³ÉÈË´óƬ

Polynomials

Polynomials are used in Numerical Methods for approximating functions. It's good to have an understanding of how they behave. This lecture on Polynomials from the old MathsTrack bridging course will help you revise the behaviour of polynomials.

Taylor's theorem

Taylor's theorem is used in Numerical Methods to figure out errors in methods of approximation.Ìý

This seminar for Maths IB students in Summer Semester 2019 gave an intro into what Taylor series and Taylor polynomials are, then gave several examples of finding them and working with the error formula.

This revision seminar for Maths IB students from 2016 was specifically about the Taylor error formula.Ìý

Integration

Numerical Methods covers ways to approximate integrals for functions you don't know. This is based on the idea of an average value using integration. This lecture from the old MathTrackX bridging course introduces integration specifically from the perspective of average values, and may help you to revise your understanding of integration.

Matrices and row operations

Solving linear equations is something that is discussed in Numerical Methods, and row operations are an explanation for why some of the methods work. This revision seminar was given for students in Maths IA inÌý2014 andÌýcovers matrix operations and also using matrices to solve linear equations (the linear equations section begins at about 58 mins).

Orthogonal matrices are one of the tools that are used to help solve equations in Numerical Methods. This revision seminar was given for students in Maths IB in 2020 and begins with a section on orthogonal matrices.

Newton's method and Euler's method

One technique in Numerical Methods is Newton's Method (also known as the Newton-Raphson method). This revision seminar for Maths IB from 2016 coveredÌýthe use of Newton's method (and the bisection method) to find solutions of equations.

Euler's method is an approximate way to solve a specific kind of differential equation. In this revision seminar for Maths IM from Semester 2 2020, there was a section on Euler's method (starting at 35m).

The course Statistics & Numerical Methods was created in 2020. Before that was a course called Engineering Mathematics IIA, which included much of the same statistics content. The resources below were mostly created for Eng Maths IIA, but should be useful for making sense of the statistics content in Stats & Numerical Methods.Ìý

In 2022, David gave a revision seminar to Stats & Numerical Methods II students whose second part was about test statistics (starting at 1h6m50s).

In 2023, David gave a revision seminar to Stats & Numerical Methods II students whose second part was about choosing the right probability distribution, both for regular probability and for statistical tests (starting at 31m50s).

In 2021, David gave a revision seminar to Stats & Numerical Methods II students about the various hypothesis tests in the course that year, including the two chi-squared tests.

In 2019, David gave a revision seminar to Eng Maths IIA students with a section on choosing what stats test to use (the section starts at 1h2m).Ìý

In 2018, David gave a revision seminar on probability distributions to students in Eng Maths IIA. David discussed all of the distributions appearing in Eng Maths IIA in turn, including how to decide which distribution you want to use and how to use it. (Note the list of distributions may be a bit different in Statistics & Numerical Methods II.)

In 2017, David gave a revision seminar to Eng Maths IIA students with a part on linear regression (this part starts at 1h12m45s).

In 2016, David gave a revision seminar to Eng Maths IIA students with some details about statistics and probability. You may find some of the advice about choosing between hypothesis tests and choosing between probability distributions useful. (Note the list of hypothesis tests may be slightly different than that used in the new course.)

In 2012, David gave a revision seminar to students in Eng MathsÌýIIAÌýabout statistics and probability. He covered confidence intervals and assumption-checking for regression, some probability distributions, and some hypothesis testing. (Note the exam formula sheet used may be different to what is available in this course now, so be careful.):

Some methods for approximating integrals are the trapezoidal rule andÌýSimpson's rule, which used to be part of the Maths IA curriculum. This revision seminar was given for Maths IA students in 2017, and it contained a section on the trapezoidal rule and Simpson's rule and their errors (starting at 1h41m). (Note the error formulas might be a bit different to the ones in Stats & Numerical Methods, but the ideas are similar.)

The revision seminar for Statistics & Numerical Methods II in Semester 2 2022 started with discussion ofÌýusing Taylor's theorem for the errors in numerical derivatives (at the start), and then Simpson's rule (starting at 58m).

This revision seminar for Statistics & Numerical Methods II in Semester 2 2023 started with discussion on what Big O notation is trying to do, both with graphs and tables, and also with algebra.

In this revision seminar for Statistics & Numerical Methods II in Semester 2 2024, David discussedÌýstiff systems of differential equations (at the start), and then various error formulas and Taylor's theorem (starting at 23m5s).

• 4

2024

In Semester 2 2024, David discussedÌýstiff systems of differential equations (at the start), and then various error formulas and Taylor's theorem (starting at 23m5s).

• 4

2023

In Semester 2 2023, David discussed various aspects of Big O notation (at the start), and then how to choose which distribution you should use both in the wild and during hypothesis testing (starting at 31m50s).

2022

In Semester 2 2022, David discussed Taylor's theorem for the errors in numerical derivatives (at the start), and Simpson's rule (starting at 58m), and test statistics (starting at 1h6m50s).

2021

In Semester 2 2021, David gave a revision seminar to Stats & Numerical Methods II students about the various hypothesis tests in the course that year, including the two chi-squared tests.