Year:11/12
Department:Mathematics and Statistics
Level:Part I
Learning Hours:80
Credit Points:8
Weight:0.2
Course Convenor:Professor G Blower
Status:Live
Assessment Rules
back to top
CMod description
back to top
Sequences and series, ordinary and partial
differentiation, maxima and minima of functions, integration techniques,
multiple integrals, line integrals.
Curriculum Design: Outline Syllabus
back to top
Syllabus
Functions of a real variable, and their graphs;
Polynomials
Rational functions and partial fractions;
Exponential and hyperbolic functions;
Compositions and inverses;
Induction;
Sequences and limits;
Differentiation;
Product and Chain rules;
Maxima and minima;
Taylor series;
Definite integral as areas;
Fundamental theorem of calculus;
Integration by parts and by substitution.
.
Educational Aims: Subject Specific: Knowledge, Understanding and Skills
back to top
To provide the student with an understanding of functions, limits, and series, and a knowledge of the
basic techniques of differentiation and integration.
The purpose of this course is to study functions of a single real variable. Some of the topics will be
familiar from A-level, others will be studied more thoroughly in subsequent courses. The course begins
by introducing examples of functions and their graphs, and techniques for building new functions from
old. We consider rational functions and the exponential function. We then consider the notion of a limit, sequences and series. The main tools of calculus are then
introduced. The derivative measures the rate of change of a function and the integral measures the
area under the graph of a function. The rules for calculating derivatives are obtained form the
definition of the derivative as a rate of change. Taylor series are calculated for functions such as sin,
cos and the hyperbolic functions. We then introduce the integral and review techniques for calculating
integrals.
Curriculum Design: Select Bibliography
back to top
GILBERT, J. & JORDAN, C. (2002)
Guide to Mathematical Methods, Second Edition. Palgrave-Macmillan.
The library has copies of the earlier edition:
GILBERT, J. (1991)
Guide to Mathematical Methods. Macmillan.
EDWARDS, C.H. & PENNEY, D.E. (2002)
Calculus, Sixth Edition. Prentice Hall.
