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Unit information: Mathematics 1A20 in 2013/14

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Unit name Mathematics 1A20
Unit code MATH11004
Credit points 20
Level of study C/4
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Professor. Porter
Open unit status Open
Pre-requisites

'C' in A level in Mathematics, IB 6 Higher or equivalent

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description

This unit is designed for students with A-level mathematics who want a 20 credit-point unit on mathematical techniques. Students who wish to study further mathematics can take the follow on units of 1AS or 1AM.

Aims:

To consolidate, develop and extend the skills in single variable calculus introduced at A level.

Syllabus

The numbers of lectures (shown in brackets) are a rough guide only. 1.General introduction, Review of algebra and trigonometry. (2) 2.Functions and graphs: important examples, inverse functions. (2) 3.Sequences and series; limits of functions; continuous functions (3) 4.Exponential function; natural logarithm; hyperbolic functions (2) 5.Complex numbers; Argand diagram, polar form, complex exponential, complex roots (4) 6.Differential calculus, differentiability, basic methods, higher derivatives, Leibniz formula; differentiation of inverse functions (3) 7.Taylor approximations; Taylor series; convergence of the series; ratio test for power series; applications of Taylor series: maxima and minima; l'Hospital's rule for limits (4) 8.Integration: integrals as antiderivatives and as area; standard techniques; infinite integrands; infinite ranges of integration. (4) 9.Differential equations: 1st-order separable and first order linear differential equations. (2) 10.2nd order linear differential equations with constant coefficients, homogenous including simple harmonic motion, inhomogeneous including resonance. (4) 11.Full-range Fourier series in [-pi, pi]. (4)

Relation to Other Units

This unit is a prerequisite for the TB2 units 1AM/1AS.

Intended learning outcomes

After taking this unit, students should have a thorough grasp of one-variable calculus and complex numbers, including simple differential equations and Fourier Series.

Transferable Skills:

Mathematical techniques for application in the physical sciences.

Teaching details

The unit is based on lectures and tutorials on how to apply the techniques of the calculus in solving problems.

The lecturer will distribute problem sheets based on the work done in lectures, and will set specific problems which you will be required to hand in to tutors for marking. From week 2 or 3 of the course, students will attend weekly tutorials in which homework questions and additional problems will be covered.

Assessment Details

100% examination.

Reading and References

The following book is recommended, but it is not essential.

  • Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (4th edition), Oxford University Press, Oxford, 2008.

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