Foundations of Calculus (U01476)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-2-FoC

Core second year course for Honours Degrees in Mathematics and/or Statistics.

Syllabus summary: Least Upper Bound axiom, sequences and series, convergence tests, limits and continuity, definition of derivative, Rolle's Theorem, Mean Value Theorem and applications, such as a positive derivative implies an increasing function. Real power series, radius of convergence, Taylor's Theorem.

Entry Requirements

? Pre-requisites : Passes at C-grade or better in MAT-1-PCa, MAT-1-SEq, MAT-1-GCo, MAT-1-GTh, or permission of the Head of the School of Mathematics

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Year 2), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
18/09/2007	12:10	13:00	Lecture Theatre A, JCMB	KB	1st Meeting

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	12:10	13:00	KB
Lecture	Friday	12:10	13:00	KB

? Additional Class Information : Tutorials: Th at 1110 and 1210.

Summary of Intended Learning Outcomes

1. Using straightforward epsilon methods to establish convergence/non-convergence of sequences.
2. Using the following tests to check convergence/non-convergence of series: comparison, ratio, root, integral, alternating series and understand absolute convergence.
3. Verifying limits of functions and check continuity using the epsilon-delta method.
4. Computing derivatives from first principles, and by manipulation rules.
5. Calculating the radius of convergence of a power series, and understand the possible behaviour at end points.
6. Performing simple proofs using epsilon-delta techniques.