Dive deeper into Calculus

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.

Enjoy your learning!

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

• Video: Chain Rule For Finding Derivatives
• HELM Exercises and Solution Booklet on the 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

• Video: Sin and cos
• Video: Tan and cot
• Video: Sec and cosec
• Video: Inverse trig functions

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

• Video: Second derivatives

Stationary points

• Video:Maxima and minima
• Video: Points of inflection
• Video: Finding stationary points
• HELM Workbook on stationary points

Implicit differentiation

• Video: Implicit differentiation
• HELM Exercises and Solution Booklet on implicit differentiation

Parametric differentiation

• Video: Introduction to parametric equations
• HELM Exercises and Solution Booklet on parametric differentiation

Partial differentiation

• Video: Introduction to partial derivatives
• Partial derivatives Workbook
• Stationary points Workbook

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 function HELM 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

• Video: Double integrals
• HELM workbook: Introduction to surface integrals
• Video: Volume integrals
• HELM workbook: Multiple integrals over non-regular regions
• HELM workbook: Volume 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

Fourier Series

• HELM Exercises and solutions on Fourier Series

Numerical methods

Numerical differentiation

• Video: Euler's method
• HELM Exercises and Solution Booklet on numerical differentiation

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