This is a second stage mathematics module for first year level 8 engineering students. It builds upon the fundamentals to expand and develop the relevant mathematical understanding and methods. It develops a more comprehensive ability to apply mathematical concepts and methods to basic engineering problems.
Taylor’s Theorem. Mc Lauran’s series. Newton-Raphson methods.
Partial derivatives and applications; small increments, rate of change problems.
Integral calculus. Integration using partial fractions, completing the square, substitution techniques. Integration by parts, reduction formulae.
Numerical integration. Applications, area under a curve, volume of solids of revolution, length of a curve segment, centroids
Ordinary differential equations; analytical solutions of separable first order and linear first order differential equations; solution of homogeneous and non-homogeneous linear second order differential equations with constant coefficients. Applications.
The course is delivered through lectures and tutorials. A comprehensive set of lecture notes and tutorial sheets with solutions are provided each week. Lecture notes and supplementary material (past exam papers with solutions, links to useful websites, etc.) are also available online.
|Module Content & Assessment