{"id":8,"date":"2020-09-17T10:58:04","date_gmt":"2020-09-17T09:58:04","guid":{"rendered":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/?page_id=8"},"modified":"2020-10-18T13:55:55","modified_gmt":"2020-10-18T12:55:55","slug":"home","status":"publish","type":"page","link":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/","title":{"rendered":"Home"},"content":{"rendered":"<p>HELM : Helping Engineers Learn Mathematics. A resource of .pdf files covering many different topics.<\/p>\n<p><strong>Section 1 : Basic Algebra<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/01_1.pdf\">1.1 Mathematical Notation and Symbols<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/01_2.pdf\">1.2 Indices<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/01_3.pdf\">1.3 Simplification and Factorisation<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/01_4.pdf\">1.4 Arithmetic of Algebraic Fractions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/01_5.pdf\">1.5 Formulae and Transposition<\/a><\/li>\n<\/ul>\n<p><strong>Section 2 : Functions<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_1.pdf\">2.1 Basic Concepts of Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.2 The graph of a function and parametric form<\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Note that, bottom of page 13, the domain stated as involving &#8216;x&#8217; should be written in terms of &#8216;t&#8217; instead.<\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.3 One to one and inverse functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_4.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.4 Characterising Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_5.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.5 The Straight Line<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_6.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.6 The Circle<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/02_7.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">2.7 Some Common Engineering Functions<\/a><\/li>\n<\/ul>\n<p><strong>Section 3 : Polynomials, Inequalities and Partial Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/03_1.pdf\">3.1 Solving Linear Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/03_2.pdf\">3.2 Solving Quadratic Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/03_3.pdf\">3.3 Solving Polynomial Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/03_4.pdf\">3.4 Solving Simultaneous Linear Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/03_5.pdf\">3.5 Solving Inequalities<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/03_6.pdf\">3.6 Partial Fractions<\/a><\/li>\n<\/ul>\n<p><strong>Section 4 : Trigonometry<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/04_1.pdf\">4.1 Right-Angled Triangles<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/04_2.pdf\">4.2 Trigonometric Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/04_3.pdf\">4.3 Trigonometric Identities<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/04_4.pdf\">4.4 Applying Trigonometry to Triangles<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/04_5.pdf\">4.5 Applying Trigonometry to Waves<\/a><\/li>\n<\/ul>\n<p><strong>Section 5 : Functions and Modelling<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/05_1.pdf\">5.1 The Modelling Cycle and Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/05_2.pdf\">5.2 Quadratic Functions and Modelling<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/05_3.pdf\">5.3 Oscillating Functions and Modelling<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/05_4.pdf\">5.4 Inverse Square Functions and Modelling<\/a><\/li>\n<\/ul>\n<p><strong>Section 6 : Logarithms and exponentials<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/06_1.pdf\">6.1 The exponential Function<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/06_2.pdf\">6.2 The hyperbolic function<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/06_3.pdf\">6.3 Logarithms<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/06_4.pdf\">6.4 The logarithm function<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/06_5.pdf\">6.5 Log-linear graphs<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/06_6.pdf\">6.6 Modelling Exercises<\/a><\/li>\n<\/ul>\n<p><strong>Section 7 : Matrices<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/07_1.pdf\">7.1 Introduction to matrices<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/07_2.pdf\">7.2 Matrix multiplication<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/07_3.pdf\">7.3 Determinants<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/07_4.pdf\">7.4 The inverse of a matrix<\/a><\/li>\n<\/ul>\n<p><strong>Section 8 : Using matrices and determinants to solve equations<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/08_1.pdf\">8.1 Cramer&#8217;s rule for solving simultaneous equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/08_2.pdf\">8.2 Solving simultaneous equations using the inverse matrix<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/08_3.pdf\">8.3 Gauss elimination<\/a><\/li>\n<\/ul>\n<p><strong>Section 9 : Vectors<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/09_1.pdf\">9.1 Basic concepts of vectors<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/09_2.pdf\">9.2 Cartesian components of vectors<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/09_3.pdf\">9.3 The Scalar Product<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/09_4.pdf\">9.4 The Vector product<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/09_5.pdf\">9.5 Vectors, Lines and Planes<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/09_6.pdf\">9.6 Vectors and Electrostatics<\/a><\/li>\n<\/ul>\n<p><strong>Section 10 : Complex numbers<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/10_1.pdf\">10.1 Complex arithmetic<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/10_2.pdf\">10.2 Argand diagrams and polar form<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/10_3.pdf\">10.3 Exponential form<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/10_4.pdf\">10.4 De Moivre&#8217;s theorem<\/a><\/li>\n<\/ul>\n<p><strong>Section 11 : Differentiation<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_1.pdf\">11.1 Introducing differentiation<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_2.pdf\">11.2 Using a table of derivatives<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_3.pdf\">11.3 Higher derivatives<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_4.pdf\">11.4 Differentiating Products and Quotients<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_5.pdf\">11.5 The Chain Rule<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_6.pdf\">11.6 Parametric Differentiation<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/11_7.pdf\">11.7 Implicit Differentiation<\/a><\/li>\n<\/ul>\n<p><strong>Section 12 : Applications of differentiation<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/12_1.pdf\">12.1 Tangents and Normals<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/12_2.pdf\">12.2 Maxima and Minima<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/12_3.pdf\">12.3 The Newton Raphson Method<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/12_4.pdf\">12.4 Curvature<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/12_5.pdf\">12.5 Differentiation of Vectors<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/12_6.pdf\">12.6 Case Study : Complex Impedance<\/a><\/li>\n<\/ul>\n<p><strong>Section 13 : Integration<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/13_1.pdf\">13.1 Basic Concepts of Integration<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/13_2.pdf\">13.2 Definite Integrals<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/13_3.pdf\">13.3 The Area bounded by a Curve<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/13_4.pdf\">13.4 Integration by Parts<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/13_5.pdf\">13.5 Integration by Substitution and by Partial Fractions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/13_6.pdf\">13.6 Integration of Trigonometric Functions<\/a><\/li>\n<\/ul>\n<p><strong>Section 14 : Applications of Integration I<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/14_1.pdf\">14.1 Integration of the Limit of a Sum<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/14_2.pdf\">14.2 Mean Value and RMS Value<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/14_3.pdf\">14.3 Volumes of Solids of Revolution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/14_4.pdf\">14.4 Lengths of Curves and Areas of Surfaces of Revolution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/14_5.pdf\">14.5 Integration by Substitution and using Partial Fractions<\/a><\/li>\n<\/ul>\n<p><strong>Section 15 : Applications of integration II<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/15_1.pdf\">15.1 Integrals involving vectors<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/15_2.pdf\">15.2 Calculating centres of mass<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/15_3.pdf\">15.3 Moment of inertia<\/a><\/li>\n<\/ul>\n<p><strong>Section 16 : Sequences and series<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/16_1.pdf\">16.1 Sequences and series<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/16_2.pdf\">16.2 Infinite series<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/16_3.pdf\">16.3 The binomial series<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/16_4.pdf\">16.4 Power series<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/16_5.pdf\">16.5 Maclaurin and Taylor series<\/a><\/li>\n<\/ul>\n<p><strong>Section 17 : Conic sections<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/17_1.pdf\">17.1 Conic sections (circle, ellipse, parabola and hyperbola)<\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Note that the answer to question 6 on page 22 is incorrect<\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/17_2.pdf\">17.2 Polar co-ordinates<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/17_3.pdf\">17.3 Parametric curves<\/a><\/li>\n<\/ul>\n<p><strong>Section 18 : Functions of several variables<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/18_1.pdf\">18.1 Functions of several variables<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/18_2.pdf\">18.2 Partial derivatives<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/18_3.pdf\">18.3 Stationary points<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/18_4.pdf\">18.4 Errors and percentage change<\/a><\/li>\n<\/ul>\n<p><strong>Section 19 : Differential equations<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/19_1.pdf\">19.1 Modelling with differential equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/19_2.pdf\">19.2 First Order Ordinary Differential Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/19_3.pdf\">19.3 Second Order Ordinary Differential Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/19_4.pdf\">19.4 Applications of Differential Equations<\/a><\/li>\n<\/ul>\n<p><strong>Section 20 : The Laplace transform<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/20_1.pdf\">20.1 Causal functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/20_2.pdf\">20.2 The transform and its inverse<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/20_3.pdf\">20.3 Further Laplace transforms<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/20_4.pdf\">20.4 Solving differential equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/20_5.pdf\">20.5 The convolution theorem<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/20_6.pdf\">20.6 Transfer functions<\/a><\/li>\n<\/ul>\n<p><strong>Section 21 : z-Transforms<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/21_1.pdf\">21.1 The z-Transform<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/21_2.pdf\">21.2 Basics of z-Transform Theory<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/21_3.pdf\">21.3 z-Transforms and Difference Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/21_4.pdf\">21.4 Engineering Applications of z-Transforms<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/21_5.pdf\">21.5 Sampled Functions<\/a><\/li>\n<\/ul>\n<p><strong>22. Eigenvalues and Eigenvectors<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/22_1.pdf\">22.1 Basic Concepts<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/22_2.pdf\">22.2 Applications of Eigenvalues and Eigenvectors<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/22_3.pdf\">22.3 Repeated Eigenvalues and Symmetric Matrices<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/22_4.pdf\">22.4 Numerical determination of Eigenvalues and Eigenvectors<\/a><\/li>\n<\/ul>\n<p><strong>Section 23 : Fourier Series<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_1.pdf\">23.1 Periodic Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_2.pdf\">23.2 Representation of Periodic Functions by Fourier Series<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_3.pdf\">23.3 Even and Odd Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_4.pdf\">23.4 Convergence<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_5.pdf\">23.5 Half Range Series<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_6.pdf\">23.6 The Complex Form<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/23_7.pdf\">23.7 Applications of Fourier Series<\/a><\/li>\n<\/ul>\n<p><strong>Section 24 : Fourier Transforms<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/24_1.pdf\">24.1 The Fourier Transform<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/24_2.pdf\">24.2 Properties of the Fourier Transform<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/24_3.pdf\">24.3 Some Special Fourier Transform Pairs<\/a><\/li>\n<\/ul>\n<p><strong>Section 25 : Partial Differential Equations<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/25_1.pdf\">25.1 Partial Differential Equations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/25_2.pdf\">25.2 Applications of PDEs<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/25_3.pdf\">25.3 Separation of Variables<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/25_4.pdf\">25.4 Solution by Fourier Series<\/a><\/li>\n<\/ul>\n<p><strong>Section 26 : Functions of a Complex Variable<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/26_1.pdf\">26.1 Complex Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/26_2.pdf\">26.2 Cauchy-Riemann Equations and Conformal Mapping<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/26_3.pdf\">26.3 Standard Complex Functions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/26_4.pdf\">26.4 Basic Complex Integration<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/26_5.pdf\">26.5 Cauchy&#8217;s Theorem<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/26_6.pdf\">26.6 Singularities and Residues<\/a><\/li>\n<\/ul>\n<p><strong>Section 27 : Multiple Integration<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/27_1.pdf\">27.1 Introduction to Surface Integrals<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/27_2.pdf\">27.2 Multiple Integrals over Non-rectangular Regions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/27_3.pdf\">27.3 Volume Integrals<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/27_4.pdf\">27.4 Changing Coordinates<\/a><\/li>\n<\/ul>\n<p><strong>Section 28 : Differential Vector Calculus<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/28_1.pdf\">28.1 Background to Vector Calculus<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/28_2.pdf\">28.2 Differential Vector Calculus<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/28_3.pdf\">28.3 Orthogonal Curvilinear Coordinates<\/a><\/li>\n<\/ul>\n<p><strong>Section 29 : Integral Vector Calculus<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/29_1.pdf\">29.1 Line Integrals Involving Vectors<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/29_2.pdf\">29.2 Surface and Volume Integrals<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/29_3.pdf\">29.3 Integral Vector Theorems<\/a><\/li>\n<\/ul>\n<p><strong>Section 30 : Introduction to Numerical Methods<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/30_1.pdf\">30.1 Rounding Error and Conditioning<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/30_2.pdf\">30.2 Gaussian Elimination<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/30_3.pdf\">30.3 LU Decomposition<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/30_4.pdf\">30.4 Matrix Norms<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/30_5.pdf\">30.5 Iterative Methods for Systems of Equations<\/a><\/li>\n<\/ul>\n<p><strong>Section 31 : Numerical Methods of Approximation<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/31_1.pdf\">31.1 Polynomial Approximation<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/31_2.pdf\">31.2 Numerical Integration<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/31_3.pdf\">31.3 Numerical Differentiation<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/31_4.pdf\">31.4 Non-linear Equations<\/a><\/li>\n<\/ul>\n<p><strong>32. Numerical Initial Value Problems<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/32_1.pdf\">32.1 Initial Value Problems<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/32_2.pdf\">32.2 Linear Multistep Methods<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/32_3.pdf\">32.3 Predictor-Corrector Methods<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/32_4.pdf\">32.4 Parabolic PDEs<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/32_5.pdf\">32.5 Hyperbolic PDEs<\/a><\/li>\n<\/ul>\n<p><strong>Section 33 : Numerical Boundary Value Problems<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/33_1.pdf\">33.1 Two Point Boundary Value Problems<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/33_2.pdf\">33.2 Elliptic PDEs<\/a><\/li>\n<\/ul>\n<p><strong>Section 34 : Modelling Motion<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/34_1.pdf\">34.1 Projectiles<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/34_2.pdf\">34.2 Forces in more than one dimension<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/34_3.pdf\">34.3 Resisted Motion<\/a><\/li>\n<\/ul>\n<p><strong>Section 35 : Sets and Probability<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/35_1.pdf\">35.1 Sets<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/35_2.pdf\">35.2 Elementary Probability<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/35_3.pdf\">35.3 Addition and Multiplication Laws of Probability<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/35_4.pdf\">35.4 Total Probability and Bayes&#8217; Theorem<\/a><\/li>\n<\/ul>\n<p><strong>Section 36 : Descriptive Statistics<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/36_1.pdf\">36.1 Describing Data<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/36_2.pdf\">36.2 Exploring Data<\/a><\/li>\n<\/ul>\n<p><strong>Section 37 : Discrete Probability Distributions<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/37_1.pdf\">37.1 Discrete Probability Distributions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/37_2.pdf\">37.2 The Binomial Distribution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/37_3.pdf\">37.3 The Poisson Distribution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/37_4.pdf\">37.4 The Hypergeometric Distribution<\/a><\/li>\n<\/ul>\n<p><strong>Section 38 : Continuous Probability Distributions<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/38_1.pdf\">38.1 Continuous probability distributions<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/38_2.pdf\">38.2 The uniform distribution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/38_3.pdf\">38.3 The Exponential Distribution<\/a><\/li>\n<\/ul>\n<p><strong>Section 39 : The normal distribution<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/39_1.pdf\">39.1 The random distribution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/39_2.pdf\">39.2 The normal approximation to the binomial distribution<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/39_3.pdf\">39.3 Sums and differences of random variables<\/a><\/li>\n<\/ul>\n<p><strong>Section 40 : Sampling Distributions and Estimation<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/40_1.pdf\">40.1 Sampling Distributions and Estimation<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/40_2.pdf\">40.2 Introduction to Confidence Intervals<\/a><\/li>\n<\/ul>\n<p><strong>Section 41 : Hypothesis Testing<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/41_1.pdf\">41.1 Statistical Tests<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/41_2.pdf\">41.2 Tests concerning a single sample<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/41_3.pdf\">41.3 Tests concerning two samples<\/a><\/li>\n<\/ul>\n<p><strong>Section 42 : Goodness of Fit and Contingency Tables<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/42_1.pdf\">42.1 Goodness of Fit<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/42_2.pdf\">42.2 Contingency Tables<\/a><\/li>\n<\/ul>\n<p><strong>Section 43 : Regression and Correlation<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/43_1.pdf\">43.1 Regression<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/43_2.pdf\">43.2 Correlation<\/a><\/li>\n<\/ul>\n<p><strong>Section 44 : Analysis of Variance<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/44_1.pdf\">44.1 One-Way Analysis of Variance<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/44_2.pdf\">44.2 Two-Way Analysis of Variance<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/44_3.pdf\">44.3 Experimental Design<\/a><\/li>\n<\/ul>\n<p><strong>Section 45 : Non-parametric Statistics<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/45_1.pdf\">45.1 Non-parametric Tests for a single sample<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/45_2.pdf\">45.2 Non-paramteric Tests for two samples<\/a><\/li>\n<\/ul>\n<p><strong>Section 46 : Reliability and Quality Control<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/46_1.pdf\">46.1 Reliability<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/46_2.pdf\">46.2 Quality Control<\/a><\/li>\n<\/ul>\n<p><strong>Section 47 : Mathematics and Physics Miscellany<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/47_1.pdf\">47.1 Dimensional Analysis in Engineering<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/47_2.pdf\">47.2 Mathematical Explorations<\/a><\/li>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/47_3.pdf\">47.3 Physics Case Studies<\/a><\/li>\n<\/ul>\n<p><strong>Section 48 : Engineering Case Studies<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/48_1.pdf\">48.1 Engineering Case Studies<\/a><\/li>\n<\/ul>\n<p><strong>Section 49 : Students&#8217; Guide<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/49_1.pdf\">49.1 Students&#8217; Guide<\/a><\/li>\n<\/ul>\n<p><strong>Section 50 : Tutor&#8217;s Guide<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-content\/uploads\/sites\/81\/2020\/09\/50_1.pdf\">50.1 Tutor&#8217;s Guide<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>HELM : Helping Engineers Learn Mathematics. A resource of .pdf files covering many different topics. Section 1 : Basic Algebra 1.1 Mathematical Notation and Symbols 1.2 Indices 1.3 Simplification and Factorisation 1.4 Arithmetic of Algebraic Fractions 1.5 Formulae and Transposition Section 2 : Functions 2.1 Basic Concepts of Functions 2.2 The graph of a function [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":9,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"class_list":{"0":"post-8","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"entry"},"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/pages\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":25,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/pages\/8\/revisions"}],"predecessor-version":[{"id":246,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/pages\/8\/revisions\/246"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/media\/9"}],"wp:attachment":[{"href":"https:\/\/www.mub.eps.manchester.ac.uk\/helm\/wp-json\/wp\/v2\/media?parent=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}