MATH129 SINGLE VARIABLE CALCULUS
| Course Code: | 2360129 |
| METU Credit (Theoretical-Laboratory hours/week): | 5 (4.00 - 2.00) |
| ECTS Credit: | 7.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Assoc.Prof.Dr. İBRAHİM ÜNAL |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course the students are expected to learn
- the meaning of limit and continuity
- the meaning of differentiability and how to apply it
- integration and its applications
- power series.
Course Content
Functions. Limits and Continuity. Tangent lines and derivatives. chain rule. Implicit differentiation. Inverse functions. Related rates. Linear approximations. Extreme values. Mean Value Theorem and its applications. Sketching graphs. Indeterminate forms and L` Hospital`s rules. Definite integral. Fundamental Theorem of Calculus. Substitution. Areas between curves. Formal definition of natural logarithm function. Techniques of integration. Improper integrals. Arc length. Volumes and surface areas of solids of revolution. Parametric plane curves. Polar coordinates. Arc length in polar coordinates. Sequences and infinite series. Power series. Taylor series and their applications.
Course Learning Outcomes
At the end of this course the students are expected
- To analyze functions using limits, derivatives, and integrals.
- To master differentiation and integration theory and techniques which are needed in various branches of sciences.
- Use various tests to determine series convergence, perform standard operations with convergent power series, find Taylor and Maclaurin representations.
- To utilize infinite series and use them for approximation.
- To be able to apply these theory and techniques to real life problems.
- To recognize the appropriate tools of calculus to solve applied problems
- To master mathematical reasoning and writing.