College of Arts and Sciences
Department of Mathematics and Physics
Course syllabus for Calculus (III)
COURSE INFORMATION:
Course Number: Math 211
Course title: Calculus III
Prerequisites: Math 102
Credit Hours: 3
Class Hours: MW 8:00-9:15, W 14:-14:50
Textbook:
 Calculus, by H. Anton, I. Bivens, and S. Davis, 8th Edition, 2005, Wiley.
References :
 Calculus with Analytic Geometry, by H. Edwards and D. E. Penny, 5 th
Edition, 1998, Prentice Hall.
 Calculus, b R.T. Smith and R.B. Minton, Second Edition, 2002, McGrawHill.
INSTRUCTOR INFORMATION:
Instructor: Dr. Martin Juras
Office Location: B211
E-mail: [email protected]
Office Hours: M 9:15—10:15, W 14:50-15:50 or by appointment
OBJECTIVES:
INSTRUCTIONS
&
REGULATIONS:
Office Phone: 485 2201
To develop the notion of vectors and their properties in the plane
and the 3-dimensional space.
 To present the calculus of vector-valued functions and curves.
 To develop the ability to differentiate functions of several
variables and use it to solve practical problems.
 To provide students with the skills of multiple integration for
functions of several variables and its application to practical
problems.
 Using Mobile phones during lectures or exams is prohibited. Shut off
your cell phone during class, any one uses mobile will be asked to leave
the lecture room.
 Students are expected to attend all classes, if they do not show up for
more than 25% of the classes, they fail the course. There are no grades
for attendance.
 Quizzes have no make up, so try not to miss any.
 Students are expected to participate actively in the class.
 Check your e-mail regularly.
 Be responsible for all class activities, announcements, and assignments
when you miss a class.
 Do not hesitate to see me if you have any question.
 Prior to class, look over the section that will be covered.
 Regularly check the BlackBoard site at: http://elearning.qu.edu.qa

Qatar University
Department of Mathematics and Physics
Calculus (III) Syllabus
Instructor: ----------------------------
LEARNING OUTCOMES:
Objective
Objective 1:
To develop the notion of
vectors and their properties
in the plane and the 3dimensional space
Learning Outcomes: By the end of the course the should be able to

Recognize the 3-space and describe surfaces for a given equation.

Do operations on vectors in the plane and the 3- space

Evaluate dot and cross product of vectors.

Find parametric equations of lines in 3-space.

Find equation of planes in 3-space.

Find all types of intersections between planes and lines

Recognize the cylindrical and spherical coordinate systems.

Identify and sketch different types of quadric surfaces

Define vector-valued functions and find their domain,
perform different types of calculus operations
Evaluate the arc length, use chain rule and find arc length
parameterization.
Objective 2:

To present the calculus of
vector-valued functions
and curves

Find unit tangent, normal and binomial vectors.


Find the curvature and radius of curvature
Define real-valued functions of several variables and
recognize their basic properties
Draw level curves and level surfaces.

Evaluate limits of functions and discuss their continuity

Find partial derivatives for functions of several variables.

Evaluate total differentials and decide whether a function
is differentiable or not.

Use the chain rule.

Find directional derivatives and gradients for real-valued
functions and find their rate of change.

Find tangent planes and normal vectors for a given
surface.

Evaluate Maxima and Minima for functions of two
variables.

Use Lagrange Multipliers to evaluate Maxima and Minima
Evaluate double and triple integrals over rectangular
regions.
Evaluate double and triple integrals over non-rectangular
regions.
Use polar coordinates to evaluate double integrals.

Objective 3:
To develop the ability to
differentiate functions of
several variables and use
it to solve practical
problems
Objective 4:
To provide students with
the skills of multiple
integration for functions of
several variables and its
application to practical
problems




Evaluate triple integrals in cylindrical and spherical coordinate
systems.
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Qatar University
Department of Mathematics and Physics
Calculus (III) Syllabus
Instructor: ----------------------------
SYLLABUS ITEMS:
Text Book: Calculus, by H. Anton, I. Bivens, and S. Davis, 8th Edition, 2005, Wiley.
Week
1
Date
Feb. 21- Feb. 25
2
Feb. 28 – Mar. 4
3
Mar. 7 – Mar 11
4
Mar. 14 – Mar 18
5
Mar. 21 – Mar. 25
6
Mar. 28 – Apr. 1
7
Apr. 4 – Apr. 8
Sec.
12.1
12.2
12.3
12.4
12.5
12.6
13.1
13.2
13.3
13.4
13.5
13.6
12.7
14.1
Apr. 9 - Apr. 18
Topics
Rectangular Coordinate systems in 3-space
Vectors
Dot product, projections
Cross product
Parametric equations of a line
Planes in 3-space
Introduction to vector-valued functions
Calculus of vector-valued functions
Change of parameters , Arc Length
Unit Tangent, Normal and Binormal vectors
First Exam: Mar. 24, 2010 (afternoon lecture)
Curvature
Motion along a curve
Quadric Surfaces
Functions of two or more variables
SPRING BREAK
8
Apr. 18 – Apr. 22
9
Apr. 25 – Apr. 29
10
May 2– May 6
11
May 9 – May 13
12
May 16 – May 20
15.1
15.2
Limits and continuity
Partial derivatives
Differentiability, Local Linearity, and differentials
The Chain rule
Directional derivatives and gradients
Tangent planes and normal vectors
Maxima and minima of functions of two variables
Lagrange multipliers
Second Exam: May 12, 2010 (afternoon lecture)
Double integrals
Double integrals over non rectangular regions
13
May 23– May 27
14
May 30– June 3
15.3
15.5
12.8
15.7
Double integrals in polar coordinates
Triple integrals
Cylindrical and spherical coordinates, Triple integrals in
cylindrical and Spherical coordinates
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
Final Exam: TBD
GRADING PLOICY
Exam
First
Second
Assignments & Quizzes
Final Exam
Total
percentage
25%
25%
10%
40%
100%
Date and time
Mar. 24, 2010 (afternoon lecture)
May 12, 2010 (afternoon lecture)
TBA
TBA
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Qatar University
Department of Mathematics and Physics
Calculus (III) Syllabus
Instructor: ----------------------------
The rules of QU to transfer numeral grades to letter grades are as follows
Percent grade
Letter grade
Earned Points
90 -100 85 - 89
A
B+
4.0
3.5
80 - 84 75 -79 70 - 74
B
C+
C
3.0
2.5
2.0
65 - 69
D+
1.5
60 - 64
D
1.0
below 60
F
0.0
Recommended Problems for Calculus 3
Chapter 15
Chapter 14
Chapter 13
Chapter 12
Text Book: Calculus, Author: Howard Anton 8th
Note to the students: The following problems are meant for the least practice. They only show the
type of the problems you will encounter in this course. You are strongly urged to solve much more
problems to develop your skills.
Chapter Section
Page
Question Numbers
12.1
794
8,11, 12, 17, 19, 25, 29, 33, 36,37,42
12.2
805
1-19 (odd numbered), 27, 29, 38.(The same as 7th edition)
12.3
814
1, 3, 7, 9, 11, 12, 13, 15, 24,26.
12.4
825
1, 3, 5, 7, 10, 13, 19, 21, 24, 25, 26, 27.(The same as 7th edition)
12.5
832
3, 5, 7, 9, 12, 13, 15, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 39, 48,49.
12.6
841
3, 11, 14, 15, 17, 19, 21, 23, 26-30, 33, 41, 43, 45.
12.7
852
1, 5, 7, 9, 11-21 (odd), 29, 32, 33, 35. (The same as 7th edition)
12.8
859
13.1
867
13.2
878
13.3
888
1-11 (odd), 15-41 (odd). (The same as 7th edition)
2, 4, 8, 11, 13, 19, 20, 21, 29, 32, 33, 37, 40, 41.(The same as 7th
edition)
2,4, 5, 7, 9, 10,11, 13, 15, 19, 21, 23, 27, 29, 31, 33, 35, 37,39, 42,
51, 54.
1, 4,6, 7,8, 9, 11, 13, 13, 15, 21, 23, 25, 27.
13.4
895
5, 7,9, 15, 16, 17,19.
13.5
901
5,7,9,11,13,15,17,19,21,26,27,29,32.
13.6
14.1
14.2
914
937
948
14.3
959
14.4
14.5
14.6
14.7
14.8
14.9
15.1
15.2
15.3
15.5
15.7
969
979
991
998
1008
1018
1028
1037
1045
1067
1088
1, 3, 5, 6, 13, 17, 19, 25, 27, 29, 31, 33, 35, 37, 39, 43
1, 3, 5, 13, 15, 19, 21, 23, 25-31, 39, 41, 43, 45, 47, 49, 51, 53, 55.
1-19 (odd), 33, 37, 41, 43.
1, 5, 11, 13, 15,17, 19, 23, 25, 27, 29, 31, 33, 35, 37,43, 43, 45, 57,
59, 61, 63, 65, 68,74, 91,93.
4,9,15,19,21,23, 37,41, 43,44,45,47,59,60.
1, 3, 5, 17,19,21,23,25,27,29,31,39,40,41,43.
1-19 (odd), 26, 29, 30, 33, 35, 37, 39, 41, 43, 47-61 (odd), 68.
1-9 (odd), 10-12, 17, 22, 23, 25.
1, 3, 9-19 (odd), 27, 29, 31, 35.
5-13 (odd), 14, 15, 19, 21, 22, 24, 25.
1-15 (odd), 19, 21, 23, 24, 25.
1-9 (odd), 14,17,19,21,23,25,29,31,35,37,38, 45-53 (odd).
1-15 (odd), 23,24,27-34.
1-11 (odd), 15, 17, 19, 25, 33.
1-19 (odd),24.
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