## MATH1050 Calculus and Mathematical Analysis

### 10 creditsClass Size: 250

Module manager: Dr C. Molina-Paris
Email: c.molina-paris@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### Pre-requisite qualifications

A good A-level Mathematics grade or equivalent.

### This module is mutually exclusive with

 MATH1035 Analysis MATH1960 Calculus

This module is approved as an Elective

### Module summary

A module aimed mainly at Joint Honours students, but recommended as an elective.Because A-level and other entry courses differ in their syllabuses, this module revises differential and integral calculus before obtaining further results. There is an extensive study of complex numbers, including the definitions of elementary functions with complex values for the variable. The course contains an introduction to mathematical analysis, the subject which provides the proofs for calculus, in discussions of the limit of a sequence, the sum of an infinite series and techniques to determine whether a series has a sum.

### Objectives

To continue the study of Differential and Integral Calculus with some revision of A-level work, in order to provide a uniform background knowledge of the subject, and then to introduce some of the basic concepts of Mathematical Analysis. On completion of this module, students should be able to: (a) Calculate the derivatives and integrals of elementary functions. (b) Do arithmetic calculations with complex numbers, including calculation of nth roots. (c) Calculate limits of simple sequences; (d) Test series for convergence using standard tests. (e) Compute Taylor series. (f) Calculate partial derivatives of any order.

### Syllabus

1. Differentiation: Revision of methods of differentiation.
2. Hyperbolic functions and their inverses: Properties; derivatives.
3. Integration: Revision of methods of integration.
4. Complex numbers: Definition of complex numbers, De Moivre's Theorem; the logarithmic function.
5. Sequences: Definition of the limit of a sequence and calculation of limits; some basic theorems.
6. Infinite Series: Tests for convergence and absolute convergence of infinite series, radius of convergence of power series, differentiation and integration of power series.
7. Taylor's Series.
8. Partial differentiation.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 11 1.00 11.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 85.00 Total percentage (Assessment Exams) 85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated