## MATH1960 Calculus

### 10 creditsClass Size: 200

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### Pre-requisite qualifications

A good grade in A-level Maths or equivalent.

### This module is mutually exclusive with

 MATH1400 Modelling with Differential Equations MATH1460 Mathematics for Geophysical Sciences 1 MATH1932 Calculus, ODEs and Several-Variable Calculus

This module is approved as an Elective

### Module summary

Since calculus is an essential tool in many areas of mathematics, the first part of this module aims to review and consolidate the calculus covered in the core A-level syllabus. The module also introduces hyperbolic functions which are not in the A-level core, but are covered in some A-level modules. The module then goes on to develop the calculus of several variables and shows how this can be used to determine the local behaviour of functions of several variables.

### Objectives

By the end of this module, students should be able to:
a. Differentiate simple functions and determine the location and nature of turning points.
b. Compute the Taylor series of functions of one variable.
c. Use a variety of methods to integrate simple functions;
d. Employ several variable calculus to determine the local properties of functions of two variables.

### Syllabus

1. Functions and their inverses: Exponential, trigonometric and hyperbolic functions and their inverses. Graphs. Addition formulas.
2. Differentiation. Definition as slope of tangent to curve. Review of basic rules of differentiation. Implicit differentiation, Chain rule. Maxima and minima. Taylor series.
3. Integration. Definite and indefinite integrals. Techniques of integration (substitution, integration by parts, reduction formulas, partial fractions).
4. Functions of several variables. Partial derivatives. Directional derivatives. Multivariable chain rule. Change of variables. Higher order derivatives. Implicit differentiation.
5. Stationary points of functions of two variables. Conditions for a stationary point. Criteria for maxima, minima and saddle points.
6. Gradients of scalar functions. Tangent planes.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 21 1.00 21.00 Tutorial 11 1.00 11.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

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

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

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 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