# CALCULUS - 2020/1

Module code: MAT1030

## 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

Mathematics

### Module Leader

TURNER Matthew (Maths)

## Overall student workload

Independent Learning Hours: 101

Lecture Hours: 44

Seminar Hours: 5

Semester 1

None

## 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.

• Power series, manipulation and application; l’Hôpital’s rule. 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.

• Second order linear ODEs with constant coefficients.

## Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 75
School-timetabled exam/test IN-SEMESTER TEST (50 MINUTES) 25

N/A

## 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.

## 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 001 Understand set notation and know the basic properties of real numbers C 002 Analyse and manipulate functions and sketch the graph of a function in a systematic way C 003 Differentiate functions by applying standard rules C 004 Obtain Taylor & Maclaurin series expansions for a variety of functions C 005 Evaluate integrals by means of substitution, integration by parts, partial fractions and other techniques C 006 Apply differentiation and integration techniques to a variety of theoretical and practical problems KT 007 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

## 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:

• 4 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.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: MAT1030

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module

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 2020/1 academic year.