MA14310 Calculus 2
Introductory description
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.
Module aims
The principal aim is to develop Analysis in dimension 1, with much greater precision and rigour than the students had at school. While the highschool Analysis is focusing on problem solving methods, the universitylevel Analysis is switching the focus to the mathematical concepts and clarity of thought.
Outline syllabus
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.
 Differentiability
 Taylor's Theorem
 Taylor’s Series
 Riemann Integral
 Methods of integration
 Fundamental Theorem of Calculus
 Improper integrals
Learning outcomes
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)
View reading list on Talis Aspire
Subject specific skills
Calculus gives firstyear 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.
Transferable skills
Students will acquire key reasoning and problem solving skills, empower them to address new problems with confidence.
Study time
Type  Required 

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%) 
Total  100 hours 
Private study description
Working on assignments, going over lecture notes, text books, exam revision.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D
Weighting  Study time  

Assignments  15%  20 hours 
Inperson Examination  85%  38 hours 

Assessment group R
Weighting  Study time  

Inperson Examination  Resit  100% 
Feedback on assessment
Marked homework (both assessed and formative) is returned and discussed in smaller classes. Exam feedback is given.
Courses
This module is Core for:
 Year 1 of USTAG302 Undergraduate Data Science
 Year 1 of USTAG304 Undergraduate Data Science (MSci)
 Year 1 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 1 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 1 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 1 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics