| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2002 | Analysis IV | Spring | 3 | 2 | 4 | 9 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor SOHEIL SALAHSHOUR |
| 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. |
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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. |
| 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. |
| 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. | ||
| Course Notes: | “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. ISBN 020179131. |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 5 | % 15 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 45 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 14 | 2 | 28 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 0 | 0 | 0 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 5 | 15 | 75 |
| Quizzes | 5 | 1 | 5 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 10 | 20 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 50 | 50 |
| Total Workload | 220 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |