HELM Workbooks

This page allows you to access the HELM workbooks, the relevant index files, the student's guide and the tutor's guide (in pdf format).

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Mathematical Notation and Symbols. Indices. Simplification and Factorisation. Arithmetic of Algebraic Fractions. Formulae and Transposition. Index.	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.	Solving Linear Equations. Solving Quadratic Equations. Solving Polynomial Equations. Solving Simultaneous Linear Equations. Solving Inequalities. Partial Fractions. Index.
Right-angled Triangles. Trigonometric Functions. Trigonometric Identities. Applications of Trigonometry to Triangles. Applications of Trigonometry to Waves. Index.	The Modelling Cycle and Functions. Quadratic Functions and Modelling. Oscillating Functions and Modelling. Inverse Square Law Modelling. Index.	The Exponential Function. The Hyperbolic Functions. Logarithms. The Logarithmic Function. Modelling Exercises. Log-linear Graphs. Index.
Introduction to Matrices. Matrix Multiplication. Determinants. The Inverse of a Matrix. Index.	Solution by Cramer's Rule. Solution by Inverse Matrix Method. Solution by Gauss Elimination. Index.	Basic Concepts of Vectors. Cartesian Components of Vectors. The Scalar Product. The Vector Product. Lines and Planes. Index.
Complex Arithmetic. Argand Diagrams and the Polar Form. The Exponential Form of a Complex Number. De Moivre's Theorem. Index.	Introducing Differentiation. Using a Table of Derivatives. Higher Derivatives. Differentiating Products and Quotients. The Chain Rule. Parametric Differentiation. Implicit Differentiation. Index.	Tangents and Normals. Maxima and Minima. The Newton-Raphson Method. Curvature. Differentiation of Vectors. Case study: Complex Impedance. Index.
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.	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.	Integration of Vectors. Calculating Centres of Mass. Moment of Inertia. Index.
Sequences and Series. Infinite Series. The Binomial Series. Power Series. Maclaurin and Taylor Series. Index.	Conic Sections. Polar Coordinates. Parametric Curves. Index.	Functions of Several Variables. Partial Derivatives. Stationary Points. Errors and Percentage Change. Index.
Modelling with Differential Equations. First Order Differential Equations. Second Order Differential Equations. Applications of Differential Equations. Index.	Causal Functions. The Transform and its Inverse. Further Laplace Transforms. Solving Differential Equations. The Convolution Theorem. Transfer Functions. Index.	The z-Transform. Basics of z-Transform Theory. z-Transforms and Difference Equations. Engineering Applications of z-Transforms. Sampled Functions. Index.
Basic Concepts. Applications of Eigenvalues and Eigenvectors. Repeated Eigenvalues and Symmetric Matrices. Numerical Determination of Eigenvalues and Eigenvectors. Index.	Periodic Functions. Representing Periodic Functions by Fourier Series. Even and Odd Functions. Convergence. Half-range Series. The Complex Form. An Application of Fourier Series. Index.	The Fourier Transform. Properties of the Fourier Transform. Some Special Fourier Transform Pairs. Index.
Partial Differential Equations. Applications of PDEs. Solution Using Separation of Variables. Solutions Using Fourier Series. Index.	Complex Functions. Cauchy-Riemann Equations and Conformal Mapping. Standard Complex Functions. Basic Complex Integration. Cauchy's Theorem. Singularities and Residues. Index.	Introduction to Surface Integrals. Multiple Integrals over Non-rectangular Regions. Volume Integrals. Changing Coordinates. Index.
Background to Vector Calculus. Differential Vector Calculus. Orthogonal Curvilinear Coordinates. Index.	Line Integrals. Surface and Volume Integrals. Integral Vector Theorems. Index.	Rounding Error and Conditioning. Gaussian Elimination. LU Decomposition. Matrix Norms. Iterative Methods for Systems of Equations. Index.
Polynomial Approximations. Numerical Integration. Numerical Differentiation. Nonlinear Equations. Index.	Initial Value Problems. Linear Multistep Methods. Predictor-Corrector Methods. Parabolic PDEs. Hyperbolic PDEs. Index.	Two-point Boundary Value Problems. Elliptic PDEs. Index.
Projectiles. Forces in More Than One Dimension. Resisted Motion. Index.	Sets. Elementary Probability. Addition and Multiplication Laws of Probability. Total Probability and Bayes' Theorem. Index.	Describing Data. Exploring Data. Index.
Discrete Probability Distributions. The Binomial Distribution. The Poisson Distribution. The Hypergeometric Distribution. Index.	Continuous Probability Distributions. The Uniform Distribution. The Exponential Distribution. Index.	The Normal Distribution. The Normal Approximation to the Binomial Distribution. Sums and Differences of Random Variables. Index.
Sampling Distributions. Interval Estimation for the Variance. Index.	Statistical Testing. Tests Concerning a Single Sample. Tests Concerning Two Samples. Index.	Goodness of Fit. Contingency Tables. Index.
Regression. Correlation. Index.	One-Way Analysis of Variance. Two-Way Analysis of Variance. Experimental Design. Index.	Non-parametric Tests for a Single Sample. Non-parametric Tests for Two Samples. Index.
Reliability. Quality Control. Index.	Dimensional Analysis in Engineering. Mathematical Explorations. Physics Case Studies. Index 1. Index 2. Index 3.	Engineering Case Studies. Index.
Student's Guide.	Tutor's Guide.

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