MA1508: CALCULUS II (2017-2018)

Last modified: 25 May 2018 11:16

Course Overview

The aim of the course is to provide an introduction to Integral Calculus and the theory of sequences and series, to discuss their applications to the theory of functions, and to give an introduction to the theory of functions of several variables.

This provides the necessary mathematical background for further study in mathematics, physics, computing science, chemistry and engineering.

Course Details

Study Type	Undergraduate	Level	1
Term	Second Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	None.	Sustained Study	No
Co-ordinators	Professor Vassili Gorbunov

Qualification Prerequisites

Either Programme Level 1 or Programme Level 2

What courses & programmes must have been taken before this course?

MA1005 Calculus 1 (Studied)
Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

EG2005 Engineering Mathematics 2 (Studied)
MA1507 Introductory Mathematics 2 (Studied)
MA1515 Mathematics for Sciences (Studied)

Are there a limited number of places available?

Course Description

The course is a continuation of Calculus I from the 1st session. It develops the basic ideas concerning the integration of a function of one variable. It introduces Taylor series and determines these series for the most common functions. It also provides a first introduction to differential equations which are fundamental in applications of Mathematics to other sciences.

Syllabus

Convergence of limits and their calculation.
Definite and indefinite integrals.
Series and their convergence.
Convergence tests for series.
Power series and Taylor series.
Partial and directional derivatives.

Further Information & Notes

Course Aims

To further develop understanding of the concepts, techniques, and tools of calculus. Calculus is the mathematical study of variation. This course emphasises integral calculus, sequences and series, and introduces multivariable calculus. Applications to the theory of functions will be discussed.

Learning Objectives

By the end of this course the student should:

-be able to state the main definitions and theorems of the course;

-be able to apply appropriate techniques to compute definite and indefinite integrals;

-understand what it means for a sequence to converge;

-be able to compute the limits of many sequences;

-understand what it means for a series (infinite sum) to converge;

-be able to apply appropriate techniques to determine whether a series converges;

-understand how functions may be represented by power series; and

-understand the meaning behind partial and directional derivatives, and how to compute them.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (70%); in-course assessment (30%).

Resit: 1 two-hour written examination paper (maximum of (100%) resit and (70%) resit with (30%) in-course assessment).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.

Course Learning Outcomes