# MA142-10 Calculus 1

Department
Warwick Mathematics Institute
Level
Roger Tribe
Credit value
10
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### 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 first in a series of modules where the subject of Anaysis 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 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.

##### 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.

• Real numbers
• Limits
• Series
• Continuity
• Uniform continuity
##### Learning outcomes

By the end of the module, students should be able to:

• develop deep understanding of the real numbers and the symbol `infinity'
• develop working knowledge of sequences and series, including limits, conditional and absolute convergence
• learn the properties of continuous and absolutely continuous functions

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.

##### 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 (48%)
Online learning (independent) 9 sessions of 1 hour (21%)
Placement 13 hours (31%)
Total 42 hours
##### Private study description

No private study requirements defined for this module.

## Costs

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
Weighting Study time
Assignments 15% 20 hours
In-person Examination 85% 38 hours
##### Assessment group R
Weighting Study time
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.

## Courses

This module is Core for:

• Year 1 of G302 Data Science
• Year 1 of G302 Data Science
• Year 1 of USTA-G304 Undergraduate Data Science (MSci)
• Year 1 of G4G1 Discrete Mathematics
• Year 1 of G4G1 Discrete Mathematics
• Year 1 of UCSA-G4G3 Undergraduate Discrete Mathematics
• Year 1 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• USTA-Y602 Undergraduate Mathematics,Operational Research,Statistics and Economics
• Year 1 of Y602 Mathematics,Operational Research,Stats,Economics
• Year 1 of Y602 Mathematics,Operational Research,Stats,Economics