# CALCULUS - 2017/8

Module code: MAT1030

Module provider

Mathematics

Module Leader

BARTUCCELLI M Dr (Maths)

Number of Credits

15

ECT Credits

7.5

Framework

FHEQ Level 4

JACs code

G100

Module cap (Maximum number of students)

N/A

Module Availability

Semester 1

Overall student workload

Independent Study Hours: 101

Lecture Hours: 34

Seminar Hours: 5

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Examination | EXAMINATION | 75% |

School-timetabled exam/test | IN-SEMESTER TEST | 25% |

Alternative Assessment

N/A

Prerequisites / Co-requisites

None

Module overview

This module introduces students to the most important techniques in Calculus. In particular the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide the fundamental tool for describing motion quantitatively. Tools and methods for differentiation and integration will be presented in detail. In addition linear first and second order differential equations will be studied and their importance for (partially) interpreting and understanding the world around us

Module aims

This module provides techniques, methods and practise in manipulating mathematical expressions using algebra and calculus, building on and extending the material of A-level syllabus.

Learning outcomes

Attributes Developed | |
---|---|

Understand set notation and know the basic properties of real numbers | C |

Analyse and manipulate functions and sketch the graph of a function in a systematic way | C |

Differentiate functions by applying standard rules | C |

Obtain Taylor & Maclaurin series expansions for a variety of functions | C |

Evaluate integrals by means of substitution, integration by parts, partial fractions and other techniques | C |

Apply differentiation and integration techniques to a variety of theoretical and practical problems | KT |

Solve first order ordinary differential equations and second order ordinary differential equations with constant coefficients | K |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Module content

Exponential, logarithmic, trigonometric and hyperbolic functions.

Properties and types of functions. Inverse, parametric and implicit functions .Limits.

Equations. Plane polar coordinates. Curve sketching. Transformation of curves.

Techniques of differentiation - parametric, implicit, logarithmic and partial derivatives.

Applications of differentiation. l’Hôpital’s rule.

Series and tests for convergence

Power series, manipulation and application. Taylor and Maclaurin series.

Techniques of integration; reduction formulae; arc length, areas of surfaces and volumes ofrevolution.

First order ODEs.Separation of variables. Integrating factor method. Homogeneous equations. Bernoulli equations. Initial value problems.

Second order linear ODEs with constant coefficients.

Methods of Teaching / Learning

The learning /teaching strategy is designed to:

A detailed introduction to differentiation, integration and ordinary differential equations with constants coefficients

Experience (through demonstration) of the methods used to interpret, understand and solve problems in calculus

The learning /teaching methods include:

3 x 1 hour lectures per week x 11 weeks, with written notes to supplement the module handbook and Q + A opportunities for students.

(every second week) 1 x 1 hour seminar for guided discussion of solutions to problem sheets provided to and worked on by students in advance.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

· Understanding of and ability to interpret and manipulate mathematical statements.

· Subject knowledge through the recall of key definitions, theorems and their proofs.

· Analytical ability through the solution of unseen problems in the test and exam.

Thus, the summative assessment for this module consists of:

One two hour examination (three best answers contribute to exam mark) at the end of Semester 1; worth 75% module mark.

One in-semester test; worth 25% module mark.

Formative assessment and feedback

Students receive written feedback via a number of marked coursework assignments over an 11 week period. In addition, verbal feedback is provided by lecturer/class tutor at biweekly seminars and weekly tutorial lectures.

Reading list

Reading list for CALCULUS : http://aspire.surrey.ac.uk/modules/mat1030

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.