# CALCULUS - 2021/2

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

### Module provider

Mathematics

TURNER Matthew (Physics)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 95

Seminar Hours: 11

Guided Learning: 11

Captured Content: 33

Semester 1

None

## Module content

• Complex numbers, modulus, argument, exponential form, De Moivre's theorem, hyperbolic functions, roots of complex numbers.

• Exponential, logarithmic and trigonometric 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 and logarithmic.

• 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 of revolution.

• 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
Online Scheduled Summative Class Test ONLINE TEST 25
Examination Online ONLINE EXAM 75

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 002 Understand set notation and know the basic properties of real numbers C 003 Analyse and manipulate functions and sketch the graph of a function in a systematic way C 004 Differentiate functions by applying standard rules C 005 Obtain Taylor & Maclaurin series expansions for a variety of functions C 006 Evaluate integrals by means of substitution, integration by parts, partial fractions and other techniques C 007 Apply differentiation and integration techniques to a variety of theoretical and practical problems KT 008 Solve first order ordinary differential equations and second order ordinary differential equations with constant coefficients K 001 Understand complex numbers, how to manipulate them and be able to solve problems involving them. KC

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 complex numbers, 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.

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 with Music 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
Economics and Mathematics BSc (Hons) 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 2021/2 academic year.