Mathematical refresher and preliminaries (~5h)

Note: The overheads are available here for download.

The first module of the course is optional and delivered as "online-only" material. It refreshes elementary mathematical concepts, which you should already be familiar with from high-school and from the first years of your undergraduate training. It also introduces preliminary math tools, which will become relevant during the second part of the course.

Videos and learning material have been made available to you in advance, for your self-paced independent learning. A total of 5 hours have been booked on the course calendar during the first week, so that you do have official scheduled time to watch and study the videos, and play with the interactive examples.

Below you find the table of content, with the individual videos. Note that videos have been "split" into three parts (i.e. part A, part B, and part C), and further decomposed in smaller "bits" you should be able to digest easily.

Part A: mathematical functions

• Pluto.jl interactive notebook on Math Functions

Functions and their graph

Adding a constant or multiplying by a constant

Notable functions: straight lines, exponentials, and logarithms

Part B: Derivatives and Integrals

Intuition for derivatives and elementary functions

Indefinite and definite integrals

Part C: Mathematical Preliminaries

The Dirac's Delta-function

The Convolution Integral

Trains of Deltas and the Sampling of a function

Algebraic versus differential equations

The inhomogenous case

Numerical solutions

• Pluto.jl interactive notebook on the Euler's method

The Euler's forward method

Taylor's expansion and comparison with the analytical solution

Resources and Links

• Khan academy on Calculus

• Plotting functions on the web

• Infinite powers (book)

• Joy of X (book)

• Calculus for Dummies (book)

• Calculus for Dummies 2 (book)

• Statistics for terrified biologists (book)