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Course Code: 
MATH 255
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
4
ECTS: 
8
Course Language: 
English
Course Objectives: 
The aim of this course is to provide students with an understanding of differentiation and integration of multivariable functions and their calculations.
Course Content: 

Vector functions; space curves, derivatives and integrals, arc length, motion in space, parametric surfaces. Multiple integrals and applications. Vector calculus; vector fields, line integrals, Green’s theorem, curl and divergence, surface integrals, Stokes’ theorem, the divergence theorem.  

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Program Learning Outcomes

Teaching Methods

Assessment Methods

1) Evaluates the arclength of space curves.

1,2,7

1,2

A

2) Evaluates double and triple integrals.

1,2,4,7

1,2

A

3) Changes variables in double and triple integrals.

1,2,4,7

1,2

A

4) Evaluates line integrals and surface integrals.

1,2,4,7

1,2

A

5) Expresses the concepts of circulation, work and flux using line and surface integrals.

1,2,3,4,7

1,2

A

6) Uses Green's, Stokes' and the divergence theorems.

1,2,3,4,7

1,2

A

Course Flow

Week

Topics

Study Materials

1

Vector-Valued Functions : Arc Length

Chapter 4

2

Vector Fields, Divergence and Curl

Chapter 4

3

(Review of) Double and Triple Integrals : The Double Integral Over a Rectangle, The Double Integral Over More General Regions

Chapter 5

4

Changing the Order of Integration, The Triple Integral

Chapter 5

5

The Change of Variables Formula and Applications of Integration: The Geometry of Maps from R2 to R2, The Change of Variables Theorem

Chapter 6

6

Applications of Double and Triple Integrals,  Improper Integrals

Chapter 6

7

Integrals: The Path Integral, Line Integrals

Chapter 7

8

Parametrized Surfaces, Area of a Surface

Chapter 7

9

Integrals of Scalar Functions Over Surfaces, Surface Integrals of Vector Functions

Chapter 7

10

The Integral Theorems of Vector Analysis: Green's Theorem

Chapter 8

11

Stokes' Theorem

Chapter 8

12

Conservative Fields

Chapter 8

13

Gauss' Theorem

Chapter 8

14

Applications

 

Recommended Sources

Textbook

“Vector Calculus”6th Edition, by J. Marsden and A. Tromba

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

100

Quizzes

   

Assignments

   

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

60

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

40

Total

 

100

 

COURSE CATEGORY

Core Courses

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

       

X

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

       

X

3

Ability form and interpret the relations between research topics in mathematics

       

X

4

Ability to define, formulate and solve mathematical problems

       

X

5

Consciousness of professional ethics and responsibilty

   

X

   

6

Ability to communicate actively

   

X

   

7

Ability of self-development in fields of interest

       

X

8

Ability to learn, choose and use necessary information technologies

         

9

Lifelong education

         

ECTS

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

5

70

Hours for off-the-classroom study (Pre-study, practice)

14

5

70

Mid-terms (Including self study)

2

17

34

Quizzes

 

 

 

Assignments

 

 

 

Final examination (Including self study)

1

23

23

Total Work Load

 

 

197

Total Work Load / 25 (h)

 

 

7.88

ECTS Credit of the Course

 

 

8