Week 1
Introduction
Welcome to the course: who we are, how the sessions run, and how to get the most out of them.
Week 1
Graphs
Plotting and reading graphs, and transforming data to reveal linear and non-linear trends.
Week 1
Indices, logs, and exponentials
The laws of indices and logarithms, log plots, and the exponential function.
Week 1
Differentiation 1
Introduction and interpretation: gradients, derivatives from first principles, and curve sketching.
Week 1
Differentiation 2
Standard derivatives, and the product, chain and quotient rules.
Week 1
Differentiation 3
Differentiating exponentials and logarithms, and partial differentiation.
Week 1
Integration 1
Integration as area, definite and indefinite integrals, and integration by substitution.
Week 1
Integration 2
Integration by parts and by partial fractions.
Week 1
Complex numbers
Imaginary and complex numbers, arithmetic, and the polar form.
Week 2
Differential equations 1
What differential equations are, and solving them by separation of variables.
Week 2
Differential equations 2
From words to maths: forming differential equations, and second order equations.
Week 2
Differential equations 3
Steady states, mass action, and solving differential equations numerically.
Week 2
Linear algebra 1
Introduction to matrices, and solving simultaneous equations.
Week 2
Linear algebra 2
Singular matrices, null spaces, eigenvalues and eigenvectors.
Week 2
Systems of differential equations 1
Coupled linear systems, solved by elimination and diagonalisation.
Week 2
Systems of differential equations 2
Simplifying systems by rescaling, conservation and quasi-steady states; phase planes.
Week 2
Systems of differential equations 3
Steady states of nonlinear systems and their stability.