Chapter one
Mathematical skills
This chapter is on the theme of supporting mathematics that are needed for engineering problem solving, analysis, design and evaluation.
Core skills include
Laplace transforms
logarithms and exponentials
complex numbers
matrices
vectors
differentiation
integration
simultaneous equations
polynomials
roots
This list is not comprehensive but summarises what is available.
Sections in chapter one
Section one: Miscellaneous school leaver topics
Topics we expect engineering undergraduates to have mastered pre-arrival. Trigonometry, binomial expansions and logarithms.
Section two: Complex numbers
What is a complex number and algebra with complex numbers. Includes exponential form and De Moivre's Theorem.
Section three: Logarithms and exponentials
Fluency with logarithms and exponentials is essential for handling many engineering scenarios.
Section four: Roots of polynomials
Students need to be skilled at moving between polynomial roots and the coefficients, and recognising patterns which facilitate estimation.
Section five: Laplace transforms
We approach this as an engineer who needs to use the tool rather than giving a rigorous development which you would get in a mathematics course.
Section six: Inverse Laplace
Given a Laplace transform, this section explains how to extract the underlying signal both in fine detail and more quickly if only a characterisation is needed. It includes partial fractions which require skills with roots and polynomials.
Section seven: Matrices and determinants
Fluency with matrices and vectors is essential for handling many engineering scenarios.
Section eight: Differentiation
Differentiation and integration to the level you would expect from school leavers who studied mathematics. Reinforced in a year one engineering curriculum.
Section nine: Simultaneous equations
Beginning from the very basics, these videos build up concepts of linear equations and simultaneous equations. They then discuss methods, such as Guassian elimination, for solving them.