Maths & Physics

General Advice for Maths & Physics:

1. Focus on understanding the concept rather than knowing the jargon, notation or mechanics of solving the problem

Understanding will stick with you longer.

2. Treat mathematics and physics like tools

They’re your tools of design. More about this over on the General Advice page.

Subject Specific Pro-Tips:

Mathematical Modelling 1:

Before attempting this course you should be comfortable with: algebra, logarithms, plotting functions and have an intuitive understanding for what differentiation and integration are.

Continuous, consistent effort and asking questions will bring the most results.

Mathematical Modelling 2:

In the early weeks, you should become well practiced in:

  • Basic matrix algebra, e.g. the do’s and don’ts
  • Integration and differentiation skills and techniques
  • Data description – both qualitative and quantitative
  • Hypotheses and their relationship to inference: null hypothesis and alternative hypothesis

This is because you’re doing Linear Algebra, Multi-Variable Calculus, Probability & Statistics and these topics will build on these skills.

Become familiar with Minitab and do work at as constant of a rate as you can manage throughout the semester.

The statistics is heavily word-based and you should get in the habit of reading questions carefully to ensure that you apply the correct technique.

Physical Modelling:

Knowing algebra is one thing, applying it to a problem that involves a real-life scenario is a separate thing. The skill will only develop with practice and having the underlying competency that the tool (i.e. the mathematics involved) requires.

A general (albeit not always applicable) model for solving a physics problem is:
Determine the Physical Law/equation involved in the question → master the maths underlying the Physical Law → model the law onto the circumstance → simplify the maths → solve

Advanced Mathematics & Physics

Spend a significant amount of time on the tutorial problems for the math side of the course. They’re well designed and brought me many ‘ah-ha’ moments.

Pick up your first-year physics textbook and read about wave functions (Chapter 39 of Fundamentals of Physics by Halliday & Resnick 10th Ed). You need a good conceptual understanding to really be bothered.

Resources:

Khan Academy on Multi-variable Calculus:

There is a lot of content here. In an ideal world, you would be able to go through it all sequentially, the advice instead is to filter what is there and to use the resources to assist you in what you’re currently trying to figure out.

Khan Academy on Linear Algebra:

Again, a lot here. Filter it down to what you need.

Graphing Website:

2D graphing only, but if you add a letter that is other than x or y you can create a ‘slider’ to allow you to see what happens when that “constant” varies.

Graphing Software:

If you’re on a Mac there’s software called ‘Grapher’ that comes pre-installed that has 2D and 3D graphing abilities. Super handy for visualising what you’re doing and checking your answers are right re: maxima and minima.

The Maths & Science Study Centre (CB04.03.331):

In building four there’s a staffed facility where graduate students and academics have posted times that they’ll be around to answer questions. Make use of it, it’s an amazing asset you won’t have access to once you’re not at university anymore.

Wavefunctions:

Chapter 39 of Fundamentals of Physics by Halliday & Resnick 10th Ed.