Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
180104004100	ENGINEERING MATHEMATICS	Compulsory	2	4	5

Level of Course Unit

First Cycle

Objectives of the Course

The aim of the course is to introduce students to the application areas of differential equations in engineering and their importance with examples. To present modern, concrete and field-specific examples and problem sets presented from nature and life in addition to theory in a language that the student can easily understand.

Name of Lecturer(s)

Prof. Dr. Halil Rıdvan Öz

Learning Outcomes

1	Will be able to formulate mathematical models of various problems.
2	Will be able to solve the model by using some analytical, qualitative and partial numerical methods.
3	They can determine the solution of a well-defined problem studied in the course.

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

no prerequisite

Recommended Optional Programme Components

no prerequisite

Course Contents

First order differential equations, higher order differential equations, vectors and 3-space, vector valued functions, partial derivatives, multiple integrals and integral calculus in vectors

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	General definitions; first order differential equations. separable equations. linear equations, mathematical models.
2	First order differential equations. Solution curves without solution, Euler's method.
3	Vectors in 2D space and Vectors in 3D space. dot product. vector multiplication.
4	Lines in 3D space. planes, cylinders and spheres. fourth-order surfaces
5	Vector-valued functions, calculus of vector functions, motion on a curve, curvature and acceleration.
6	Partial derivatives, multivariable functions, limit continuity, partial derivatives, linearization and differentials, chain rule.
7	chain rule, directional derivatives, tangent plane and normal line, extremums of multivariable functions, least squares method, lagrange multipliers.
8	Multiple integrals, double integrals, sequential integrals, calculation of double integrals, center of mass and moments, double integrals in polar coordinates.
9	Surface area, triple integrals.
10	triple int., variable replacement in multiple integrals in other coordinate systems.
11	Line integrals, curve integrals of vector fields, path independence, Green's theorem.
12	parametric surfaces and area, surface integrals, curl and divergence, stokes theorem, divergence theorem.
13	first order full diff. equations, homogeneous diff. equations, inhomogeneous linear equations.
14	mathematical models, power series solutions
15	midterm

Recommended or Required Reading

Calculus II Early Transcendentals. Dennis G. ZILL, Warren S. WRIGHT, Jones. 4th edition.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

no prerequisite

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	20	20
Final Examination	1	90	90
Homework	1	40	40
TOTAL WORKLOAD (hours)			150

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO1
LO2
LO3

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High