MAT4223

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1	7.1	Uniform Convergence of Sequences of Functions	Convergence of sequences of numbers, Cauchy criterion Limits of functions, continuity, differentiability, Riemann integrability
Week 1	7.2	Uniform Convergence of Series of Functions	Convergence of series of numbers
Week 2	7.3 and 7.4	Power Series and Analytic Functions	Tests for convergence of series of numbers Taylor expansion formula
Week 2	7.5	Weierstrass Example	Uniform Convergence of Sequences of Functions
Week 3	8.1 and 8.3	Euclidean Spaces: Algebraic Structure and Inner Product
Week 3	8.2 and 8.3	Linear Tranformations
Week 3	8.3 and 8.4	The Topology of Higher Dimensions: interior, closure and boundary
Week 4	9.1 and 9.2	Limits of Sequences in Higher Dimensions
Week 4	8.3 and 8.4	The Bolzano-Weierstrass Theorem and The Heine-Borel Theorem
Week 5	9.3 and 9.4	Limits of Functions
Week 5	9.3 and 9.4	Continuous Functions
Week 6	11.1	Partial Derivatives and Integrals
Week 7	11.2, 11.3 and 11.4	Differentiation in Higher Dimensions
Week 7	11.2, 11.3 and 11.4	Rules for Differentiation in Higher Dimensions
Week 8	11.5 and 11.6	Mean-Value Theorems
Week 8	11.5 and 11.6	Taylor's Formula in Higher Dimensions
Weeks 8 and 9	11.6	The Inverse Function Theorem
Week 10	9.6	Lebesque theorem for Riemann Integrability on the Real Line
Weeks 11 and 12	12.1
Weeks 13 and  14	12.2	Riemann Integration on Jordan Regions in Higher Dimensions
Week 15	12.3	Iterated Integrals and Fubini's Theorem