BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2002 | Analysis IV | Spring | 3 | 2 | 4 | 9 |
Basic information
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor SOHEIL SALAHSHOUR |
| Recommended Optional Program Components: | There is none. |
| Course Objectives: | The main objective of this course is to introduce the fundamental concepts of multivariable calculus and vector analysis. Advanced Calculus is one of the most useful of all mathematical tools, and this quarter we develop one of the basic concepts, the double integrals, and discuss its applications and consequences. The course begins with an introduction of double integrals, vector fields, line integrals. At the last stage of the course, some applications of flux integral and the triple integrals will be addressed. This course will conclude with an introduction to vector fields in 3D and surface integrals. The concept of line integrals in space and Stokes’ theorem is an essential part of advanced calculus and mathematics in general. |
Learning Outcomes
|
The students who have succeeded in this course; Will be able to calculate double integrals. Will be able to use change of variables in double integrals. Will be able to apply work and line integrals. Will be able to use Green’s theorem. Will be able to calculate triple integrals in rectangular and cylindrical coordinates. Will be able to solve surface integrals and flux. Will be able to translate real-life situations into the symbolism of mathematics and find solutions for the resulting models. |
Course Content
| In this course basic concepts of double integrals will be discussed. Double integrals in polar coordinates; change of variables in double integrals; work and line integrals; flux, Green’s theorem for flux; surface integrals; divergence theorem; Stokes’ theorem. |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Application of partial derivatives. | |
| 2) | Double integrals. Exchanging order of integration. | |
| 3) | Double integrals in polar coordinates; applications. | |
| 4) | Change of variables in double integrals | |
| 5) | Vector fields. | |
| 6) | Work and line integrals | |
| 7) | Line integrals continued | |
| 8) | Fundamental theorem of calculus for line integrals. | |
| 9) | Gradient fields and potential functions. Green’s theorem. | |
| 10) | Flux. Green’s theorem for flux. | |
| 11) | Simply connected regions. Triple integrals in rectangular and cylindrical coordinates | |
| 12) | Spherical coordinates; surface area. Vector fields in 3D; surface integrals and flux. | |
| 13) | Divergence theorem; applications and proof | |
| 14) | Line integrals in space, curl, exactness and potentials. Stoke's theorem. |
Sources
| Course Notes / Textbooks: | “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 020179131. |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Quizzes | 5 | % 15 |
| Midterms | 2 | % 45 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Application | 14 | 2 | 28 |
| Homework Assignments | 5 | 15 | 75 |
| Quizzes | 5 | 1 | 5 |
| Midterms | 2 | 10 | 20 |
| Final | 1 | 50 | 50 |
| Total Workload | 220 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |