HELM workbooks in pdf format

HELM - Helping Engineers Learn Mathematics - is a major 3-year curriculum development project to support the mathematical education of engineering students. The project is sponsored by the Higher Education Funding Council for England (HEFCE) through phase 4 of the Fund for the Development for Teaching and Learning (FDTL4).

HELM Workbooks

This page allows you to access all currently available HELM workbooks (in pdf format).

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Click on a link below to make your choice.

1. Basic Algebra	2. Basic Functions	3. Equations, Inequalities And Partial Fractions
Notation, Symbols, Indices,Simplification, Factorisation,Algebraic Fractions,Formulae,Transposition.	Basics,graphs,parametric form,1-1 and inverse,characterising,straight line,circle,common engineering functions .	Solving equations: linear, quadratic,polynomial,simultaneous linear,partial fractions .
4. Trigonometry	5. Functions and modelling	6. Exponential and Logarithmic functions
Right-angled triangles, trigonometric functions,identities,applications of trigonometry to triangles and waves.	Functions and modelling: quadratic, oscillating, inverse square law.	Exponential, hyperbolic,logarithmic function, modelling,log-linear graphs.
7. Matrices	8. Matrix solution of equations	9. Vectors
Introduction, multiplication, determinants,inverse .	Solving simultaneous linear equations: Cramer's rule, inverse matrix, Gaussian elimination.	Basics, Cartesian components, scalar product, electrostatics, vector product, lines,planes .
10. Complex Numbers	11. Differentiation	12. Applications Of Differentiation
Complex arithmetic, Argand Diagram,polar form,exponential form,De Moivre.	Introduction, tables of derivatives, higher derivatives, products, quotients,chain rule,parametric and implicit differentiation.	Tangents normals, maxima, minima, Newton-Raphson,curvature,vectors,complex impedance.
13. Integration	14. Applications of integration 1	15. Applications of integration 2
Basic concepts, definite integral, area under curve, integration by parts, substitution, partial fractions, trigonometric functions.	Integration as the limit of a sum, mean and root-mean-square value, volume and surface of revolution,length of curve .	Integration of vectors, centre of mass, moment of inertia.
16. Sequences And Series	17. Conics and polar coordinates	18. Functions Of Several Variables
Sequences, series, infinite, binomial,power, Maclaurin, Taylor series.	Conic sections, polar coordinates, parametric curves.	Functions of several variables, partial derivatives, stationary points, errors and percentage change.
19. Differential Equations	20. The Laplace Transform	21. The Z transform
Modelling with ODEs, first-order, second-order,applications.	Causal functions, transform and inverse, further transforms, solving ODEs,convolution,transfer function.	z-Transforms: basics, difference equations, engineering applications,sampled functions.
22. Eigenvalues and eigenvectors	23. Fourier series	24. Fourier transforms
Basic concepts, applications of eigenvalues/vectors,repeated eigenvalues and symmetric matrices,numerical determination.	Periodic functions, representation by Fourier series,even and odd functions,convergence, half-range series, complex form, application.	The Fourier transform, properties, special pairs of transforms.
25. Partial Differential Equations	26. Functions of complex variables	27. Multiple Integration
Partial differential equations, applications,separation of variables, Fourier series solution.	Complex functions, Caucy-Riemann equations, conformal mappings, standard functions,complex integration,Cauchy's theorem, singularities, residues.	Introduction to surface integrals, multiple integrals over non-rectangular regions,volume integrals,changing coordinates.
28. Vector Calculus 1	29. Vector Calculus 2	30. Introduction to Numerical Methods
Background to vector calculus, differential vector calculus,orthogonal curvilinear coordinates.	Line integrals involving vectors, surface and volume vector integrals,integral vector theorems .	Rounding error and conditioning, Gaussian elimination, LU-decomposition,matrix norms,iterative methods.
31. Numerical methods of approximation	32. Numerical solution of initial value problem	33. Numerical solution of boundary value problem
Polynomial approximations, numerical integrations and differentiation, nonlinear equations.	Initial value problems, linear multistep methods, predictor-corrector methods, parabolic PDEs, hyperbolic PDEs.	Two-point boundary value problems, elliptic PDEs.
34. Modelling Motion	35. Sets and Probability	36. Descriptive Statistics
Projectiles, forces in more than one dimension, resisted motion.	Sets, elementary probability,addition and multiplication laws,total probability, Bayes' theorem.	Describing and exploring data.
37. Discrete Probability Distributions	38. Continuous Probability Distributions	39. Normal Distribution
Discrete probability distributions, binomial, Poisson and hypergeometric distribution.	Continuous probability distributions, uniform and exponential distribution.	The normal distribution, normal approximation to the binomial distribution, sums and differences of random variables.
40. Sampling Distributions and Estimation	41. Hypothesis Testing	42. Goodness of Fit and Contingency Tables
Sampling distributions, interval estimation for variance.	Statistics testing, tests concerning a single sample and two samples.	Goodness of fit, contingency tables.
43. Regression and Correlation	44. Analysis of Variance (ANOVA)	45. Non-parametric statistics
Regression, correlation.	One-way, two-way ANOVA, experimental design.	Non-parametric statistics for a single sample, for two samples.
46. Reliability and Quality Control	47. Mathematics and Physics Miscellany	48.Engineering Case studies
Reliability, quality control.	Dimensional analysis in engineering, explorations, physics case studies.	Sound waves, reflection, microphones, refraction, beams,columns,bending,cables, water in channel,pendulum, snowflake,satellite,railway signals,wine cellar,2-D flow past obstacle, on plate,force on cylinder
49. Student's guide	50. Tutor's guide
Introduction, workbooks,general advice, index.	Introduction, HELM consortium, institutions, contributors, transferability,structure and notation,issues and notes, layout, list of sections, commentaries, index of engineering contexts.

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