## MATH1050 Calculus and Mathematical Analysis

### 10 creditsClass Size: 270

Module manager: Dr Evy Kersale
Email: E.Kersale@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

### Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.

### This module is mutually exclusive with

 LUBS1275 Mathematics and Statistics for Economics and Business 1A LUBS1285 Mathematics and Statistics for Economics and Business 1B MATH1005 Core Mathematics

This module is approved as a discovery module

### Module summary

Because A-level and other entry courses differ in their syllabuses, this module revises differential and integral calculus before obtaining further results which fall outside the core A-level syllabus (eg on hyperbolic functions).The differential calculus of functions of several variables is developed, also.

### 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.
- To extend differential calculus to functions of several variables, and functions defined by power series.

On completion of this module, students should be able to:
(a) calculate the derivatives and integrals of elementary functions;
(b) determine whether functions are injective, surjective, odd or even;
(c) compute Taylor series, compute the radius of convergence of a power series;
(d) calculate partial derivatives of any order, compute Taylor series of multivariate functions.

### Syllabus

1. Basic function terminology: domain, codomain, range, injectivity, surjectivity, odd and even functions.
2. Differentiation: Limits (informal), definition of the derivative, methods of differentiation, the Mean Value Theorem.
3. Hyperbolic functions and their inverses: Properties; derivatives.
4. Integration: The Riemann integral (informal), Fundamental Theorem of the Calculus, methods of integration.
5. Taylor's Series: Taylor's Theorem, power series, radius of convergence.
6. Partial differentiation: partial derivative of all orders, multivariate Taylor's series.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 5 1.00 5.00 Private study hours 84.00 Total Contact hours 27.00 Total hours (100hr per 10 credits) 111.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular example sheets.

!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

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

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

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

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