 MATHEMATICS (TURKISH, PHD) PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

# Course Introduction and Application Information

 Course Code Course Name Semester Theoretical Practical Credit ECTS MAT5101 Engineering Mathematics Spring 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