HELM Workbooks & Their Contents 
The full list of 50 HELM
workbooks is given below.
List of HELM workbooks:
Click on any workbook title below to see its list of contents. If
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HELM Workbooks: Details of topics covered 
Workbook 01: Basic Algebra
· Mathematical Notation and Symbols.
· Indices.
· Simplification and Factorisation.
·
· Formulae and Transposition.
Workbook 02: Basic Functions
· Basic Concepts of Functions.
· Graphs of Functions and Parametric Form.
· Onetoone and Inverse Functions.
·
· The Straight Line.
· The Circle.
· Some Common Functions.
Workbook 03: Equations, Inequalities and Partial Fractions
· Solving Linear Equations.
· Solving Quadratic Equations.
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· Solving Simultaneous Linear Equations.
· Solving Inequalities.
· Partial Fractions.
Workbook 04: Trigonometry
· Rightangled Triangles.
· Trigonometric Functions.
· Trigonometric Identities.
· Applications of Trigonometry to Triangles.
· Applications of trigonometry to Waves.
Workbook 05: Functions and Modelling
· Modelling Cycle and Functions.
· Quadratic Functions & Modelling.
· Oscillating Functions and Modelling.
· Inverse Square Law Modelling.
Workbook 06: Exponential and Logarithmic Functions
· The Exponential Function.
· The Hyperbolic Functions.
· Logarithms.
· The Logarithmic Function.
· Modelling Exercises.
· Loglinear Graphs.
Workbook 07: Matrices
· Introduction to Matrices.
· Matrix Multiplication.
· Determinants.
· The Inverse of a Matrix.
Workbook 08: Matrix Solution of Equations
· Solution by Cramer's Rule.
· Solution by Inverse Matrix Method.
· Solution by Gauss Elimination.
Workbook 09: Vectors
· Basic Concepts of Vectors.
· Cartesian Components of Vectors.
· The Scalar Product.
· The Vector Product.
· Lines and Planes.
Workbook 10: Complex Numbers
· Complex Arithmetic.
· Argand Diagrams and the Polar Form.
·
· DeMoivre's Theorem.
Workbook 11: Differentiation
· Introducing Differentiation.
· Using a Table of Derivatives.
· Higher Derivatives.
· Differentiating Products and Quotients.
· The Chain Rule.
· Parametric Differentiation.
· Implicit Differentiation.
Workbook 12: Applications of Differentiation
· Tangents and Normals.
· Maxima and Minima.
· The NewtonRaphson Method.
· Curvature.
· Differentiation of Vectors.
· Case Study: Complex Impedance.
Workbook 13: Integration
· Basic Concepts of Integration.
· Definite Integrals.
· The Area Bounded by a Curve.
· Integration by Parts.
· Integration by Substitution and Using Partial
Fractions.
· Integration of Trigonometric Functions.
Workbook 14: Applications of Integration 1
· Integration as the Limit of a Sum.
· The Mean Value and the Rootmeansquare Value.
· Volumes of Revolution.
· Lengths of Curves and Surfaces of Revolution.
Workbook 15: Applications of Integration 2
· Integration of Vectors.
· Calculating Centres of Mass.
· Moment of Inertia.
Workbook 16: Sequences and Series
· Sequences and Series.
· Infinite Series.
· The Binomial Series.
· Power Series.
· Maclaurin and Taylor Series.
Workbook 17: Conics and Polar Coordinates
· Conic Sections.
· Polar Coordinates.
· Parametric Curves.
Workbook 18: Functions of several variables
· Functions of Several Variables.
· Partial Derivatives.
· Stationary Points.
· Errors and Percentage Change.
Workbook 19: Differential Equations
· Modelling with Differential Equations.
· First Order Differential Equations.
· Second Order Differential Equations.
· Applications of Differential Equations.
Workbook 20: Laplace Transforms
· Causal Functions.
· The Transform and its Inverse.
· Further Laplace Transforms.
· Solving Differential Equations.
· The Convolution Theorem.
· Transfer Functions.
Workbook 21: Z transforms
· The zTransform.
· Basics of zTransform Theory.
· zTransforms and Difference Equations.
· Engineering Applications of zTransforms.
· Sampled Functions.
Workbook 22: Eigenvalues and Eigenvectors
· Basic Concepts.
· Applications of Eigenvalues and Eigenvectors.
· Repeated Eigenvalues and Symmetric Matrices.
· Numerical Determination of Eigenvalues and Eigenvectors.
Workbook 23: Fourier Series
· Periodic Functions.
· Representing Periodic Functions by Fourier Series.
· Even and Odd Functions.
· Convergence.
· Halfrange Series.
· The Complex Form.
· An Application of Fourier Series.
Workbook 24: Fourier Transforms
· The Fourier transform.
· Properties of the Fourier Transform.
· Some Special Fourier Transform Pairs.
Workbook 25: Partial Differential Equations
· Partial Differential Equations.
· Applications of PDEs.
· Solution using Separation of Variables.
· Solutions using Fourier Series.
Workbook 26: Functions of a Complex Variable
· Complex Functions.
· CauchyRiemann Equations and Conformal Mappings.
· Standard Complex Functions.
· Basic Complex Integration.
· Cauchy's Theorem.
· Singularities and Residues.
Workbook 27: Multiple Integration
· Introduction to Surface Integrals.
· Multiple Integrals over Nonrectangular Regions.
· Volume Integrals.
· Changing Coordinates.
Workbook 28: Differential Vector Calculus
· Background to Vector Calculus.
· Differential Vector Calculus.
· Orthogonal Curvilinear Coordinates.
Workbook 29: Integral Vector Calculus
· Line Integrals Involving Vectors.
· Surface and Volume Vector Integrals.
· Integral Vector Theorems.
Workbook 30: Introduction to Numerical Methods
· Rounding Error and Conditioning.
· Gaussian Elimination.
· LU Decomposition.
· Matrix Norms.
· Iterative Methods for Systems of Equations.
Workbook 31: Numerical Methods of Approximation
· Polynomial Approximations.
· Numerical Integration.
· Numerical Differentiation.
· Nonlinear Equations.
Workbook 32: Numerical Initial Value Problems
· Initial Value Problems.
· Linear Multistep Methods.
· PredictorCorrector Methods.
· Parabolic PDEs.
· Hyperbolic PDEs.
Workbook 33: Numerical Boundary Value Problems
· Twopoint Boundary Value Problems.
· Elliptic PDEs.
Workbook 34: Modelling Motion
· Projectile.
· Forces in More Than One Dimension.
· Resisted Motion.
Workbook 35: Sets and Probability
· Sets.
· Elementary Probability.
· Addition and Multiplication Laws of Probability.
· Total Probability & Bayes' Theorem.
Workbook 36: Descriptive Statistics
· Describing Data.
· Exploring Data.
Workbook 37: Discrete Probability Distributions
· Discrete Probability Distributions.
· The Binomial Distribution.
· The Poisson Distribution.
· The Hypergeometric Distribution.
Workbook 38: Continuous Probability Distributions
· Continuous Probability Distributions.
· The Uniform Distribution.
· The Exponential Distribution.
Workbook 39: The Normal Distribution
· The Normal Distribution.
· The Normal Approximation to the Binomial Distribution.
· Sums and Differences of Random Variables.
Workbook 40: Sampling Distributions and Estimation
· Sampling Distributions.
· Interval Estimation for the Variance.
Workbook 41: Hypothesis Testing
· Statistics Testing.
· Tests Concerning a Single Sample.
· Tests Concerning Two Samples.
Workbook 42: Goodness of Fit and Contingency Tables
· Goodness of Fit.
· Contingency Tables.
Workbook 43: Regression and Correlation
· Regression.
· Correlation.
Workbook 44: Analysis of Variance
· OneWay ANOVA.
· TwoWay ANOVA.
· Experimental Design.
Workbook 45: Nonparametric Statistics
· Nonparametric Tests for a Single Sample.
· Nonparametric Tests for Two Samples.
Workbook 46: Reliability and Quality Control
· Reliability.
· Quality Control.
Workbook 47: Mathematics and Physics Miscellany
· Dimensional Analysis in Engineering.
· Mathematical Explorations.
· Physics Case Studies.
Workbook 48: Engineering Case Studies
· Engineering Case Studies.
Workbook 49: Student's Guide
· Student's Guide.
Workbook 50: Tutor’s Guide
· Tutor’s Guide.
