Next steps for STEM Subjects
These resources cover more advanced topics which may be useful to students on STEM courses.
Algebra
Video | Written Resource | Exercises | |
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Partial fractions |
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Partial fractions | Introduction to partial fraction expansion | Booklet | See Written Resource |
Complex Numbers |
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Complex arithmetic | |||
Exponential form | HELM Workbook | See Written Resource | |
Complex arithmetic | |||
Exponential form | HELM Workbook | See Written Resource | |
Modulus-argument form | Workbook | See Written Resource | |
De Moivre's theorem and roots of complex numbers | HELM Workbook | See Written Resource | |
Sequences and series |
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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 |
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Binomial theorem | Pascal's triangle and binomial expansion | Workbook | See Written Resource |
Numerical Methods |
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Interval Bisection | Video | Webpage | |
Iteration | |||
Newton Raphson Method | Video | Written Resource | See Written Resource |
Conic Sections |
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Conic Sections | HELM Booklet | See Written Resource | |
Polar Coordinates |
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Introduction | HELM Booklet | See Written Resource | |
Parametric Equations | HELM Booklet | See Written Resource |
Calculus
Video | Written Resource | Exercises | |
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Differentiation |
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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 | |||
Differentiation with logs and exponentials | |||
Higher-order derivatives | Second derivatives | ||
Stationary points | HELM Workbook | ||
Implicit differentiation | Workbook | ||
Parametric differentiation | Introduction to parametric equations | Workbook | |
Partial differentiation | Introduction to partial derivatives | ||
Integration |
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Methods for integration |
HELM workbook: Using a table of anti-derivatives |
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Integration with specific functions | Using trig identities | ||
Multiple integrals |
HELM workbook: Introduction to surface integrals |
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Series |
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Maclaurin's and Taylor's series | Taylor & Maclaurin polynomials intro | Workbook | |
For Fourier Series click here | |||
Numerical methods |
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Numerical differentiation | Euler's method | Workbook |
Vectors and matrices
Video | Written Resource | Exercises | |
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Vectors |
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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 |
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Introduction to matrices | Khan Academy Video | HELM Booklet | See Written Resource |
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 |
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Gaussian elimination | Video | 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 | Video | 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 | |
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Differential equations |
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First-order differential equations | HELM Workbook | ||
Second-order differential equations | HELM Workbook | ||
Use of differential equations | |||
Fourier Transforms |
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Introduction | Video | HELM Workbook | |
Properties of Fourier transforms | HELM Workbook | ||
Special Fourier transform pairs | HELM Workbook | ||
Fourier Series |
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Periodic functions | Video | HELM Workbook | |
Representing periodic functions by Fourier series | Video | HELM Workbook | |
Even and odd functions | Video | HELM Workbook | |
Convergence | HELM Workbook | ||
Half-range series | HELM Workbook | ||
The complex form | HELM Workbook | ||
Applications of Fourier series | HELM Workbook | ||
Laplace Transforms |
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Causal functions | HELM Workbook | ||
The transform and its inverse | HELM Workbook | ||
Further Laplace transforms | HELM Workbook | ||
Solving differential equations | Video | HELM Workbook | |
The convolution theorem | HELM Workbook | ||
Transfer functions | HELM Workbook | ||
Partial Differential equations |
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Introduction | Video | HELM Workbook | |
Applications of PDEs | HELM Workbook | ||
Solutions using separation of variables | Video | HELM Workbook | |
Solution using Fourier series | Video | HELM Workbook |

Book a 1:1 appointment or workshop
Would you like to explore a maths or stats topic in greater depth? Why not book a 1:1 with an advisor or a workshop (current students only).