Description of Individual Course Units
Course Unit CodeCourse Unit TitleType of Course UnitYear of StudySemesterNumber of ECTS Credits
180104004100ENGINEERING MATHEMATICSCompulsory245
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)
Dr. Muhammet Raci AYDIN
Learning Outcomes
1Will be able to formulate mathematical models of various problems.
2Will be able to solve the model by using some analytical, qualitative and partial numerical methods.
3They 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
WeekTheoreticalPracticeLaboratory
1General definitions; first order differential equations. separable equations. linear equations, mathematical models.
2First order differential equations. Solution curves without solution, Euler's method.
3Vectors in 2D space and Vectors in 3D space. dot product. vector multiplication.
4Lines in 3D space. planes, cylinders and spheres. fourth-order surfaces
5Vector-valued functions, calculus of vector functions, motion on a curve, curvature and acceleration.
6Partial derivatives, multivariable functions, limit continuity, partial derivatives, linearization and differentials, chain rule.
7chain rule, directional derivatives, tangent plane and normal line, extremums of multivariable functions, least squares method, lagrange multipliers.
8Multiple integrals, double integrals, sequential integrals, calculation of double integrals, center of mass and moments, double integrals in polar coordinates.
9Surface area, triple integrals.
10triple int., variable replacement in multiple integrals in other coordinate systems.
11Line integrals, curve integrals of vector fields, path independence, Green's theorem.
12parametric surfaces and area, surface integrals, curl and divergence, stokes theorem, divergence theorem.
13first order full diff. equations, homogeneous diff. equations, inhomogeneous linear equations.
14mathematical models, power series solutions
15midterm
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 ActivitiesQuantityWeight
Midterm Examination1100
SUM100
End Of Term (or Year) Learning ActivitiesQuantityWeight
Final Examination1100
SUM100
Term (or Year) Learning Activities40
End Of Term (or Year) Learning Activities60
SUM100
Language of Instruction
Turkish
Work Placement(s)
no prerequisite
Workload Calculation
ActivitiesNumberTime (hours)Total Work Load (hours)
Midterm Examination12020
Final Examination19090
Homework14040
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
LO1
LO2
LO3
* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High
 
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