TYPE OF COURSE UNIT	Compulsory Course
LEVEL OF COURSE UNIT	Master's Degree Without Thesis
YEAR OF STUDY	-
SEMESTER	-
NUMBER OF ECTS CREDITS ALLOCATED	10
NAME OF LECTURER(S)	Assistant Professor Banu Aytar
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) An ability of numerical solution of ordinary and partial differential equations in the engineering problems. 2) An ability to apply knowledge of mathematics, science, and engineering 3) An ability to identify, formulate, and solve engineering problems 4) An ability to use the modern engineering techniques
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	None
COURSE DEFINITION	Systems of linear equations; linear vector spaces; theory of matrices and the eigenvalue problem; multivariable differential calculus; ordinary differential equations; vectors in R3; vector field theory, Fourier series and Fourier transform; Laplace transform; calculus of variations.
COURSE CONTENTS	WEEK TOPICS 1st Week Matrices, Operations on Matrices, Inverse Matrices 2nd Week Determinants, Vectors 3rd Week Gauss Elimination Method, Cramer?s Rule, Eigen Values, Eigen Vectors 4th Week Similar Matrices, Diagonalization, Ordinary differential equations 5th Week Ordinary differential equations 6th Week Maclaurin and Taylor series, power series solutions of ordinary differential equations 7th Week Bessel?s equation and Bessel?s Functions 8th Week Exam Week 9th Week Integral transformations; Laplace, Fourier, Hankel, Mellin Transformations. 10th Week Integral transformations; Laplace, Fourier, Hankel, Mellin Transformations. 11th Week Fourier Series 12th Week Complex numbers, Complex valued functions, Analytic functions, Cauchy-Riemann Equations 13th Week An introduction to partial differential equations; the method of separation of variables. 14th Week Variational Calculus, optimization.
RECOMENDED OR REQUIRED READING	Erwin Kreyszig, Advanced Engineering Mathematics, 10th Ed. Peter V. O Neil, Advanced Engineering Mathematics
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS	Lecture
ASSESSMENT METHODS AND CRITERIA	Quantity Percentage(%) Mid-term 1 30 Assignment 3 30 Total(%) 60 Contribution of In-term Studies to Overall Grade(%) 60 Contribution of Final Examination to Overall Grade(%) 40 Total(%) 100
ECTS WORKLOAD	Activities Number Hours Workload Midterm exam 1 2 2 Preparation for Quiz Individual or group work 16 8 128 Preparation for Final exam 6 7 42 Course hours 14 3 42 Preparation for Midterm exam 8 7 56 Laboratory (including preparation) Final exam 1 2 2 Homework 4 8 32 Total Workload 304 Total Workload / 30 10,13 ECTS Credits of the Course 10
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No