Information Package / Course Catalogue
Advanced Maths
Course Code: FEK525
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 5
Objectives of the Course

The sequence Math 1001-1002 is the standard complete introduction to the concepts and methods of calculus. It is taken by all engineering students. The emphasis is on concepts, solving problems, theory and proofs. Students will develop their reading, writing and questioning skills in Mathematics.

Course Content

To be able to develop advanced math skills

Name of Lecturer(s)
Lec. Mesut ÇAKIR
Learning Outcomes
1.Define the sequence of partial sum for an infinite series and relate the convergence of this sequence to the convergence of the series. Then find or estimate the sum.
2.Find the interval and radius of convergence for a given power series.
3.Understand and identify vectors in the plane and in the three dimensional space.
4.Find the total differential of a function of several variables and use it to approximate incremental change in the function.
5.Do simple manipulations involving gradient, divergence, and curl, and understand their geometrical/physical meaning
Recommended or Required Reading
1.Thomas Calculus (12th Edition), George B. Thomas, Maurice D. Weir, Joel Hass, 2010
Weekly Detailed Course Contents
Week 1 - Theoretical
Infinite series; Convergence tests for positive series; Power series, Taylor and Maclaurin series
Week 2 - Theoretical
Quadratic forms(Conic Sections)
Week 3 - Theoretical
Vectors and coordinate geometry in three dimensional space Analytic geometry in three dimensions, Plane, lines, and quadratic surfaces
Week 4 - Theoretical
Functions of several variables; Limits and continuity
Week 5 - Theoretical
Partial derivatives; Higher-order derivatives, The chain rule
Week 6 - Theoretical
Partial derivatives; Higher-order derivatives, The chain rule
Week 7 - Theoretical
Linear approximation; Gradients and directional derivatives, Implicit functions
Week 8 - Intermediate Exam
Mid-term
Week 9 - Theoretical
Extreme values; Extreme values of functions defined on restricted domains
Week 10 - Theoretical
Lagrange multipliers; Multiple integration; Double integrals, iteration of double integrals in Cartesian- Coordinates
Week 11 - Theoretical
Surface area using by double integrals; Double integrals in Polar Coordinates
Week 12 - Theoretical
Vector and scalar fields; Line integrals
Week 13 - Theoretical
Conservative fields
Week 14 - Theoretical
Surface integrals; Green s theorem, divergence theorem, and Stokes s theorem.
Week 15 - Theoretical
Surface integrals; Green s theorem, divergence theorem, and Stokes s theorem.
Week 16 - Final Exam
Final
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142370
Individual Work72228
Midterm Examination110111
Final Examination115116
TOTAL WORKLOAD (hours)125
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
OÇ-1
4
3
2
5
3
2
5
2
3
OÇ-2
2
3
2
3
2
5
3
2
3
OÇ-3
4
3
3
3
4
2
3
4
3
OÇ-4
3
4
3
3
4
2
5
2
3
OÇ-5
3
4
3
4
3
2
2
3
4
Adnan Menderes University - Information Package / Course Catalogue
2026