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Open Learning Support for Mathematical Education for Engineers



 

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 given, click on the "" sign to view (or to download) a sample workbook. To obtain other workbooks, please contact the project.

01: Basic Algebra (Sample workbook available to try)
02: Basic Functions(Sample workbook available to try)
03: Equations, Inequalities and Partial Fractions (Sample workbook available to try)
04: Trigonometry
05: Functions and Modelling
06: Exponential and Logarithmic Functions
07: Matrices
08: Matrix Solution of Equations
09: Vectors
10: Complex Numbers (Sample workbook available to try)
11: Differentiation
12: Applications of Differentiation
13: Integration
14: Applications of Integration 1
15: Applications of Integration 2
16: Sequences and Series
17: Conics and Polar Coordinates
18: Functions of Several Variables
19: Differential Equations
20: Laplace Transforms
21: z-transforms
22: Eigenvalues and Eigenvectors
23: Fourier Series
24: Fourier Transforms
25: Partial Differential Equations
26: Functions of a Complex Variable
27: Multiple Integration
28: Differential Vector Calculus
29: Integral Vector Calculus
30: Introduction to Numerical Methods
31: Numerical Methods of Approximation
32: Numerical Initial Value Problems
33: Numerical Boundary Value Problems
34: Modelling Motion
35: Sets and Probability
36: Descriptive Statistics
37: Discrete Probability Distributions
38: Continuous Probability Distributions
39: The Normal Distribution
40: Sampling Distributions and Estimation
41: Hypothesis Testing
42: Goodness of Fit and Contingency Tables
43: Regression and Correlation
44: Analysis of Variance
45: Non-parametric Statistics
46: Reliability and Quality Control
47: Mathematics and Physics Miscellany
48: Engineering Case Studies
49: Student's Guide
50: Tutor's Guide

 

HELM Workbooks: Details of topics covered

Workbook 01: Basic Algebra

 ·   Mathematical Notation and Symbols.
 ·   Indices.
 ·   Simplification and Factorisation.
 ·   Arithmetic of Algebraic Fractions.
 ·   Formulae and Transposition.

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Workbook 02: Basic Functions

 ·   Basic Concepts of Functions.
 ·   Graphs of Functions and Parametric Form.
 ·   One-to-one and Inverse Functions.
 ·   Characterising Functions
 ·   The Straight Line.
 ·   The Circle.
 ·   Some Common Functions.

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Workbook 03: Equations, Inequalities and Partial Fractions

 ·   Solving Linear Equations.
 ·   Solving Quadratic Equations.
 ·   Solving Polynomial Equations.
 ·   Solving Simultaneous Linear Equations.
 ·   Solving Inequalities.
 ·   Partial Fractions.

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Workbook 04: Trigonometry

 ·   Right-angled Triangles.
 ·   Trigonometric Functions.
 ·   Trigonometric Identities.
 ·   Applications of Trigonometry to Triangles.
 ·   Applications of trigonometry to Waves.

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Workbook 05: Functions and Modelling

 ·   Modelling Cycle and Functions.
 ·   Quadratic Functions & Modelling.
 ·   Oscillating Functions and Modelling.
 ·   Inverse Square Law Modelling.

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Workbook 06: Exponential and Logarithmic Functions

 ·   The Exponential Function.
 ·   The Hyperbolic Functions.
 ·   Logarithms.
 ·   The Logarithmic Function.
 ·   Modelling Exercises.
 ·   Log-linear Graphs.

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Workbook 07: Matrices

 ·   Introduction to Matrices.
 ·   Matrix Multiplication.
 ·   Determinants.
 ·   The Inverse of a Matrix.

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Workbook 08: Matrix Solution of Equations

 ·   Solution by Cramer's Rule.
 ·   Solution by Inverse Matrix Method.
 ·   Solution by Gauss Elimination.

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Workbook 09: Vectors

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

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Workbook 10: Complex Numbers

 ·   Complex Arithmetic.
 ·   Argand Diagrams and the Polar Form.
 ·   The Exponential Form of a Complex Number.
 ·   DeMoivre's Theorem.

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Workbook 11: Differentiation

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

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Workbook 12: Applications of Differentiation

 ·   Tangents and Normals.
 ·   Maxima and Minima.
 ·   The Newton-Raphson Method.
 ·   Curvature.
 ·   Differentiation of Vectors.
 ·   Case Study: Complex Impedance.

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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.

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Workbook 14: Applications of Integration 1

 ·   Integration as the Limit of a Sum.
 ·   The Mean Value and the Root-mean-square Value.
 ·   Volumes of Revolution.
 ·   Lengths of Curves and Surfaces of Revolution.

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Workbook 15: Applications of Integration 2

 ·   Integration of Vectors.
 ·   Calculating Centres of Mass.
 ·   Moment of Inertia.

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Workbook 16: Sequences and Series

 ·   Sequences and Series.
 ·   Infinite Series.
 ·   The Binomial Series.
 ·   Power Series.
 ·   Maclaurin and Taylor Series.

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Workbook 17: Conics and Polar Coordinates

 ·   Conic Sections.
 ·   Polar Coordinates.
 ·   Parametric Curves.

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Workbook 18: Functions of several variables

 ·   Functions of Several Variables.
 ·   Partial Derivatives.
 ·   Stationary Points.
 ·   Errors and Percentage Change.

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Workbook 19: Differential Equations

 ·   Modelling with Differential Equations.
 ·   First Order Differential Equations.
 ·   Second Order Differential Equations.
 ·   Applications of Differential Equations.

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Workbook 20: Laplace Transforms

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

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Workbook 21: Z transforms

 ·   The z-Transform.
 ·   Basics of z-Transform Theory.
 ·   z-Transforms and Difference Equations.
 ·   Engineering Applications of z-Transforms.
 ·   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.

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Workbook 23: Fourier Series

 ·   Periodic Functions.
 ·   Representing Periodic Functions by Fourier Series.
 ·   Even and Odd Functions.
 ·   Convergence.
 ·   Half-range Series.
 ·   The Complex Form.
 ·   An Application of Fourier Series.

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Workbook 24: Fourier Transforms

 ·   The Fourier transform.
 ·   Properties of the Fourier Transform.
 ·   Some Special Fourier Transform Pairs.

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Workbook 25: Partial Differential Equations

 ·   Partial Differential Equations.
 ·   Applications of PDEs.
 ·   Solution using Separation of Variables.
 ·   Solutions using Fourier Series.

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Workbook 26: Functions of a Complex Variable

 ·   Complex Functions.
 ·   Cauchy-Riemann Equations and Conformal Mappings.
 ·   Standard Complex Functions.
 ·   Basic Complex Integration.
 ·   Cauchy's Theorem.
 ·   Singularities and Residues.

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Workbook 27: Multiple Integration

 ·   Introduction to Surface Integrals.
 ·   Multiple Integrals over Non-rectangular Regions.
 ·   Volume Integrals.
 ·   Changing Coordinates.

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Workbook 28: Differential Vector Calculus

 ·   Background to Vector Calculus.
 ·   Differential Vector Calculus.
 ·   Orthogonal Curvilinear Coordinates.

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Workbook 29: Integral Vector Calculus

 ·   Line Integrals Involving Vectors.
 ·   Surface and Volume Vector Integrals.
 ·   Integral Vector Theorems.

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Workbook 30: Introduction to Numerical Methods

 ·   Rounding Error and Conditioning.
 ·   Gaussian Elimination.
 ·   LU Decomposition.
 ·   Matrix Norms.
 ·   Iterative Methods for Systems of Equations.

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Workbook 31: Numerical Methods of Approximation

 ·   Polynomial Approximations.
 ·   Numerical Integration.
 ·   Numerical Differentiation.
 ·   Nonlinear Equations.

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Workbook 32: Numerical Initial Value Problems

 ·   Initial Value Problems.
 ·   Linear Multistep Methods.
 ·   Predictor-Corrector Methods.
 ·   Parabolic PDEs.
 ·   Hyperbolic PDEs.

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Workbook 33: Numerical Boundary Value Problems

 ·   Two-point Boundary Value Problems.
 ·   Elliptic PDEs.

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Workbook 34: Modelling Motion

 ·   Projectile.
 ·   Forces in More Than One Dimension.
 ·   Resisted Motion.

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Workbook 35: Sets and Probability

 ·   Sets.
 ·   Elementary Probability.
 ·   Addition and Multiplication Laws of Probability.
 ·   Total Probability & Bayes' Theorem.

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Workbook 36: Descriptive Statistics

 ·   Describing Data.
 ·   Exploring Data.

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Workbook 37: Discrete Probability Distributions

 ·   Discrete Probability Distributions.
 ·   The Binomial Distribution.
 ·   The Poisson Distribution.
 ·   The Hypergeometric Distribution.

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Workbook 38: Continuous Probability Distributions

 ·   Continuous Probability Distributions.
 ·   The Uniform Distribution.
 ·   The Exponential Distribution.

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Workbook 39: The Normal Distribution

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

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Workbook 40: Sampling Distributions and Estimation

 ·   Sampling Distributions.
 ·   Interval Estimation for the Variance.

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Workbook 41: Hypothesis Testing

 ·   Statistics Testing.
 ·   Tests Concerning a Single Sample.
 ·   Tests Concerning Two Samples.

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Workbook 42: Goodness of Fit and Contingency Tables

 ·   Goodness of Fit.
 ·   Contingency Tables.

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Workbook 43: Regression and Correlation

 ·   Regression.
 ·   Correlation.

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Workbook 44: Analysis of Variance

 ·   One-Way ANOVA.
 ·   Two-Way ANOVA.
 ·   Experimental Design.

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Workbook 45: Non-parametric Statistics

 ·   Non-parametric Tests for a Single Sample.
 ·   Non-parametric Tests for Two Samples.

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Workbook 46: Reliability and Quality Control

 ·   Reliability.
 ·   Quality Control.

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Workbook 47: Mathematics and Physics Miscellany

 ·   Dimensional Analysis in Engineering.
 ·   Mathematical Explorations.
 ·   Physics Case Studies.

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Workbook 48: Engineering Case Studies

 ·   Engineering Case Studies.

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Workbook 49: Student's Guide

 ·   Student's Guide.

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Workbook 50: Tutor’s Guide

 ·   Tutor’s Guide.

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Page last updated: November 2006