Vickers, James - School of Mathematics, University of Southampton

• Nonlinear Equations Introduction
• Solving polynomial Introduction
• Acta Applicandae Mathematicae 80: 221241, 2004. 2004 Kluwer Academic Publishers. Printed in the Netherlands.
• Probability Introduction
• Modelling Exercises Introduction
• J. Phys. A: Math. Gen. 14 (1981)L389-L391. Printed in Great Britain LETTER TO THE EDITOR
• The Vector Product Introduction
• Class. Quantum Cmv. 12 (1995) 753-768. Printed in the UK 2 +2 decompositionof Ashtekarvariables
• Complex Impedance Electronic Filters
• Contents10ntsnts1010ntsnts10complex 1. Complex arithmetic
• Contents11ntsnts1111ntsnts11differentiation differentiation
• Formulae and transposition
• Combining Cauchy and characteristic codes. V. Cauchy-characteristic matching for a spherical spacetime containing a perfect fluid
• IOP PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 26 (2009) 235014 (23pp) doi:10.1088/0264-9381/26/23/235014
• Differences of Random Variables
• Dynamic cosmic strings. I K. R. P. Sjodin,* U. Sperhake,
• The Exponential Distribution
• The Inverse of a Matrix Introduction
• Contents20ntsnts2020ntsnts20the laplace 1. Causal functions
• J. Phys. A: Math. Gen. 15 (1982) L67-L70. Printed in Great Britain LETI'ER TO THE EDITOR
• ContentsContents2424Fourier 1. The Fourier transform
• TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• J. Phys. A: Math. Gen. 16 (1983) 1169-1174. Printed in Great Britain An inequality relating mass and electric charge in general
• Total Probability and Bayes' Theorem
• journal of number theory 58, 298 316 (1996) Simultaneous Diophantine Approximation and
• Determination of Eigenvalues
• The Chain Rule Introduction
• Tests Concerning Two Samples
• /0001-8708/02 $35.00 2002 Elsevier Science (USA)
• Applications of Trigonometry
• Characterising Introduction
• Solution using Separation of Variables
• The Transform and its Inverse
• Quality Control Introduction
• news and views NATURE|VOL403|10FEBRUARY2000|www.nature.com 609
• Solving simultaneous equations using the
• Class. Quantum Grav. 16 (1999) 589604. Printed in the UK PII: S0264-9381(99)96655-8 Integration using invariant operators: conformally flat
• ContentsContents1133integration integration
• ContentsContents3366Descriptive 1. Describing data
• ContentsContents3131numerical methods of approximation
• Dynamic cosmic strings. II. Numerical evolution of excited cosmic strings U. Sperhake,* K. R. P. Sjodin,
• Class. Quantum Grav. 13 (1996) 15791587. Printed in the UK A spacetime calculus based on a single null direction
• Percentage Change Introduction
• Journal of Geometry and Physics 39 (2001) 265275 Metric-affine gravity and the NesterWitten 2-form
• IOP PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 26 (2009) 065001 (19pp) doi:10.1088/0264-9381/26/6/065001
• Introduction to Confidence Intervals
• Maple 11 Tutorial SECTION 1. INTRODUCTION...................................................................................... 2
• Exploring Data Introduction
• Correlation Introduction
• Trigonometric Introduction
• The Exponential Form of a Complex Number
• Stationary Points Introduction
• Arithmetic of algebraic Introduction
• Properties of the Fourier Transform
• De Moivre's Theorem Introduction
• J. Phys. A: Math. Gen. 16 (1983) 1155-1168. Printed in Great Britain Momentum, angular momentum and their quasi-local null
• A Spacetime Calculus Invariant under Null Rotations M. P. Machado Ramos; J. A. G. Vickers
• The Area Bounded Introduction
• ContentsContents3377discrete probability distributions
• Changing Coordinates Introduction
• Contents18ts18functions of several variables
• Solving Differential Introduction
• Approximation to the Binomial Distribution
• Contents19ntsnts1919ntsnts19differential 1. Modelling with differential equations
• Contents17entsnts1717ntsnts17conics and polar coordinates
• Singularities and Residues
• Simplification and Factorisation
• Representing Periodic Functions by Fourier
• Contents7tss7ss 1. Introduction to matrices
• COMPUTER LAB WORKSHEETS MAPLE lab worksheet for week 1: Introduction to MAPLE
• ContentsContents66exponential and logarithmic functions
• Inverse Square Law Introduction
• International Journal of Modern Physics A, Vol. 17, No. 20 (2002) 2779 c World Scientific Publishing Company
• J. Phys. A: Math. Gen. 15 (1982) L473-L476. Printed in Great Britain LE'lTER TO THE EDITOR
• General Relativity and Gravitation, Vol. 18, No. ll, 1986 Everywhere Invariant Spaces of Metrics
• Class. Quantum Grav. 4 (1987) 1-9. Printed in the UK Generalised cosmic strings
• Nonlineariiy 2 (1989) 137-1 48. Printed in the UK Averaging in multifrequency systems
• Class. Quantum Grav. 7 (1990) 1-14. Printed in the UK The large-scale bending of cosmic strings
• Combining Cauchy and characteristic codes. III. The interface problem in axial symmetry Ray A. d'Inverno and James A. Vickers
• Class. Quantum Grav. 13 (1996) 24852498. Printed in the UK Generalized functions and distributional curvature of cosmic
• Class. Quantum Grav. 16 (1999) 579588. Printed in the UK PII: S0264-9381(99)95414-X Invariance of the distributional curvature of the cone under
• INTRINSIC CHARACTERIZATION OF MANIFOLD-VALUED GENERALIZED FUNCTIONS
• Math. Proc. Camb. Phil. Soc. (2005), 139, 497 c 2005 Cambridge Philosophical Society doi:10.1017/S0305004105008649 Printed in the United Kingdom
• INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 23 (2006) R91R114 doi:10.1088/0264-9381/23/10/R01
• INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 23 (2006) 45114522 doi:10.1088/0264-9381/23/13/014
• Contents11basic 1. Mathematical notation and symbols
• ContentsContents22basic functions 1. Basic concepts of functions
• The straight line Introduction
• Some common engineering functions
• ContentsContents33 equations, inequalities
• Solving simultaneous linear equations
• Solving inequalities Introduction
• Partial fractions Introduction
• Trigonometric Introduction
• Applications of Trigonometry
• Contents5ntss55ss5 functions and
• Quadratic Functions and Modelling
• Oscillating functions and Modelling
• The Hyperbolic Introduction
• Introduction In this Section we introduce the logarithm: loga b. The operation of taking a logarithm essentially
• The Logarithmic Introduction
• Log-linear Graphs Introduction
• Matrix Multiplication Introduction
• Contents8ts88fmatrix solution off 1. Cramer's rule for solving simultaneous linear equations
• Gauss elimination Introduction
• The Scalar Product Introduction
• Argand Diagrams and the Polar Form
• Using a table of derivatives
• Higher Derivatives Introduction
• Differentiation Introduction
• ContentsContents1122applications of differentiation
• The Newton-Raphson Introduction
• Introduction Curvature is a measure of how sharply a curve is turning as it is traversed. At a particular
• Integration by Parts Introduction
• Integration by Substitution and using
• Integration of Trigonometric
• ContentsContents1414applications of integration 1
• Volumes of revolution Introduction
• Lengths of curves and surfaces of revolution
• ContentsContents1515applications of integration 2
• Moment of inertia Introduction
• Contents16ts16Sequences and 1. Sequences and series
• Infinite Series Introduction
• Maclaurin and Taylor Introduction
• Polar Coordinates Introduction
• First Order ODEs Introduction
• Applications of Differential Equations
• Further Laplace Introduction
• The Convolution Introduction
• ContentsContents2222eigenvalues and eigenvectors
• Applications of Eigenvalues and
• Repeated Eigenvalues Symmetric Matrices
• ContentsContents2323Fourier 1. Periodic functions
• Even and Odd Introduction
• Convergence Introduction
• Half-Range Series Introduction
• Some Special Fourier Transform Pairs
• ContentsContents2525partial differential 1. Partial Differential Equations
• Solutions using Fourier Series
• ContentsContents2266functions of a complex 1. Complex functions
• Cauchy-Riemann Equations and
• Standard Complex Introduction
• Basic Complex Integration
• Multiple Integrals over Non-rectangular
• ContentsContents2828vector 1. Background to Vector Calculus
• Curvilinear Coordinates
• ContentsContents2929vector 1. Line integrals involving vectors
• Integral Vector Introduction
• Gaussian Elimination Introduction
• LU decomposition Introduction
• Matrix norms Introduction
• Iterative methods for systems of equations
• Numerical integration Introduction
• differentiation Introduction
• ContentsContents3535Sets and probability probability
• Addition and Multiplication Laws
• The Binomial distribution
• The Hypergeometric distribution
• ContentsContents3838continuous probability distributions
• ContentsContents3399the normal distribution
• ContentsContents4040sampling distributions and estimation
• Tests Concerning a Single Sample
• ContentsContents4422goodness of fit and contingency tables
• ContentsContents4343Regression and correlation
• Applications of PDEs Introduction
• Differentiation of Introduction
• Introduction A circle is one of the most familiar geometrical figures. In this brief Section we discuss the basic
• Partial Derivatives Introduction
• Lines and Planes Introduction
• Second Order ODEs Introduction
• Cartesian Components Introduction
• Surface and Volume Integrals
• Differentiation Introduction
• Cauchy's Theorem Introduction
• The graph of a function and parametric form
• Contents9entsnts99ntsnts9vectors 1. Basic concepts of vectors
• Class. Quantum Grav. 7 (1990) 731-741. Printed in the UK Quasi-regular singularities and cosmic strings
• One-to-one and inverse functions
• Class. Quantum Grav. 17 (2000) 13331360. Printed in the UK PII: S0264-9381(00)06757-5 Generalized hyperbolicity in conical spacetimes
• Electrostatics Introduction
• The Uniform Distribution
• Calculating centres of mass
• Transfer Functions Introduction
• Differentiating ProductsandQuotients
• ContentsContents4411hypothesis 1. Statistical testing
• The Poisson distribution
• ContentsContents2277Multiple integration
• Determinants Introduction
• The Complex Form Introduction
• The mean value and the root-mean-square
• Differential Vector Introduction
• Parametric Curves Introduction
• Application of Fourier Series
• Introduction Indices, or powers, provide a convenient notation when we need to multiply a number by itself
• ContentsContents44trigonometry trigonometry
• Power Series Introduction
• Maxima and Minima Introduction
• J. Phys. A: Math. Gen. 19 (1986) 349-374. Printed in Great Britain Exceptional sets in Kolmogorov-Amol'd-Moser theory
• INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 23 (2006) 37473761 doi:10.1088/0264-9381/23/11/005
• Combining Cauchy and characteristic codes. IV. The characteristic field equations in axial symmetry
• The Hausdorff Dimension of Small Divisors for Lower-Dimensional KAM-Tori M. M. Dodson; J. Poschel; B. P. Rynne; J. A. G. Vickers
• ContentsContents3030introduction to numerical methods
• Class.Quantum Gray. 8 (1991) L215-LZI7. Printed in the UK LE'ITER TO THE EDITOR
• Volume Integrals Introduction
• Solving quadratic Introduction
• Definite Integrals Introduction
• The Binomial Series Introduction
• ContentsContents4466Reliability and quality control