MATH251 ADVANCED CALCULUS I
| Course Code: | 2360251 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (4.00 - 0.00) |
| ECTS Credit: | 10.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
The students will learn
- the standard notions of differential calculus of several variables (limits, continuity, differentiability), the basic results (mean value theorem, inverse function theorem, implicit function theorem)
- the basic differences between calculus of one variable and the calculus of several variables
- the techniques of problem solving (extrema problems, geometric applications, approximation problems).
Course Content
Topology of R, R2 and R 3 . Functions of several variables; limits and continuity. Partial derivatives, directional derivatives, gradients. Differentials and the tangent plane: the Fundamental Lemma, approximations. The Mean Value, implicit and Inverse function theorems. Extreme values. Introduction to vector differential calculus: the gradient, divergence and curl. Curvilinear coordinates.
Course Learning Outcomes
- The students are expected to develop mathematical maturity at a level sufficient to provide proofs for abstract statements.
- The students will hopefully attain a good command of technical tools to solve concrete problems related to applications in geometry of curves and surfaces, approximations in several variables and extrema of functions of several variables.
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