# 2021/22 Undergraduate Module Catalogue

## MATH1050 Calculus and Mathematical Analysis

### 10 creditsClass Size: 255

**Module manager:** Frank Nijhoff**Email:** f.w.nijhoff@leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2021/22

### 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 | 11 | 1.00 | 11.00 |

Tutorial | 5 | 1.00 | 5.00 |

Private study hours | 84.00 | ||

Total Contact hours | 16.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### 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 |

Open Book exam | 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

### Reading list

The reading list is available from the Library websiteLast updated: 29/03/2022 15:20:26

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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