MAT 302 ANALYSIS II CA 2022
About this paper
MAT 302: Test II for MAT302 Analysis II, Department of Mathematics, Faculty of Science, University of Buea, 24 May 2022. Exercise 1: definitions of continuity, uniform continuity, pointwise/uniform convergence, fixed points and contraction maps, plus statements of the Uniform Cauchy Criterion, Weierstrass M-Test and Contraction Mapping Principle. Exercise 2: Lipschitz implies uniformly continuous, and f(x)=sqrt(x^2+1) on R being non-expansive with no fixed point, reconciled with the Contraction Mapping Principle. Exercise 3: Weierstrass M-Test application to a series on [1,infinity), and pointwise/non-uniform convergence analysis of x^2/(x^2+n) on [0,infinity) and on bounded subintervals.
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University of Buea
Faculty of Science - FS
Mathematics - MAT
ANALYSIS II
CA · Second Semester · Level 300
From this paper
- 1.
Define the following notions: continuous function, uniformly continuous function, pointwise and uniform convergence of sequences of functions, fixed point of a map, a contraction map. (6 marks)
- 2.
State without proof: Uniform Cauchy Criterion, Weierstrass M-Test Theorem, Contraction Mapping Principle. (6 marks)
At a glance
- Course code
- MAT302 (MAT 302)
- Type
- CA
- Year
- 2022
- Level
- Level 300
- Semester
- Second Semester
- Proposed solution
- Included
Where it's from
University
University of BueaFaculty
Faculty of Science - FSDepartment
Mathematics - MAT
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