# 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.

### Rapid summary

Relatively quick overview videos introducing some core topics:

• Laplace transforms video and notes (PDF, 531KB) - the basic signals.

• Inverse Laplace video and notes (PDF, 874KB) - partial fractions, tables and simple signals.

• Solving ODEs with Laplace video - low order examples.

## 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.

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### Section two: Complex numbers

What is a complex number and algebra with complex numbers. Includes exponential form and De Moivre's Theorem.

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### Section three: Logarithms and exponentials

Fluency with logarithms and exponentials is essential for handling many engineering scenarios.

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### Section four: Roots of polynomials

Students need to be skilled at moving between polynomial roots and the coefficients, and recognising patterns which facilitate estimation.

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### 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.

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### 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.

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### Section seven: Matrices and determinants

Fluency with matrices and vectors is essential for handling many engineering scenarios.

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### 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.

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### 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.

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