# 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.