Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171

# Mathematics Education Centre

## Activities

### HELM Workbook List

 Workbook Numbers Workbook Titles Workbook Sections (workbooks 1,2,3 and 10 each have a link providing a sample section) 1 Basic Algebra Mathematical Notation and Symbols. Indices. Simplification and Fractorisation. Arithmetic of Algebraic Fractions Formulae and Transposition. Index. 2 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. 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 Right-angled 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. Log-linear 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 Complex Arithmetic. Argand Diagrams and the Polar Form. The Exponential Form of a Complex Number De Moivre's Theorem. Index. 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 Newton-Raphson 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 Root-Mean-Square 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 z-Transforms The z-Transform. Basics of z-Transform Theory. z-Transforms and Difference Equations. Engineering Applications of z-Transforms. 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. Half-range 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. Cauchy-Riemann 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 Non-rectangular 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. Predictor-Corrector Methods. Parabolic PDEs. Hyperbolic PDEs. Index. 33 Numerical Boundary Value Problems Two-point 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 One-Way Analysis of Variance. Two-Way Analysis of Variance. Experimental Design. Index. 45 Non-parametric Statistics Non-parametric Tests for a Single Sample. Non-parametric 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 Tutor's Guide