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 Booklet See Written Resource

Complex Numbers

      
Complex arithmetic

   
Exponential form HELM Workbook See Written Resource
Modulus-argument form

HELM 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 Workbook See Written Resource

Numerical Methods

      
Interval Bisection  
Iteration    
Newton Raphson Method 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 Workbook  
Product rule Workbook
Quotient rule  
Differentiation and trigonometry

   
Differentiation with logs and exponentials

Differentiation by taking logs

Differentiating logs and exponentials

  
Higher-order derivatives    
Stationary points

HELM Workbook  
Implicit differentiation

Workbook  
Parametric differentiation Workbook  
Partial differentiation

Partial derivatives Workbook

Stationary points Workbook

  

Integration

      
Methods for integration

HELM workbook: Using a table of anti-derivatives

HELM workbook: Integration by parts

HELM workbook: Substitution

  
Integration with specific functions

HELM workbook: Integration leading to logs

HELM workbook: Trigonometric functions and integration

  
Multiple 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 Workbook  
For Fourier Series click here      

Numerical methods

      
Numerical differentiation 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 HELM Booklet See Written Resource
Matrix multiplication

HELM Booklet See Written Resource
Matrix addition and subtraction    
Determinants HELM Booklet See Written Resource
The inverse of a matrix HELM Booklet See Written Resource
Eigenvectors and eigenvalues - Introduction 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  

Related information

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