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|IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE|
DEPARTMENTS OF MATHEMATICS & PHYSICS
ANCILLARY - MATHS & PHYSICS PART 2 (MPC2)
LECTURE COURSE INFORMATION
Client Department: CHEMISTRY
Chemistry Co-ordinator: Professor John Seddon
Lecture Course: MPC2 - Mathematics & Physics for Chemists Part 2
Year : Second (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: Prof. N. Bingham. Physics: Dr. J. Pasternak (QM) and Dr. D. Eakins (EM)
AIMS : To continue Mathematics and Physics as logical and structured disciplines; to introduce students to further mathematical and physical techniques that will be of value to them as professional chemists.
OBJECTIVES: By the end of the MPC2 course, students will be able to:
COURSE TOPICS in chronological order are as follows:
TOPICS NUMBER OF LECTURES
1 Inhomogeneous ODEs 3 AUTUMN TERM
2 Complex Numbers 2 AUTUMN TERM
3 Partial differential equations 4 AUTUMN TERM
4 Linear Algebra 4 AUTUMN TERM
5 Fourier methods 4 AUTUMN TERM
6 Field theory 3 AUTUMN TERM
7 Quantum mechanics 10 SPRING TERM
8 Electricity and Magnetism 10 SPRING TERM
(i) A weekly problem class/tutorial.
(ii) 6 Maths and 6 Physics problem sheet will be issued regularly.
SYLLABUS: Mathematics: Mathematical Methods
1. Inhomogeneous Ordinary Differential equations:
Variation of one parameter and Green function methods.
2. Complex numbers:
Algebraic properties and geometrical interpretation, polar representation, de Moivre’s theorem, functions.
3. Partial differential equations:
Separation of variables, application to Wave, heat-conduction, Laplace’s and Schroedinger’s equations, use of polars and spherical harmonics.
4. Linear Algebra:
Solution of sets of simultaneous linear equations by Gaussian elimination, Eigen problems and diagonalisation of matrices. Cayley-Hamilton theorem.
5. Fourier series and transforms:
Standard formulae for Fourier series of periodic functions, role of symmetry, convergence and the Gibbs’ phenomenon, Parseval’s theorem and applications. Standard formulae for Fourier transforms of non-periodic functions, basic introduction and application to signal processing.
6. Vector Field theory:
Calculus of scalar and vector fields, introduction and physical interpretation of the basic operators - div, grad and curl, Integral theorems (if time permits).
SYLLABUS: Physics: Quantum Mechanics
1. The Schrodinger Equation:
Meaning of H, probabilities, the quantum description of a particle.
2. One dimensional problems:
The wave equation, wavepackets, superposition, potential steps and wells. Particle in a box, simple harmonic oscillator.
3. Postulates of quantum mechanics:
Uncertainty relations, Hermitian operators, mathematical properties of the wavefunction.
4. Three dimensional problems:
Spherical coordinates and separation of variables, angular momentum.
5. The hydrogen atom:
The radial equation, quantum numbers, hydrogen and the periodic table.
6. Two electron systems:
Pauli exclusion and spin, helium and the H2 molecule.
SYLLABUS: Physics: Electricity and Magnetism
1. Electric fields (4 lectures)
Charges and currents, Coulomb’s Law, electric fields, electric flux, Gauss’s Law, electric potential, circuital law, differential forms of Gauss’s law and circuital law, electric dipoles
2. Electric properties of materials (2 lectures)
Capacitance, energy stored in electric field, dielectrics, dipoles, classical hydrogen atom, types of electrostatic bonding
3. Magnetic fields (2 lectures)
Magnetic force, motion of particles in magnetic fields, motors, MRI, Ampere’s Law, magnetic materials, mass spectrometer
4. Maxwell’s equations and electromagnetic waves (2 lectures)
Faraday’s law, Induction, Displacement current, Maxwell’s equations, the wave equation, electromagnetic waves
Extra suggested reading title:
"Foundations of Physics for Chemists", Ritchie & Sivia, 6th Ed. (Oxford University Press, 2000)
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.
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