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Informationen zum Autor Brian Martin was a full-time member of staff of the Department of Physics & Astronomy at UCL from 1968 to 1995, including a decade from 1994 to 2004 as Head of the Department. I retired in 2005 and now hold the title of Emeritus Professor of Physics. I have extensive experience of teaching undergraduate mathematics classes at all levels and experience of other universities via external examining for first degrees at Imperial College and Royal Holloway College London. I was also the external member of the General Board of the Department of Physics at Cambridge University that reviewed the whole academic programme of that department, including teaching. Graham Shaw is a full-time member of staff of the School of Physics & Astronomy at Manchester University and will retire in September 2009. I have extensive experience of teaching undergraduate physics and the associated mathematics, and have been a member of the department's Teaching Committee and the Course Director of the Honours School of Mathematics and Physics for many years. Klappentext Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. This text will be an excellent resource for undergraduate students in physics and a quick reference guide for more advanced students, as well as being appropriate for students in other physical sciences, such as astronomy, chemistry and earth sciences. Mathematics for Physicists features: Interfaces with modern school mathematics syllabuses All topics usually taught in the first two years of a physics degree Worked examples throughout Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website. Zusammenfassung Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics! from a starting point that is compatible with modern school mathematics syllabuses. Inhaltsverzeichnis Editors' preface to the Manchester Physics Series xi Authors' preface xiii Notes and website information xv 1 Real numbers, variables and functions 1 1.1 Real numbers 1 1.1.1 Rules of arithmetic: rational and irrational numbers 1 1.1.2 Factors, powers and rationalisation 4 1.1.3 Number systems 6 1.2 Real variables 9 1.2.1 Rules of elementary algebra 9 1.2.2 Proof of the irrationality of 2 11 1.2.3 Formulas, identities and equations 11 1.2.4 The binomial theorem 13 1.2.5 Absolute values and inequalities 17 1.3 Functions, graphs and co-ordinates 20 1.3.1 Functions 20 1.3.2 Cartesian co-ordinates 23 Problems 1 28 2 Some basic functions and equations 31 2.1 Algebraic functions 31 2.1.1 Polynomials 31 2.1.2 Rational functions and partial fractions 37 2.1.3 Algebraic and transcendental functions 41 2.2 Trigonometric functions 41 2.2.1 Angles and polar co-ordinates 41 2.2.2 Sine and cosine 44 2.2.3 More trigonometric functions 46 2.2.4 Trigonometric identities and equations 48 2.2.5 Sine and cosine rules 51 2.3 Logarithms and exponentials 53 2.3.1 The laws of logarithms 54 2.3.2 Expone...
