Mathematical Methods in Chemistry II

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Learn and explain mathematical methods for scientists

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Apply mathematical methods to solve problems in chemistry

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Combine and implement numerical methods to numerically approximate solutions to problems in Chemistry

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Learn and use simple numerical methods for mathematical operations

1Vector and matrix spaces I – definitions and properties 2Variables (integer, real, etc.), programs and subroutines 3Vector and matrix spaces II – expansions and basis sets 4Intrinsic mathematical functions, combining these to compute new functions, outputting and plotting 5Vector and matrix spaces III – linear transformations 6Arrays, loops, vector addition and dot products, matrix multiplication 7Vector and matrix spaces III – eigensystems 8Matrix diagonalization, Jacobi method 9Fourier transform 10Discrete Fourier Transform in one dimension 11Multivariate integration – line integrals 12Discretisation. Numerical derivatives and error. 13Multivariate integration – multiple integrals 14Numerical integration, trapezium rule, Simpson’s rule and higher order quadratures 15Polar, cylindrical, and spherical coordinates 16Multivariate integration – polar and spherical integrals 17Optimisation using gradients (steepest descents, conjugate gradients) and 2nd derivatives (Newton Raphson) 18Algebraic foundations of quantum theory I 19Matrix functions. Calculation of matrix exponentials, matrix inverse and other matrix functions. 20Algebraic foundations of quantum theory II 21Discretisation of Newton’s law of motion, molecular dynamics concepts, Verlet integrator algorithm for MD 22Partial differential equations

Material will be delivered and supported in a number of ways. Some material will be provided in lectures supported by handouts, while other learning will take place in workshops which will support more extended practical exercises that will also form part of the assessment.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.