MATHEMATICS FOR ENGINEERS

MATH251

Course Code: MATH251
Semester: Third Term (Fall)
Theory+Practice: 3 + 1
ECTS: 5

Course Type

Compulsory Course

Course Level

Bachelor's Degree

Year of Study

Semester

Third Term (Fall)

ECTS

Name of Lecturer(s)

Associate Professor Müjdat Kaya

Learning Outcomes

At the end of this course, the students;

Increase the awareness of his mental potential and abilities; gain an ability to utilize a higher percentage the capacity of the mind via brain exercises.
Solidify the patterns of rational or mathematical (and therefore exact) thinking.
Have a knowledge with the Engineering Mathematics needed in diverse areas of science and technology in general, and specific areas of engineering in particular.
Acquire effective analytical thinking ability and study habits; and also deepen and widen his thought and vision.
Develop problem-solving skills.
Will be able to apply the Engineering Mathematics knowledge for solving science and engineering problems.
Acquire the ability of keeping up with the constantly changing science, technology and engineering methods.

Mode of Delivery

Face to face

Prerequisites

Yes(MATH152)

Recommended Optional Programme Components

Course Description

Systems of Linear Equations. Cramer's Rule. Gaussian Elimination Method. Gauss-Jordan Method. Matrices. Matrix Operations. Determinant of a Matrix. Properties of Determinants. Inverse of Matrix. Vectors in Rn. Linear Transformations. Matrix Representation of Linear Transformations. Change of Basis. Applications. Eigenvalues and Eigenvectors. Diagonalization of a Matrix. Double Integrals. Line Integrals. Line Integrals of Vector Functions. Path Independent Line Integrals. Potential Functions and Conservative Fields. Green's Theorem. Surface Integrals. Stokes' Theorem. Divergence Theorem. Complex Numbers. Arithmetic Operations of Complex Numbers. Polar Forms of Complex Numbers. Euler's Formula. Power and Root of a Complex Number. Analytic Functions.

Course Contents

WEEK	TOPICS
1^st Week	Systems of Linear Equations. Cramer's Rule. Gaussian Elimination Method. Gauss-Jordan Method.
2^nd Week	Matrices. Matrix Operations. Determinant of a Matrix.
3^rd Week	Properties of Determinants. Inverse of Matrix.
4^th Week	Vectors in Rn.
5^th Week	Linear Transformations. Matrix Representation of Linear Transformations.
6^th Week	Change of Basis. Applications. Quiz I.
7^th Week	Eigenvalues and Eigenvectors. Diagonalization of a Matrix.
8^th Week	Midterm Exam
9^th Week	Double Integrals. Line Integrals. Line Integrals of Vector Functions.
10^th Week	Path Independent Line Integrals. Potential Functions and Conservative Fields.
11^th Week	Green's Theorem. Surface Integrals. Stokes' Theorem.
12^th Week	Divergence Theorem. Quiz II.
13^th Week	Complex Numbers. Arithmetic Operations of Complex Numbers. Polar Forms of Complex Numbers.
14^th Week	Euler's Formula. Power and Root of a Complex Number. Elementary Functions on Complex Numbers.
15^th Week	Analytic Functions.

Recommended or Required Reading

Reference:
Thomas Jr., G.B., Weir, M.D., Hass, J.R., Giordano, F.R. Thomas' Calculus, 11th edition, Pearson, 2005.
Additional Resources:
Adams, R.A., Essex, C. Calculus a Complete Course, 7th edition, Pearson, 2010.
Kreyszig, E. Advanced Engineering Mathematics, 10th edition, Wiley, 2011.

Planned Learning Activities and Teaching Methods

Lecture
Questions/Answers

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	35
Quiz	2	20
Total(%)		55
Contribution of In-term Studies to Overall Grade(%)		55
Contribution of Final Examination to Overall Grade(%)		45
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	2	2
Preparation for Quiz	2	5	10
Individual or group work
Preparation for Final exam	1	45	45
Course hours	14	4	56
Preparation for Midterm exam	1	30	30
Laboratory (including preparation)
Final exam	1	2	2
Homework
Quiz	2	1	2
Total Work Load			147
Total Work Load / 30 (h)			4.9
ECTS Credit of the Course			5

Language of Instruction

English

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4	LO5	LO6	LO7
K1	X	X	X	X	X	X	X
K2
K3
K4
K5
K6
K7
K8
K9
K10
K11