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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