MATH250 ADVANCED CALCULUS IN STATISTICS
| Course Code: | 2360250 |
| METU Credit (Theoretical-Laboratory hours/week): | 5 (4.00 - 2.00) |
| ECTS Credit: | 9.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
The goal of the course is to familiarize the student with the conceptual as well as computational aspects of derivatives and integrals of functions of several variables, sequences and series of functions and more advanced topics like Riemann-Stieltjes Integral, Bounded Convergence and Riesz Representation Theorems.
Course Content
Review of Multidimensional Calculus. Derivatives of multivariable functions, continuity of multivariable functions. Fundamental Lemma for differentiability. Chain rule and Taylor`s Theorem for multivariable functions. Jacobian. Inverse and Implicit Function Theorems. Topology of R2 and R3. Riemann-Stieltjes Integral, integrability. Integrability of continuous functions, sequences of integrable functions. Bounded convergence and Riesz Representation Theorems. Theorems of Integral Calculus: Integration in Cartesian spaces. Improper and infinite integrals. Series of functions.
Course Learning Outcomes
Students are expected to understand and to be able to apply both theoretical and computational aspects of derivatives and integrals of functions of several variables, sequences and series of functions and more advanced topics like Riemann-Stieltjes Integral, Bounded Convergence and Riesz Representation Theorems.