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|IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE|
DEPARTMENTS OF MATHEMATICS & PHYSICS
ANCILLARY - MATHS & PHYSICS PART 1 (MPC1)
LECTURE COURSE INFORMATION
Client Department: CHEMISTRY
Chemistry Co-ordinator: Professor John Seddon
Lecture Course: MPC1 - Mathematics & Physics for Chemists Part 1
Year : First (c. 40 students)
Duration : Maths: 20 lectures+10 problem classes. Physics: 20 lectures +10 problem classes
Terms : Maths: Autumn (20+10) & Physics: Spring (20+10)
Lecturers : Maths: Dr O Makarenkov & Physics: Dr D Colling
AIMS : To introduce Mathematics and Physics as logical and structured disciplines; to introduce students to mathematical and physical techniques that will be of value to them as professional chemists.
OBJECTIVES: By the end of the MPC1 course, students will be able to:
COURSE TOPICS in chronological order are as follows:
TOPICS NUMBER OF LECTURES
1 Functions and Limits 4 AUTUMN TERM
2 Differentiation and Integration 6 AUTUMN TERM
3 Polar Coordinates 2 AUTUMN TERM
4 Sequences, Series, Expansions 4 AUTUMN TERM
5 Ordinary differential equations 4 AUTUMN TERM
6 Mechanics 7 SPRING TERM
7 Simple Harmonic Motion 6 SPRING TERM
8 Waves 7 SPRING TERM
(i) A weekly problem class/tutorial.
(ii) 6 Mathematics and 6 Physics problem sheets will be issued regularly.
SYLLABUS: Mathematics: Mathematical Methods
Functions: General properties (injective, surjective, even, odd, periodic, monotic, increasing and decreasing, inverse), intervals (open, closed), notation, plotting functions, discontinuities, limits and asymptotes.
Sequences and Series: Convergence, divergence, ratio test, geometric series, power series, radius of convergence, Taylor series expansions, remainder terms, L’Hôpital’s rule.
Differentiation and Integration: Definition, rules, stationary points, extrema, asymptotes, coordinate systems, partial differentiation, total differentials, practice of integration (partial fractions, substitution, integration by parts), improper integrals.
Ordinary Differential Equations: First order; separable, linear, integrating factor, homogeneous, exact, second order, trial solution, characteristic equation, particular integral, complementary function, applications.
SYLLABUS: Physics: Basic Mechanics, Vibrations and Waves
Mechanics: Linear mechanics, Newton’s Laws of motion, conservation of energy and momentum, classical scattering, motion in a potential field, conservative forces.
Rotational mechanics; angular momentum, torque, moment of inertia, central forces.
Simple Harmonic Motion (SHM): Undamped oscillations, effect of resistive forces, forced oscillations and resonance, coupled oscillations – elementary considerations.
Waves: One dimensional treatment of waves; differential form of the wave equation, velocity of waves in strings, gases and rods, wave superposition – standing waves and beating, group velocity and dispersion. Interference and diffraction; elementary considerations – optical interference from slits and X-ray diffraction.
Rubric: “Answer 4 questions from section A and 3 questions from section B. Use separate answer books for section A and section B. The same maximum mark is available for section A and section B.” The exam contributes 90% to the course assessment.
(ii) Coursework: Either a 1-hour progress test at the end of each term or an assessed question in each problem sheet or some combination of these, contributing 10% to the course assessment.
E. Steiner The Chemistry Maths Book, OUP, (Oxford, 2008)
M.C.R.Cockett & G.Doggett: Maths for Chemists Vol. I, Tutorial Chemistry Text 18, RSC, (Cam., 2003)
H.D.Young & R.A.Freedman: University Physics - International Edition, 11th Ed. (Addison Wesley, 2004)
H.J.Pain: The Physics of Vibrations and Waves, 6th Ed. (Wiley, 2005)
A.P.French & M.G.Ebison: Introduction to Classical Mechanics, (Van Nostrand Reinhold, 1986)
Autumn Term: Saturday 1 October to Friday 16 December 2011
Spring Term: Saturday 7 January to Friday 23 March 2012
Summer Term: Saturday 28 April to Friday 29 June 2012
Commemoration Day (no academic work): Wednesday 19th October 2011
AUTUMN TERM - Mathematics: Dr O. Makarenkov
SPRING TERM - Physics: Dr D. Colling
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