3 14.1 1, 13, 25, 27, 31, 39, 47, 55-59 odd
14.2 7-17 odd, 23, 27, 29, 31, 37, 39
14.3 5-9 odd, 15, 17, 25, 33, 37, 43, 45, 49, 57, 61
Feb 16-20  14.4, 14.5 14.4 1, 3, 13, 15, 25, 27, 33, 35
14.5 1, 3, 7, 13, 15, 19, 23, 25, 27, 31, 35, 39
Feb 23-27

 Review, Feb 23

 Exam 1, Feb 24 on Ch. 12, 13, 14.1-5 See Sample test?

14.6
Review Ch. 12
Review
Ch. 13

14.6 1, 5, 7, 19, 27, 33, 37, 39, 43, 47
Mar 2-6  14.7, 14.8 14.7 1, 3, 9, 19, 21, 27, 29, 31, 37, 39, 41
14.8
1-11 odd, 19, 21, 41
Mar 9-13  15.1, 15.2, 15.3 15.1 11, 13
15.2 5, 13, 15, 19, 23, 25
15.3 3, 9, 15, 25, 31, 33, 39-43 odd, 47, 49, 51, 53, 55, 61
Mar 23-27  15.4, 15.5, 15.6 15.4 1, 3, 5, 9, 15, 17, 19, 25, 29, 31, 35
15.5
3, 7, 27
15.6 3, 11, 15, 21, 27-31 odd, 33
Mar 30-Apr 3  15.7, 15.8, 15.9
15.7 1, 3, 5, 9, 15, 17, 21, 27
15.8 1, 3, 5, 9, 13, 15, 17, 19, 21, 23, 39
Apr 6-10 Review, Apr 6
 Exam 2, Apr 7 on Chs. 14.6-8, 15 See Sample test?
Review Ch. 14, 15

16.1
3, 11, 13, 15, 17, 23, 25
Apr 13-17  16.2, 16.3, 16.4 16.2 5, 11, 15, 17, 29(a), 41, 43
16.3 1, 3, 9, 11, 13, 21, 23, 27, 31
16.4 1, 5, 7, 13, 17, 23, 29
 Apr 20-24
16.5, 16.6, 16.7 16.5 1, 3, 5, 7, 9, 13, 15, 17, 19, 25, 29
16.6 1, 3, 11, 13, 15, 23, 39, 41, 43
16.7 5, 7, 13, 17, 19, 21, 23, 27
Apr 27-May 1  16.8, 16.9 16.8 1, 3, 5, 7, 9, 11(a,c), 13, 17
16.9
1, 5, 7, 11, 19, 23, 27
Exam period Review, May 7
 Final Exam, May 12 on Chs. 12-16 See Sample test?
Review