The resources below revisit complex Maths topics included your STEM course. Watch the videos and work through the exercises to boost your knowledge and understanding. If you need to 'dig deeper', please check the Higher section on the previous page or if you are looking for something more specific, use "Ctrl+F" for a faster search.
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Differentiation
Differentiating sine and cosine from first principles
- Video: Proof of the derivative of sin(x) | Derivatives introduction
- Maths Centre Exercises and Solution Booklet on first principles
Standard derivatives
- Video: Basic Differentiation Rules For Derivatives
- HELM Exercises and Solution Booklet on standard derivatives
Chain rule
Product rule
- Video: The product rule
- Maths Centre Exercises and Solution Booklet on the product rule
- Interactive Exercises with Worked Solutions on the product rule
Quotient rule
- Video: Introduction to the quotient rule
- Interactive Exercises with Worked Solutions on the quotient rule
Trigonometry
Logarithms and exponentials
- Video: Derivative of 𝑒ˣ
- Maths Centre Exercises and Solution Booklet on logs and exponentials
- Maths Centre Exercises and Solution Booklet on Differentiating logs and exponentials
Higher-order derivatives
Stationary points
- Video:Maxima and minima
- Video: Points of inflection
- Video: Finding stationary points
- HELM Workbook on stationary points
Implicit differentiation
Parametric differentiation
- Video: Introduction to parametric equations
- HELM Exercises and Solution Booklet on parametric differention
Partial differentiation
Integration
Methods for integration
- Video: Integration by Parts
- HELM workbook: Integration by parts
- HELM workbook: Using a table of anti-derivatives
- Video: Introduction to u-substitution to find the anti-derivative of a functionHELM workbook: Integration by parts
- HELM workbook: Substitution
Specific functions
- Video: Using trig identities
- HELM workbook: Integration leading to logs
- HELM workbook: Trigonometric functions and integration
Multiple integrals
Series
Maclaurin's and Taylor's series
- Video: Taylor & Maclaurin polynomials intro
- HELM Exercises and Solution Booklet on Maclaurin's and Taylor's Series