MA143-10 Calculus 2
Mathematical Analysis is the heart of modern Mathematics. Calculus usually stands for Analysis, focused on calculations rather than proving theorems. This module is the second in a series of modules where the subject of Analysis is developed with a focus on calculations.
The principal aim is to develop Analysis in dimension 1, with much greater precision and rigour than the students had at school. While the high-school Analysis is focusing on problem solving methods, the university-level Analysis is switching the focus to the mathematical concepts and clarity of thought.
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
- Taylor's Theorem
- Taylor’s Series
- Riemann Integral
- Methods of integration
- Fundamental Theorem of Calculus
- Improper integrals
By the end of the module, students should be able to:
- learn differentiability, including higher derivatives and properties of differentiable functions
- develop the working knowledge of Taylor's series and theorem, ultimately understanding representability of a function by a power series
- develop general understanding of the construction of the Riemann integral
- understand and apply the fundamental properties of the integral such as integrability of continuous functions on bounded intervals or the Fundamental Theorem of Calculus
Indicative reading list
M. Hart, Guide to Analysis, Macmillan.
M. Spivak, Calculus, Benjamin. R.G Bartle and D.R Sherbert, Introduction to Real Analysis (4th Edition), Wiley (2011)
L. Alcock, How to think about Analysis, Oxford University Press (2014)
Subject specific skills
Calculus gives first-year undergraduates a first excursion in to pure mathematics. The students will gain a new perspective and a deeper understanding of familiar mathematics which they have seen in school (e.g. real numbers, functions and differentiation). In Calculus, these concepts are developed with mathematical rigour, which characterises much of university mathematics to follow.
Students will acquire key reasoning and problem solving skills, empower them to address new problems with confidence.
|Lectures||20 sessions of 1 hour (20%)|
|Online learning (independent)||9 sessions of 1 hour (9%)|
|Private study||13 hours (13%)|
|Assessment||58 hours (58%)|
Private study description
Working on assignments, going over lecture notes, text books, exam revision.
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
|In-person Examination||85%||38 hours|
Assessment group R
|In-person Examination - Resit||100%|
Feedback on assessment
Marked homework (both assessed and formative) is returned and discussed in smaller classes. Exam feedback is given.
This module is Core for:
- Year 1 of USTA-G302 Undergraduate Data Science
- Year 1 of USTA-G304 Undergraduate Data Science (MSci)
- Year 1 of UCSA-G4G1 Undergraduate Discrete Mathematics
- Year 1 of UCSA-G4G3 Undergraduate Discrete Mathematics
- Year 1 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
- Year 1 of USTA-Y602 Undergraduate Mathematics,Operational Research,Statistics and Economics