Next steps for STEM Subjects

These resources cover more advanced topics which may be useful to students on STEM courses.

On

Algebra

  Video Written Resource Exercises

Partial fractions

     
Partial fractions Introduction to partial fraction expansion Booklet See Written Resource

Complex Numbers

     
Complex arithmetic

Adding and subtracting

Multiplying

Complex conjugates and dividing

   
Exponential form   HELM Workbook See Written Resource
Complex arithmetic

Adding and subtracting

Multiplying

Complex conjugates and dividing

   
Exponential form   HELM Workbook See Written Resource
Modulus-argument form

Finding modulus and argument

Writing in the modulus-argument form

Workbook See Written Resource
De Moivre's theorem and roots of complex numbers   HELM Workbook See Written Resource

Sequences and series

     
Sequences and series   Booklet See Written Resource
Infinite series   Booklet See Written Resource
Power series   Booklet See Written Resource
Binomial series   Workbook See Written Resource

Binomial theorem

     
Binomial theorem Pascal's triangle and binomial expansion Workbook See Written Resource

Numerical Methods

     
Interval Bisection Video Webpage  
Iteration      
Newton Raphson Method Video Written Resource See Written Resource

Conic Sections

     
Conic Sections   HELM Booklet See Written Resource

Polar Coordinates

     
Introduction   HELM Booklet See Written Resource
Parametric Equations   HELM Booklet See Written Resource

Calculus

  Video Written Resource Exercises

Differentiation

     
Differentiating sine and cosine from first principles   Workbook  
Standard derivatives   Workbook  
Chain rule Introduction to chain rule Workbook  
Product rule   Workbook Exercise
Quotient rule Introduction to the quotient rule   Exercise
Differentiation and trigonometry

Sin and cos

Tan and cot

Sec and cosec

Inverse trig functions

   
Differentiation with logs and exponentials  

Differentiation by taking logs

Differentiating logs and exponentials

 
Higher-order derivatives Second derivatives    
Stationary points

Maxima and minima

Points of inflection

Finding stationary points

HELM Workbook  
Implicit differentiation

Implicit differentiation

Workbook  
Parametric differentiation Introduction to parametric equations Workbook  
Partial differentiation Introduction to partial derivatives

Partial derivatives Workbook

Stationary points Workbook

 

Integration

     
Methods for integration

Parts

Substitution

HELM workbook: Using a table of anti-derivatives

HELM workbook: Integration by parts

HELM workbook: Substitution

 
Integration with specific functions Using trig identities

HELM workbook: Integration leading to logs

HELM workbook: Trigonometric functions and integration

 
Multiple integrals

Double integrals

Volume integrals

HELM workbook: Introduction to surface integrals

HELM workbook: Multiple integrals over non-regular regions

HELM workbook: Volume integrals

 

Series

     
Maclaurin's and Taylor's series Taylor & Maclaurin polynomials intro Workbook  
For Fourier Series click here      

Numerical methods

     
Numerical differentiation Euler's method Workbook  

Vectors and matrices

  Video Written Resource Exercises

Vectors

     
Introduction to Vectors   HELM Booklet See Written Resource
Cartesian components of vectors   HELM Booklet See Written Resource
Lines and planes   HELM Booklet See Written Resource
Scalar product   HELM Booklet See Written Resource
Vector product   HELM Booklet See Written Resource

Matrices

     
Introduction to matrices Khan Academy Video HELM Booklet See Written Resource
Matrix multiplication

Multiplying by Scalars

Matrix Multiplication

HELM Booklet See Written Resource
Matrix addition and subtraction Khan Academy Video    
Determinants Determinant of a 2x2 matrix HELM Booklet See Written Resource
The inverse of a matrix Khan Academy Video HELM Booklet See Written Resource
Eigenvectors and eigenvalues - Introduction Khan Academy Video HELM Booklet See Written Resource
Applications of eigenvalues and eigenvectors   HELM Booklet See Written Resource
Repeated eigenvalues and symmetric matrices   HELM Booklet See Written Resource
Numerical determination of eigenvalues and eigenvectors   HELM Booklet See Written Resource

Solving Systems of Equations

     
Gaussian elimination   HELM Booklet See Written Resource
Solution by Cramer's rule   HELM Booklet See Written Resource
Solution by inverse matrix method   HELM Booklet See Written Resource
Solution by Gaussian elimination   HELM Booklet See Written Resource
LU decomposition   HELM Booklet See Written Resource
Matrix norms   HELM Booklet See Written Resource
Iterative methods for systems of equations   HELM Booklet See Written Resource

Differential equations and transforms

  Video Written Resource Exercises

Differential equations

     
First-order differential equations   HELM Workbook  
Second-order differential equations   HELM Workbook  
Use of differential equations  

Modelling with differential equations

Applications of differential equations

 

Fourier Transforms

     
Introduction   HELM Workbook  
Properties of Fourier transforms   HELM Workbook  
Special Fourier transform pairs   HELM Workbook  

Fourier Series

     
Periodic functions   HELM Workbook  
Representing periodic functions by Fourier series   HELM Workbook  
Even and odd functions   HELM Workbook  
Convergence   HELM Workbook  
Half-range series   HELM Workbook  
The complex form   HELM Workbook  
Applications of Fourier series   HELM Workbook  

Laplace Transforms

     
Causal functions   HELM Workbook  
The transform and its inverse   HELM Workbook  
Further Laplace transforms   HELM Workbook  
Solving differential equations   HELM Workbook  
The convolution theorem   HELM Workbook  
Transfer functions   HELM Workbook  

Partial Differential equations

     
Introduction   HELM Workbook  
Applications of PDEs   HELM Workbook  
Solutions using separation of variables   HELM Workbook  
Solution using Fourier series   HELM Workbook  
Two people sitting at a table looking at some work together
Two people sitting at a table looking at some work together

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