# Imperial college of science, technology and medicine

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IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE

DEPARTMENTS OF MATHEMATICS & PHYSICS

ANCILLARY - MATHS & PHYSICS PART 1 (MPC1)

LECTURE COURSE INFORMATION

## 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:

1. carry out simple manipulations of functions of one variable;

2. differentiate and integrate simple expressions of the elementary functions;

3. determine the Maclaurin expansions of simple functions and find intervals of convergence;

4. carry out calculations involving the differentiation of functions of two or more variables;

5. find analytic solutions of some first and second order ordinary differential equations;

6. carry out simple calculations in vector algebra;

7. understand the basic concepts of Newtonian mechanics and apply them in simple linear and rotational situations;

8. understand undamped, damped, forced and coupled oscillations and understand the concept of resonance;

9. understand basic concepts relating to waves and in particular the phenomena of interference and diffraction.

COURSE TOPICS in chronological order are as follows:

TOPICS NUMBER OF LECTURES

MATHEMATICS

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

PHYSICS

6 Mechanics 7 SPRING TERM

7 Simple Harmonic Motion 6 SPRING TERM

8 Waves 7 SPRING TERM

TUTORIAL ARRANGEMENTS

(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.

ASSESSMENT:

1. Examination: One 3-hour written examination in June in two sections: section A consists of 6 Mathematics questions and section B consists of 5 Physics questions. Section A questions are marked out of 15 and section B questions are marked out of 20.

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.

## RECOMMENDED TEXTS:

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)

2011/2012 TIMETABLE:

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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