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