Math 102 Multivariable Calculus

TED UNIVERSITY
Math 102
Multivariable Calculus
SYLLABUS
Dr. İlker S. Yüce
2/18/2013

Required or
Elective
Semester
Course Credit
Hours/ ECTS
credits
Level of Course
Instructor
Instructor’s Office
& Phone Numbers
Teaching
Assistant(s)
Teaching Assistants’
Office Phone
Required
Elective
Fall 12-13
Spring 12-13
Summer 12-13
(3,2,0) 4 / 7
Freshman
Dr. İlker S. Yüce
Building A, O421,
312 585 01 15
Date February, 18th 2013
Class Hours
Pre-requisite/
Co-requisite
Language of
Instruction
Instructor’s Office
Hours
Instructor’s E-mail
Address
Teaching Assistants’
Office Number(s)
Teaching Assistants’
Email Addresses
M. 9am-10am, Rm 316
W. 10am, Rm. 316
F. 10am-11am, Rm 316
Math 101
English
Turkish
Monday 11am,
Wednesday 11am
Friday 9am, or by
appointment.
ilkers.yuce@tedu.edu.tr
Course
Description
Course
Learning
Outcomes
Vectors in R 2 and R 3 , Dot and Cross Products, Lines and Planes in R 3 . Vector-Valued
Functions, and Their Limits, Continuity and Derivatives, Curvature. Functions of
Several Variables and Their Limit and Continuity, Partial derivatives, Directional
Derivatives, Maximum-Minimum Problems, Lagrange multipliers. Double Integrals,
Triple Integrals, Vector Fields, Line Integrals, Green’s Theorem, Surface Integrals,
Stokes’s and Divergence Theorem.
On successful completion of this module, the students should be able to
1. Recall basic principles of mathematical writing together with conventions,
mathematical notation and fundamental definitions related to
multivariable scalar and vector valued functions,
2. Write equations of lines and planes in R 3 by the help of dot and cross of
vector.
3. Extend the concepts of limit and continuity to multi-variable scalar and
vector valued functions.
4. Calculate limits, partial derivatives, directional derivatives, and multiintegrals
of multi-variable scalar functions in various coordinate systems
algebraically, graphically, and numerically
5. Compute limits, derivatives and curvature of vector valued functions
algebraically, graphically and numerically.
6. Solve problems of Maximum-Minimum Values and Lagrange Multipliers
for multi-variable scalar functions.
7. Calculate line integrals, divergence, gradient and curl of vector fields.
8. Use main theorems of vector calculus such as Green’s Theorem, Stokes’s
Theorem and Divergence Theorem.
2

Bloom’s Taxonomy Levels: K. Knowledge, C. Comprehension, a. Application.
1 (K), 2(K),3(C),4(a),5(a),6(a),7(a),8(a)
Teaching Methods
& Learning
Activities
Telling/Explaining
Discussions/Debates
Questioning
Reading
Peer Teaching
Scaffolding/Coaching
Demonstrating
Problem Solving
Inquiry
Collaborating
Think-Pair-Share
Predict-Observe-Explain
Microteaching
Case Study/Scenario Analysis
Simulations & Games
Video Presentations
Oral Presentations/Reports
Concept Mapping
Brainstorming
Drama/Role Playing
Seminars
Field Trips
Guest Speakers
Hands-on Activities
Service Learning
Web Searching
Experiments
Other(s): ....Written
Homework......
Student Workload
(Total 175 Hrs)
Lectures .....................................70.. hrs
Course Readings ....................25.. hrs
Workshop ......................................... hrs
Online Discussion .......................... hrs
Debate ................................................. hrs
Work Placement ............................. hrs
Field Trips/Visits ........................... hrs
Observation ...................................... hrs
Lab Applications ............................ hrs
Hands-on Work ............................. hrs
Exams/Quizzes .......................20.. hrs
Resource Review ........................... hrs
Research Review ........................... hrs
Report on a Topic ......................... hrs
Case Study Analysis ..................... hrs
Oral Presentation ......................... hrs
Poster Presentation ...................... hrs
Demonstration ................................ hrs
Web Designs .................................... hrs
Mock Designs ................................... hrs
Team Meetings................................ hrs
Other: Written Homework..60. hrs
Assessment
Methods (Formal
& Informal)
Test/Exam
Quiz
Oral Questioning
Performance Project
WrittenOral
Observation
Self-evaluation
Peer Evaluation
Portfolio
Presentation (Oral, Poster)
Other(s): Written Homework
Textbook
Calculus, A Complete Course, 7 th Edition, by Adams and Essex.
Recomended Readings
James Stewart, Calculus, 7 th Edition
Thomas’ Calculus, 12 th Edition
Calculus, Single and Multivariable, 2 nd Edition, Blank and Krantz
3

Module and Instructor
Evaluation Date
Design Content
Computer Usage
Evaluation will be held on Monday May 20 th , 2013 at 10:40 am in the
class.
Problem Sets from WeBWorK will be assigned for extra credit. Please see
the web page http://math.tedu.edu.tr/webwork2
COURSE ASSESSMENTS & LEARNING OUTCOMES MATRIX
Assessment Methods
Course Learning Outcomes
Weekly Quizzes #1, #2, #3, #4, #5, #6, #7, #8
Weekly Homework #1, #2, #3, #4, #5, #6, #7, #8
Exam 1 #1, #2, #3, #4
Exam 2 #1, #2, #3, #4, #5,#6
Exam 3 #1, #2, #3, #4, #5, #6, #7, #8
Final Exam #1, #2, #3, #4, #5, #6, #7, #8
GRADING SCALE
Grade Grade Points Percentage Scores
AA 4.00 90-100
BA 3.50 85-89
BB 3.00 80-84
CB 2.50 75-79
CC 2.00 70-74
DC 1.50 65-69
DD 1.00 60-64
F 0.00 0-59
FX 0.00 -
4
COURSE ASSIGNMENTS
A. Quiz [%5]
There will be 12 quizzes given weekly. They will be held on Friday of each week. Some of quiz
grades MAY be dropped.
B. Homework [%10]
There will be 12 homework given weekly. They will be collected on Monday of each week. Some of
homework grades MAY be dropped.
C. Exams[%15+%15+%20]
There will be 3 one hour in class exams. Exam 1 is on 10/23 covering Sections P1-2.3 Exam2 is on
11/27 covering Sections 2.3-4.6. Exam 3 is on 12/25 covering Section 4.8-6.5.

D. Final[%35]
There will a cumulative final. Date of the final will be announced at the end of the semester.
E. Extra Credit Work[%10]
There will be extra credit work assigned via WeBWorK for interested students. Visit the web page
http://math.tedu.edu.tr/webwork2 .
TENTATIVE COURSE OUTLINE
W Day Topics Objectives
1
2
3
4
5
6
5
2/18
2/20
2/22
2/25
2/27
3/1
3/4
3/6
3/8
3/11
3/13
3/15
3/18
3/20
3/22
3/25
3/27
3/29
Improper Integrals
Volumes by slicing, solids
of revolution
Arc Length and Surface
area
Sequences and
convergence
Infinite series
Convergence tests for
positive series
Absolute and conditional
convergence
Power series
Taylor and Maclaurin
series
Applications of Taylor and
Maclaurin Series
Analytic Geometry in
Three Dimensions
Vectors
The Cross Product in 3-
Space
ONE HOUR EXAM 1
Planes and Lines
Quadratic Surfaces
Cylindrical and Spherical
Coordinates
Functions of Several
Variables
Limits and continuity
Partial Derivatives

7
8
9
10
11
12
13
14
4/1
4/3
4/5
4/8
4/10
4/12
4/15
4/17
4/19
4/22
4/24
4/26
4/29
5/3
5/6
5/8
5/10
5/13
5/15
5/17
5/20
5/22
5/24
Higher-Order Derivatives
The Chain Rule
Linear Approximations,
Differentiability, and
Differentials
Gradients and directional
derivatives
Implicit Functions
Extreme Values
Extreme Values of
functions defined on
restricted domains
Lagrange multipliers
ONE HOUR EXAM 2
Double Integrals
Iteration of double
integrals in Cartesian
coordinates
Polar coordinates and
polar curves
Double integrals in polar
coordinates
Triple Integrals
Change of Variables in
Triple Integrals
Vector and Scalar Fields
Conservative fields
Line integrals
Line Integrals of vector
fields
Gradient, Divergence, and
Curl
Green’s Theorem
ONE HOUR EXAM 3
Review
Module & Instructor
Evaluation
FINAL EXAMS WEEKS
May 27-June 7, 2013
6

COURSE POLICIES AND SOME REMARKS
I. Attendance
You are expected to attend all classes. Classes start on the hour. Please be respectful of your
classmates by being on time. Cell phones should be turned off and kept out of sight. Please do not
use your computers during class time.
II. Calculator Policy
You may use a graphing calculator or software that does symbolic calculations. The recommended
models are TI-83, or TI-89 from Texas Instruments or a suitable alternative. But you will NOT be
allowed to use them during exams. You should have an owner’s manual for your calculator. It will
be your responsibility to be familiar with the workings of the calculator.
III. Course Web Pages
Please check the link http://math.tedu.edu.tr regularly to have access to sources like sample
exams and quizzes, solutions of homework assignments, exams, quizzes, and practice exercises,
copies of handouts, summaries of each lectures, etc.
IV. Tutoring
In addition to office hours, there will be tutoring hours offered by appointment to get help. If you
feel that you need to sign up for tutoring, please visit Dr. Mana Ece Tuna (Rm. 147, Phone: 585 00
45, email: mana.tuna@tedu.edu.tr) for necessary arrangements.
V. Assignment Rules
Written homework is a very important part of this course. It is evident that your understanding of
the module material will improve dramatically if you do the homework. Because of the size of this
class there will be strict written homework rules:
1. Use standard size 21cm x 29.7 cm paper, NOT torn from a spiral notebook.
2. Multiple pages must be stapled. Please do not use paper clips. No loose sheets or
folded corners.
3. Written homework must be readable. If the grader can’t read it, you don’t get the
credit.
4. LATE HOMEWORK WILL NOT BE ACCEPTED.
VI. Plagiarism
Collaboration on non-collected homework and in studying is strongly encouraged; however, the
work you hand in must be solely your own. Sharing written work before it is turned in to be graded
is academic dishonesty. For more information on TEDU policy on intellectual integrity see the link
http://www.tedu.edu.tr/Assets/Documents/News/Public/TEDU_Ogrenci_El_Kitabi_2012.pdf
.
VII. Disability Support
If you have a disabling condition which may interfere with your ability to successfully complete this
module, please contact Dr. Aslı Bugay (email: asli.bugay@tedu.edu.tr ) or Dr. Tolga İnan (email:
tolga.inan@tedu.edu.tr). For more information please see Handbook for Registered Students.
VIII. Make Up Exams
Make-up exams for Exam 1, 2, and 3 will NOT be offered generally. If you have a legitimate reason
for missing an exam, then you must arrange to make up the exam BEFORE the scheduled time of the
exam. The only exceptions are illness or emergency (e.g., death in family, a traffic accident, etc.). In
case of an illness or emergency you need to supply a documentation that supports your claim.
7

The dates for Make-up exams for Finals are decided by Make-up Exam Commission according to the
rules and regulation of TEDU. Please see the link http://www.tedu.edu.tr/en-
US/Content/Default.aspxSectionID=114 .
Also please read the document given in the link http://www.tedu.edu.tr/tr-
TR/Content/Akademik/Akademik_Belgeler/Yonetmelikler_ve_Yonergeler.aspx
IX. Study Habits
You need to read each section in the text book before the lecture covers it. Memorize every
notation, definition and theorem in the book. After each class, go back and read it again. YOU LEARN
MATH BY DOING. Please work as many problems as you can. If you get help from someone, go back
and work it by yourself the next day. Remember that it is your responsibility to learn the material.
Most of the learning takes place at home. On the average you should study at least 2 or 3 hours
outside of class for every 50 minutes of class time. See the table Student’s Workload for details.
A CHART FOR YOU TO KEEP RECORD OF YOUR GRADES
1 2 3 4 5 6 7 8 9 10 11 12 Av.
Quiz X%5 =
HW
Exam 1
Exam 2
Exam 3
Final
WBWK
Total
X%10=
X%15=
X%15=
X%20=
X%35=
X%10=
CONTRIBUTION OF THE MODULE TO PROGRAM OUTCOMES
Program EEE IE CMPE ECON BA IR ARCH
Outcomes
1
2
3
5
11
8

TENTATIVE TIMETABLE
D
M T W Th F
W
1 2/18
Classes start.
6.5
2/20
7.1
2/22
7.3
Quiz 1, Rm. 316
2 2/25
9.1, 9.2
HW 1 is due.
2/27
9.3
3/1
9.3
Quiz 2, Rm. 331
3 3/4
9.4
HW 2 is due.
4 3/11
9.7, 10.1
HW 3 is due.
5 3/18
HW 4 is due.
Exam 1 (P.1-2.7)
6 3/25
12.1, 12.2
HW 5 is due.
7 4/1
12.5, 12.6
HW 6 is due.
8 4/8
13.1, 13.2
HW 7 is due.
9 4/15
HW 8 is due
Exam 2 (2.8-4.9)
10 4/22
8.5,14.4
HW 9 is due.
11 4/29
11.1, 15.1
HW 10 is due.
12 5/6
15.3
HW 11 is due.
13 5/13
HW 12 is due.
Exam 3 (5.1-7.1)
3/6
9.5
3/13
10.2
3/20
10.4
3/27
12.3
4/3
12.7
4/10
13.3
4/17
14.1
4/24
14.5
5/1
NO CLASS.
5/8
15.4
5/15
16.1
3/8
9.6
Quiz 3, Rm. 316
3/15
10.3, Review
Quiz 4, Rm. 331
3/22
10.5
Quiz 5, Rm. 316
3/29
12.4
Quiz 6, Rm 331
4/5
12.8
Quiz 7, Rm. 316
4/12
Review
Quiz 8, Rm. 331
4/19
14.2
Quiz 9, Rm. 316
4/26
14.6
Quiz 10, Rm. 331
5/3
15.2
No Quiz, Rm. 316
5/10
Review
Quiz 11, Rm. 331
5/17
16.3
Quiz 12, Rm. 316
9

HW 1
HOMEWORK ASSIGNMENTS
HW 2
HW 3
HW 4
HW 5
HW 6
HW 7
HW 8
HW 9
HW 10
HW 11
HW 12
NOTE. You may use the table to list assigned homework problems. The rest of the homework will
follow.
10