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# Rationale and Purpose of the Module:

To develop, through an advanced mathematics module, a high level of numerate skills in chemical engineering problem solving.

# Syllabus:

Differential Calculus. L'Hopital's Rule and Power Series. Taylor and Maclaurin Series of a univariate function. Indefinite and Definite Integrals. Numerical integration techniques. Ordinary Differential Equations. Solution of linear, first, and higher order ODEs. Applications of first order ODEs in mass and energy balance calculations. Partial Differential Equations: boundary conditions, PDE classification scheme. Analytical solution of PDEs: separation of variables; variable transformation; integral transforms. Numerical solution methods. Applications of ODEs and PDEs in chemical engineering.

# Learning Outcomes:

## Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

On completion of this module the student will (will be able to): 1. given a real valued function of a real variable, find its limit, derivative, Taylor and MacLaurin series 2. given a power series, find its sum and interval of convergence 3. evaluate definite and indefinite integrals analytically and numerically 4. solve initial value problems for linear ordinary differential equations analytically, and general initial value problems numerically, and apply these techniques to solve mass and energy balance problems 5. classify 2nd order linear partial differential equations and solve them using separation of variables, variable transformation, integral transforms and finite difference methods. 6. Solve ordinary and partial differential equations arising in chemical engineering.

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# How the Module will be Taught and what will be the Learning Experiences of the Students:

Lectures and tutorials

# Prime Texts:

Loney, N.W., (2000) Applied Mathematical Methods for Chemical Engineers , CRC Press
Fanchi, J.R. (2000) Maths Refresher for Scientists and Engineers , Wiley

# Other Relevant Texts:

Kreyszig, E. (2004) Advanced Engineering Mathematics , Wiley

Autumn