Real Analysis 2

, Real Analysis 2

MTH2301 Introduction to Real Analysis

3 hours One requisite

1 Differentiation on : / Review on Limits, continuity, Uniform continuity. / Derivative and Examples. Intermediate value Theorem / Rolle's Theorem and The Mean Value Theorem, Convex Functions , L’Hospital’s Rule, Taylor’s Theorem on

2 Riemann Integration on : The Riemann–Darboux Integral, Properties of the Integral , Evaluation of the integral, Stirling’s Formula, Integral Mean Value Theorems, Improper Integrals, A Deeper Look at Riemann Inerrability

3 Sequences and Series of Functions: / Review on numerical Infinite Series / Convergence of Sequences of Functions, Properties of the Limit Function, Convergence of Series of Functions, Uniform convergence and differentiation. Examples of uniform convergence Power Series

4 Others: Quizzes, Revision and Activities, Exam …

1.1 Mapped to: K1, k2

Have knowledge and understanding on the basics of continuity and differentiability concepts as well as series, sequences and their convergences

Teaching Strategy Lectures

Assessment Methods Homework, periodic and final exams

2.1 Mapped to: S1

Apply mathematical reasoning to analyze the continuous and the uniformly continuous functions

Teaching Strategy Lectures, Individual or group work