To establish an appreciation and working knowledge of the premise that analytical (deterministic) and statistical tools are components of a larger integrated tool kit for addressing and evaluating multiple solutions to a variety of engineering-based problems.

Outline Syllabus

Functions:

a. Special functions (Sinc, Bessel, Error, Delta). b. Multivariate functions:

Partial derivatives, differentials, small increments, turning points & their classification when applied to general & specific (chemical/civil/electrical,/ndustrial/mechanical/medical) engineering problems.

Multiple integration, change of order, change to polar coordinates, applications to general & specific (chemical/civil/electrical/industrial/mechanical/medical) engineering problems

Linear algebra: eigenvalues and eigenvectors

Vector calculus: grad, div, curl & associated formulas

Laplace transforms:

a. Standard transforms, shift theorems, transforms of derivatives & integrals

b. Solution of ODEs including systems

c. Transforms of step, delta and periodic functions, convolution

Fourier analysis:

a. Fourier Series: Waves, representation of periodic functions by trigonometric series, half range series, complex form of the Fourier series, solutions of the two dimensional heat & wave equations.

b. Fourier transforms: periodic transforms, convolution

Statistics:

a. The engineering method & statistical thinking; data collection & presentation; modelling random behaviour; estimation & testing; building empirical models through linear regression analysis; design of engineering experiments; introduction to response surface methodology; application to statistical quality control & life data analysis.

Specific (chemical/civil/electrical/industrial/mechanical/medical) engineering applications & context will be explored.