A course of 44 lectures and 15 practice classes.
SYLLABUS (i) Dynamics. Fields of force. Celestial orbits. Aggregates of particles. Rigid bodies. Impulses.
(ii) One-dimensional continuum mechanics Characteristics. Waves on strings and rods. Equations of fluid flow. Sound waves. Flow in ducts.
BOOKS
Preliminary reading:
Readings from Scientific American, Mathematics in the Modern World, Freeman
Kline M Mathematics in the Physical World, Murray Peierls R E The Laws of Nature, Allen & Unwin Maxwell J C Matter and Motion, Dover
Vallentine H R Water in the Service of Man, Penguin Sutton 0 G Mathematics in Action, Bell
Mc-
144
Recommended for reference:
Sullen K E An Introduction to the Theory of Mechanics, Science Press or
Synge J L & Griffith B A Principles of Mechanics, McGraw-Hill Armit A P Advanced Level Vectors, Heinemann
EXAMINATION Two 2-hour papers.
200 LEVEL
201 PURE MATHEMATICS PART II (PASS)
A course of three lectures per week with practice classes throughout the year. Allocation to lecture groups will be listed on the notice boards of the Mathematics department in the week preceding first term.
SYLLABUS Complex functions. Exponential and related functions of a complex variable.
Differential equations. Applications of ordinary differential equations of the first and second orders.
Integrals. Infinite and improper integrals. Reduction formulae. Multiple integrals. Curvilinear and surface integrals.
Functions of several variables. Analytical geometry in space. Directional derivatives, differentiable functions, tangent planes, stationary points, Lagrange multipliers. Change of variables. Mappings. Jacoblans.
Linear Algebra. Linear transformations. Matrix algebra; partitioned mat- rices. Eigenvalues and eigenvectors. Diagonalization and the identification of quadric surfaces.
Convergence. Sequences and series. Comparison and ratio tests. Absolute and conditional convergence. Power series and their use in approximate calculations. Series solution of linear differential equations with variable coefficients.
Algebraic structure. Groups, rings, fields.
BOOKS
Background reading:
Sawyer W W Prelude to Mathematics, Pelican Courant R & Robbins H E What is Mathematics? OUP Polya G How to Solve it, Anchor
Pedoe D The Gentle Art of Mathematics, Pelican
Reid C Introduction to Higher Mathematics, Routledge & Kagan Paul Prescribed textbooks:
Maxwell E A Algebraic Structure and Matrices, CUP Spiegel M R Advanced Calculus, Schaum
Recommended for reference:
Thomas G B Calculus and Analytic Geometry, 4th ed Addison-Wesley Courant R Differential and Integral Calculus, 2 vols Blackie
Thomas G B Limits, Addison-Wesley
Green J A Sequences and Series, Routledge & Kegan Paul Cohn P M Linear Equations, Routledge & Kegan Paul Ledermann W Multiple Integrals, Routledge & Kagan Paul
EXAMINATION Two 3-hour papers. Class work and written work done during the year will be taken into account. ..
145
221 PURE MATHEMATICS PART II (HONOURS)
A course of four lectures per week, with practice class work and a pro- ject. The project is unit 227 (see below for details).
Pure Mathematics Il (Honours) may be taken by those who have ob- tained adequate honours in Pure Mathematics I, and by those with satis- factory passes in Pure Mathematics II (Pass), subject to the approval of faculty. Substantilally more than the quota number of students will be admitted provisionally in first term, but at the end of first term the class will be reduced to within the quota number, those who are found to be less suited to the subject moving to Pure Mathematics II (Pass). The lecturers will make this transition as smooth as possible for those involved.
Attention is drawn to the four-year courses for B.Sc. Hons on pages 222-223 headed School of Mathematics, School of Mathematical Statis- tics, and Combined School of Mathematics and Physics.
SYLLABUS (i) Project, see unit 227 for details. This project is to be done in the long vacation preceding the course; no lectures are given.
Intending students should obtain the instructions and exercises from the Mathematics department in December or January, before lectures begin, and should hand in their work complete not later than 31st March.
(ii) Analysis (about 45 lectures)
Convergence of sequences and series. Upper and lower limits.
Continuous and differentiable functions of one real variable.
Convergence of infinite and improper integrals.
Uniform convergence of series of functions. Power series.
Continuous and differentiable functions of several real variables. Multiple integrals.
(iii) Algebra and Geometry (about 30 lectures) Quadric surfaces. Envelopes.
Vector spaces. Linear transformations. Matrix algebra. Systems of linear equations. Characteristic polynomial. Quadratic forms.
(iv) Group theory (about 15 lectures)
Permutation groups. Normal sub-groups. Abelian groups.
BOOKS
Recomended for preliminary reading:
Courant R & Robbins H E What is Mathematics? OUP Sawyer W W Prelude to Mathematics, Pelican
Reid C Introduction to Higher Mathematics, Routledge & Kegan Paul Bell E T Mathematics, Queen and Servant of Science, McGraw-Hill Prescribed textbooks:
Ferrar W L Textbook of Convergence, OUP or
Hyslop J M Infinite Series, Oliver & Boyd Brand L Advanced Calculus, Wiley or
Fulks W Advanced Calculus, Wiley or
Olmsted J M H Advanced Calculus, Appleton or
Buck R C Advanced Calculus, McGraw-Hill 146
Murdoch D C or
Tropper A M Ledermann W
Linear Algebra for Undergraduates, Wiley Linear Algebra, Nelson
Finite Groups, Oliver & Boyd Recommended for reference:
Hall M Theory of Groups, Macmillan
Wielandt H Finite Permutation Groups, Academic Press Coxeter H S M Introduction to Geometry, Wiley
Hilbert D & Cohn-Vossen Geometry and the Imagination, Chelsea Kasner E & Newman J R Mathematics and the Imagination, Simon &
Schuster
Stabler E R Introduction to Mathematical Thought, Addison-Wesley Waismann F Introduction to Mathematical Thinking, Harper
EXAMINATION Two 3-hour papers. Class work and written work done during the year will be into account. Candidates who do not obtain honours may be credited with a pass in 201 Pure Mathematics Il.