APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5101 Engineering Mathematics Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. MESUT EROL SEZER
Course Lecturer(s): Dr. Öğr. Üyesi CAVİT FATİH KÜÇÜKTEZCAN
Recommended Optional Program Components: None
Course Objectives: To equip the student with advanced topics of vector calculus and complex calculus.

Learning Outcomes

The students who have succeeded in this course;
The student will be able to understand differences and similarities of fundamental mathematical concepts as they apply to functions of a single variable or several variables, and to apply concepts of advanced calculus and complex calculus to engineering problems

Course Content

Vector differential and integral calculus, and applications. Complex calculus and applications. Fourier series and Fourier transform.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Review of single-variable calculus.
2) Functions of several variables. Partial derivatives, differentials, implicit functions, Jacobian.
3) Vector functions. Gradient, divergence, curl and Laplacian. Directional derivative.
4) Maxima and minima, Lagrange multipliers.
5) Multiple integrals. Line integrals, Green's theorem.
6) Surface integrals, the divergence theorem, Stoke's theorem.
7) Cylindrical and spherical coordinates.
8) Applications of vector calculus.
9) Functions of a complex variable. Continuity and differentiation.
10) Complex integration. Cauchy's theorem and integral formula.
11) Taylor and Laurent series. Poles and residues.
12) Conformal mapping and applications.
13) Fourier series.
14) Fourier transform.

Sources

Course Notes / Textbooks:
References: 1. D. Bachman, Advanced Calculus Demystified, McGraw-Hill, 2007.
2. F. J. Flanigan, Complex Variables, Dover, 1983.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 15 % 15
Homework Assignments 5 % 15
Midterms 1 % 30
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 7 98
Homework Assignments 5 5 25
Midterms 1 10 10
Final 1 15 15
Total Workload 190

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,