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- MTH424: Convex Analysis (Spring 2024)
- vex hull and their properties, Best approximation theorem. Convex functions, Basic definitions, properties,
- MTH103: Exploring Quantitative Skills
- amentals of Geometry, Applications of Pythagorean theorem, Introduction to unit circles, trigonometric func
- MTH322: Real Analysis II (Spring 2023)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests
- MTH321: Real Analysis I (Spring 2023)
- sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emph... d uniform continuity of a function, prove various theorems about continuous functions and emphasize the pro... efine the derivative of a function, prove various theorems about the derivatives of functions and emphasize... accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the
- MTH321: Real Analysis I (Fall 2022)
- sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emph... d uniform continuity of a function, prove various theorems about continuous functions and emphasize the pro... efine the derivative of a function, prove various theorems about the derivatives of functions and emphasize... accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the
- MTH604: Fixed Point Theory and Applications (Fall 2022)
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- MTH321: Real Analysis I (Fall 2021)
- sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emph... d uniform continuity of a function, prove various theorems about continuous functions and emphasize the pro... efine the derivative of a function, prove various theorems about the derivatives of functions and emphasize... accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the
- MTH251: Set Topology
- write, in logical manner, proofs using important theorems and properties of metric spaces and topological ... present brief solutions based on definitions and theorems of topology. Students are expected not only to g... y continuous mappings. Pseudometrics. Fixed point theorem for metric spaces; Topological Spaces. Open bases... ces, Urysohn's Lemma; Compact spaces, Tychonoff's theorem and locall compact spaces, Compactness for Metric
- MTH322: Real Analysis II (Spring 2022)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests
- MTH322: Real Analysis II (Fall 2021)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests... (x)dx}$ is convergent. - State and prove Abel's theorem for infinite integral. - If $f(x)$ is bounded,
- MTH604: Fixed Point Theory and Applications (Spring 2021)
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- MTH321: Real Analysis I (Spring 2020)
- sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emph... d uniform continuity of a function, prove various theorems about continuous functions and emphasize the pro... efine the derivative of a function, prove various theorems about the derivatives of functions and emphasize... accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the
- MTH604: Fixed Point Theory and Applications (Spring 2020)
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- MTH633: Advanced Convex Analysis (Spring 2019)
- x sets, convex hull, their properties, separation theorems, hyperplane, Best approximation theorem and its applications, Farkas and Gordan Theorems, Extreme points and Polyhedral. Convex functions, Basic D
- MTH322: Real Analysis II (Spring 2019)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests