Difference between revisions of "MAT4223"

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* Tests for convergence of series of numbers
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Revision as of 06:07, 5 August 2020

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


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

Integration in Higher Dimensions: Jordan regions and Volume


Weeks 13 and  14
12.2

Riemann Integration on Jordan Regions in Higher Dimensions


Week 15
12.3

Iterated Integrals and Fubini's Theorem