2017/2018, Semester 2

School of Continuing & Lifelong Edn (School of Continuing & Lifelong Edn)

Modular Credits: TCN1411 ( 4 ) / TC1411 ( 4 )

Limits of functions and sequences, types of limits, the sandwich theorem, evaluation of limits, continuity of functions, properties of continuous functions.

Definition of derivatives, physical meanings of derivatives in Chemical Engineering problems including rate of change, reaction rate, heat and mass flux, shear rate, rules and properties of derivatives, differentiation of transcendental functions, higher order derivatives, implicit differentiation, mean value theorem, indeterminate form, l’Hopital’s rule, curve sketching, extreme values and their applications in process design and optimization.

Integration as antidifferentiation, fundamental theorem of calculus, basic rules of integration, integration of polynomial, trigonometric, exponential and logarithmic functions, inverse functions, integration by substitution, integration by parts, Riemann sum, applications of integration in Chemical Engineering such as average flow rate, total yield and total flux in transport phenomena.

Geometric interpretation, continuity, partial derivatives, chain rule, directional derivatives, normal lines and tangent planes to surfaces, extrema of functions: concavity and convexity, multiple integrals.

Vectors, dot and cross products, vector identities, equations of lines and planes, applications in Chemical Engineering (e.g. heat transfer and mass transfer).

Curves, tangents and arc length, gradient, divergence and curl, line, surface and volume integrals, elementary treatment of Green’s theorem, divergence theorem, Stoke’s theorem, applications in Chemical Engineering (e.g. fluid mechanics and transport phenomena).

Matrix algebra, determinants, linear system of equations, matrix inversion, linear dependence and independence of vectors, basis and dimension, orthogonality, rank of a matrix, determinant and tensor of stress and strain, component mass balance in mixing, distillation, extraction and other unit operations in Chemical Engineering.

Formulation of mass balance equations into a matrix, properties of linear transformations, eigenvalues and eigenvectors, diagonalisation.