MATH213 CALCULUS III
| Course Code: | 2360213 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (3.00 - 2.00) |
| ECTS Credit: | 7.5 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of the course students are expected to:
Compute double integrals and use them to find certain areas and volumes. Use Rectangular, Cylindrical and Spherical Coordinates Systems to define space curves and surfaces in Cartesian and Parametric forms. Integrate functions of several variables. Examine vector fields and define and evaluate line integrals using the Fundamental Theorem of line integrals and Green’s Theorem; compute arc length. Define and compute the Curl and Divergence of vector fields and apply Green’s Theorem to evaluate line integrals. Compute surface integrals and flux integrals. Be able to use Stokes and Divergence theorems.
Course Content
Multiple integrals: Iterated integrals, Double Integrals, Triple Integrals, General change of variables. Double integrals in Polar coordinates, Triple integrals in Cartesian, cylindrical and spherical coordinates. Parametrization and orientation of curves. Line integrals. Independence of path, exact differentials, Greens Theorem. Parametrization and orientation of surfaces. Surface Integrals. Divergence and Stokes Theorems, applications
Course Learning Outcomes
By the end of the course, a student expect to learn the concepts of
- multivariable integration; double-triple integrals
- parametrization of lines and surfaces,
- line integrals and surface integrals,
- the concept of gradient, divergence and curl,
- some important theorems such as Green's, Stokes' and Divergence theorems.
Also a student should be able to do basic calculations related to the above concepts and be able to use above mentioned theorems.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution