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 | |||
| Standard derivatives | Workbook | ||
| Chain rule | Workbook | ||
| Product rule | Workbook | ||
| Quotient rule | |||
| Differentiation and trigonometry | |||
| Differentiation with logs and exponentials | |||
| Higher-order derivatives | |||
| Stationary points | HELM Workbook | ||
| Implicit differentiation | Workbook | ||
| Parametric differentiation | Workbook | ||
| Partial differentiation | |||
Integration | |||
| Methods for integration | HELM workbook: Using a table of anti-derivatives | ||
| Integration with specific functions | |||
| Multiple integrals | HELM workbook: Introduction to surface 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 | |||
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 |
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).