Next steps for STEM Subjects

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

On

Algebra

 VideoWritten ResourceExercises

Partial fractions

   
Partial fractionsIntroduction to partial fraction expansionBookletSee Written Resource

Complex Numbers

   
Complex arithmetic

Adding and subtracting

Multiplying

Complex conjugates and dividing

  
Exponential formVideoHELM WorkbookSee Written Resource
Modulus-argument form

Finding modulus and argument

Writing in the modulus-argument form

HELM WorkbookSee Written Resource
De Moivre's theorem and roots of complex numbersVideoHELM WorkbookSee Written Resource

Sequences and series

   
Sequences and seriesVideoBookletSee Written Resource
Infinite seriesVideoBookletSee Written Resource
Power seriesVideoBookletSee Written Resource
Binomial seriesVideoWorkbookSee Written Resource

Binomial theorem

   
Binomial theoremPascal's triangle and binomial expansionWorkbookSee Written Resource

Numerical Methods

   
Interval BisectionVideoWebpage 
IterationVideo  
Newton Raphson MethodVideoWritten ResourceSee Written Resource

Conic Sections

   
Conic SectionsVideoHELM BookletSee Written Resource

Polar Coordinates

   
IntroductionVideoHELM BookletSee Written Resource
Parametric EquationsVideoHELM BookletSee Written Resource

Calculus

 VideoWritten ResourceExercises

Differentiation

   
Differentiating sine and cosine from first principlesVideoWebpage 
Standard derivativesVideoWorkbook 
Chain ruleIntroduction to chain ruleWorkbook 
Product ruleVideoWorkbookExercise
Quotient ruleIntroduction to the quotient rule Exercise
Differentiation and trigonometry

Sin and cos

Tan and cot

Sec and cosec

Inverse trig functions

  
Differentiation with logs and exponentialsVideo

Differentiation by taking logs

Differentiating logs and exponentials

 
Higher-order derivativesSecond derivatives  
Stationary points

Maxima and minima

Points of inflection

Finding stationary points

HELM Workbook 
Implicit differentiationImplicit differentiationWorkbook 
Parametric differentiationIntroduction to parametric equationsWorkbook 
Partial differentiationIntroduction 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 functionsUsing 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 seriesTaylor & Maclaurin polynomials introWorkbook 
For Fourier Series click here   

Numerical methods

   
Numerical differentiationEuler's methodWorkbook 

Vectors and matrices

 VideoWritten ResourceExercises

Vectors

   
Introduction to VectorsVideoHELM BookletSee Written Resource
Cartesian components of vectorsVideoHELM BookletSee Written Resource
Lines and planesVideoHELM BookletSee Written Resource
Scalar productVideoHELM BookletSee Written Resource
Vector productVideoHELM BookletSee Written Resource

Matrices

   
Introduction to matricesKhan Academy VideoHELM BookletSee Written Resource
Matrix multiplication

Multiplying by Scalars

Matrix Multiplication

HELM BookletSee Written Resource
Matrix addition and subtractionKhan Academy Video  
DeterminantsDeterminant of a 2x2 matrixHELM BookletSee Written Resource
The inverse of a matrixKhan Academy VideoHELM BookletSee Written Resource
Eigenvectors and eigenvalues - IntroductionKhan Academy VideoHELM BookletSee Written Resource
Applications of eigenvalues and eigenvectorsVideoHELM BookletSee Written Resource
Repeated eigenvalues and symmetric matricesVideoHELM BookletSee Written Resource
Numerical determination of eigenvalues and eigenvectorsVideoHELM BookletSee Written Resource

Solving Systems of Equations

   
Gaussian eliminationVideoHELM BookletSee Written Resource
Solution by Cramer's ruleVideoHELM BookletSee Written Resource
Solution by inverse matrix methodVideoHELM BookletSee Written Resource
Solution by Gaussian eliminationVideoHELM BookletSee Written Resource
LU decompositionVideoHELM BookletSee Written Resource
Matrix normsVideoHELM BookletSee Written Resource
Iterative methods for systems of equationsVideoHELM BookletSee Written Resource

Differential equations and transforms

 VideoWritten ResourceExercises

Differential equations

   
First-order differential equationsVideoHELM Workbook 
Second-order differential equationsVideoHELM Workbook 
Use of differential equationsVideo

Modelling with differential equations

Applications of differential equations

 

Fourier Transforms

   
IntroductionVideoHELM Workbook 
Properties of Fourier transformsVideoHELM Workbook 
Special Fourier transform pairsVideoHELM Workbook 

Fourier Series

   
Periodic functionsVideoHELM Workbook 
Representing periodic functions by Fourier seriesVideoHELM Workbook 
Even and odd functionsVideoHELM Workbook 
ConvergenceVideoHELM Workbook 
Half-range seriesVideoHELM Workbook 
The complex formVideoHELM Workbook 
Applications of Fourier seriesVideoHELM Workbook 

Laplace Transforms

   
Causal functionsVideoHELM Workbook 
The transform and its inverseVideoHELM Workbook 
Further Laplace transformsVideoHELM Workbook 
Solving differential equationsVideoHELM Workbook 
The convolution theoremVideoHELM Workbook 
Transfer functionsVideoHELM Workbook 

Partial Differential equations

   
IntroductionVideoHELM Workbook 
Applications of PDEs HELM Workbook 
Solutions using separation of variablesVideoHELM Workbook 
Solution using Fourier seriesVideoHELM Workbook 

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