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 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

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Apply mathematical methods to solve problems in chemistry

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 (slow) 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 (prove it) and possibly higher order quadratures

15Polar, cylindrical, and spherical coordinates

16Optimisation. Methods using the objective function only (simplex)

17Multivariate integration – polar and spherical integrals

18Optimisation using gradients (steepest descents, conjugate gradients) and 2nd derivatives (Newton Raphson)

19Algebraic foundations of quantum theory I

20Matrix functions. Calculation of matrix exponentials, matrix inverse and other matrix functions.

21Algebraic foundations of quantum theory II

22Discretisation of Newton’s law of motion, molecular dynamics concepts, Verlet integrator algorithm for MD

23Partial differential equations

24Revision lecture

Teaching and learning methods

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.

Resources & Reading list

Textbooks

Gene H. Golub, Charles F. van Van Loan (1996). Matrix Computations. Johns Hopkins.

E. Steiner (2008). The Chemistry Maths Book. Oxford: OUP.

William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery. Numerical Recipes. Cambridge University Press.

P. Monk, L.J. Munro (2010). Maths for Chemists. Oxford: OUP.

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.

Repeat Information

Repeat type: Internal & External