Workbook Numbers 
Workbook Titles 
Workbook Sections (workbooks 1,2,3 and 10 each have a link providing a sample section) 
1 
Basic Algebra 

2 
Basic Functions 
 Basic Concepts of Functions.
 Graphs of Functions and Parametric Form.
 Onetoone and Inverse Functions.
 Characterising Functions
 The Straight Line.
 The Circle.
 Some Common Functions.
 Index.

3 
Equations, Inequalities & Partial Fractions 
 Solving Linear Equations.
 Solving Quadratic Equations.
 Solving Polynomial Equations
 Solving Simultaneous Linear Equations.
 Solving Inequalities.
 Partial Fractions.
 Index.

4 
Trigonometry 
 Rightangled Triangles.
 Trigonometric Functions.
 Trigonometric Identities.
 Applications of Trigonometry to Triangles.
 Applications of Trigonometry to Waves.
 Index.

5 
Functions and Modelling 
 The Modelling Cycle and Functions.
 Quadratic Functions and Modelling.
 Oscillating Functions and Modelling.
 Inverse Square Law Modelling.
 Index.

6 
Exponential and Logarithmic Functions 
 The Exponential Function.
 The Hyperbolic Functions.
 Logarithms.
 The Logarithmic Function.
 Modelling Exercises.
 Loglinear Graphs.
 Index.

7 
Matrices 
 Introduction to Matrices.
 Matrix Multiplication.
 Determinants.
 The Inverse of a Matrix.
 Index.

8 
Matrix Solution of Equations 
 Solution by Cramer's Rule.
 Solution by Inverse Matrix Method.
 Solution by Gauss Elimination.
 Index.

9 
Vectors 
 Basic Concepts of Vectors.
 Cartesian Components of Vectors.
 The Scalar Product.
 The Vector Product.
 Lines and Planes.
 Index.

10 
Complex Numbers 

11 
Differentiation 
 Introducing Differentiation.
 Using a Table of Derivatives.
 Higher Derivatives.
 Differentiating Products and Quotients.
 The Chain Rule.
 Parametric Differentiation.
 Implicit Differentiation.
 Index.

12 
Applications Of Differentiation 
 Tangents and Normals.
 Maxima and Minima.
 The NewtonRaphson Method.
 Curvature.
 Differentiation of Vectors.
 Case study: Complex Impedance.
 Index.

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.
 Index.

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.
 Index.

15 
Applications Of Integration 2 
 Integration of Vectors.
 Calculating Centres of Mass.
 Moment of Inertia.
 Index.

16 
Sequences And Series 
 Sequences and Series.
 Infinite Series.
 The Binomial Series.
 Power Series.
 Maclaurin and Taylor Series.
 Index. 17

17 
Conics And Polar Coordinates 
 Conic Sections.
 Polar Coordinates.
 Parametric Curves.
 Index.

18 
Functions Of Several Variables 
 Functions of Several Variables.
 Partial Derivatives.
 Stationary Points.
 Errors and Percentage Change.
 Index.

19 
Differential Equations 
 Modelling with Differential Equations.
 First Order Differential Equations.
 Second Order Differential Equations.
 Applications of Differential Equations.
 Index.

20 
Laplace Transforms 
 Causal Functions.
 The Transform and its Inverse.
 Further Laplace Transforms.
 Solving Differential Equations.
 The Convolution Theorem.
 Transfer Functions.
 Index.

21 
zTransforms 
 The zTransform.
 Basics of zTransform Theory.
 zTransforms and Difference Equations.
 Engineering Applications of zTransforms.
 Sampled Functions.
 Index.

22 
Eigenvalues And Eigenvectors 
 Basic Concepts.
 Applications of Eigenvalues and Eigenvectors.
 Repeated Eigenvalues and Symmetric Matrices.
 Numerical Determination of Eigenvalues and Eigenvectors.
 Index.

23 
Fourier Series 
 Periodic Functions.
 Representing Periodic Functions by Fourer Series.
 Even and Odd Functions.
 Convergence.
 Halfrange Series.
 The Complex Form.
 An Application of Fourier Series.
 Index.

24 
Fourier Transforms 
 The Fourier Transform.
 Properties of the Fourier Transform.
 Some Special Fourier Transform Pairs.
 Index.

25 
Partial Differential Equations 
 Partial Differential Equations.
 Applications of PDEs.
 Solution Using Separation of Variables.
 Solutions Using Fourier Series.
 Index.

26 
Functions Of A Complex Variable 
 Complex Functions.
 CauchyRiemann Equations and Conformal Mapping.
 Standard Complex Functions.
 Basic Complex Integration.
 Cauchy's Theorem.
 Singularities and Residues.
 Index.

27 
Multiple Integration 
 Introduction to Surface Integrals.
 Multiple Integrals over Nonrectangular Regions.
 Volume Integrals.
 Changing Coordinates.
 Index.

28 
Differential Vector Calculus 
 Background to Vector Calculus.
 Differential Vector Calculus.
 Orthogonal Curvilinear Coordinates.
 Index.

29 
Integral Vector Calculus 
 Line Integrals.
 Surface and Volume Integrals.
 Integral Vector Theorems.
 Index.

30 
Introduction To Numerical Methods 
 Rounding Error and Conditioning.
 Gaussian Elimination.
 LU Decomposition.
 Matrix Norms.
 Iterative Methods for Systems of Equations.
 Index.

31 
Numerical Methods Of Approximation 
 Polynomial Approximations.
 Numerical Integration.
 Numerical Differentiation.
 Nonlinear Equations.
 Index.

32 
Numerical Initial Value Problems 
 Initial Value Problems.
 Linear Multistep Methods.
 PredictorCorrector Methods.
 Parabolic PDEs.
 Hyperbolic PDEs.
 Index.

33 
Numerical Boundary Value Problems 
 Twopoint Boundary Value Problems.
 Elliptic PDEs.
 Index.

34 
Modelling Motion 
 Projectiles.
 Forces in More Than One Dimension.
 Resisted Motion.
 Index

35 
Sets And Probability 
 Sets.
 Elementary Probability.
 Addition and Multiplication Laws of Probability.
 Total Probability and Bayes' Theorem.
 Index.

36 
Descriptive Statistics 
 Describing Data.
 Exploring Data.
 Index.

37 
Discrete Probability Distributions 
 Discrete Probability Distributions
 The Binomial Distribution.
 The Poisson Distribution.
 The Hypergeometric Distribution.
 Index.

38 
Continuous Probability Distributions 
 Continuous Probability Distributions.
 The Uniform Distribution
 The Exponential Distribution.
 Index.

39 
The Normal Distribution 
 The Normal Distribution.
 The Normal Approximation to the Binomial Distribution.
 Sums and Differences of Random Variables.
 Index.

40 
Sampling Distributions And Estimation 
 Sampling Distributions.
 Interval Estimation for the Variance.
 Index.

41 
Hypothesis Testing 
 Statistical Testing.
 Tests Concerning a Single Sample.
 Tests Concerning Two Samples.
 Index.

42 
Goodness Of Fit And Contingency Tables 
 Goodness of Fit.
 Contingency Tables.
 Index.

43 
Regression And Correlation 
 Regression.
 Correlation.
 Index.

44 
Analysis Of Variance 
 OneWay Analysis of Variance.
 TwoWay Analysis of Variance.
 Experimental Design.
 Index.

45 
Nonparametric Statistics 
 Nonparametric Tests for a Single Sample.
 Nonparametric Tests for Two Samples.
 Index.

46 
Reliability And Quality Control 
 Reliability.
 Quality Control.
 Index.

47 
Mathematics And Physics Miscellany 
 Dimensional Analysis in Engineering.
 Mathematical Explorations.
 Physics Case Studies.
 Index 1.
 Index 2.
 Index 3.

48 
Engineering Case Studies 
 Engineering Case Studies.
 Index.

49 
Student's Guide 
 Introduction to HELM
 HELM Workbooks
 General Advice to Students Studying Mathematics
 Index of Engineering Contexts in Workbooks 1 to 48

50 
Tutor's Guide 
