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Leif Mejlbro Real Functions in Several Variables Examples of Maximum and Minimum Integration Calculus 2b Download free ebooks at bookboon.com Calculus 2b – Real Functions in Several Variables © 2006 Leif Mejlbro & Ventus Publishing ApS ISBN 87-7681-207-3 Download free ebooks at bookboon.com Real Functions in Several Variables Contents Contents 1. Preface 6 2. The range of a function in several variables 7 2.1 Maximum and minimum 7 2.2 Extremum 29 3. The plane integral 37 3.1 Rectangular coordinates 37 3.2 Polar coordinates 44 4. The space integral 51 4.1 Rectangular coordinates 51 4.2 Semi-polar coordinates 54 4.3 Spherical coordinates 58 5. The line integral 66 6. The surface integral 72 7. Transformation theorems 84 The next step for top-performing graduates Masters in Management Designed for high-achieving graduates across all disciplines, London Business School’s Masters in Management provides specific and tangible foundations for a successful career in business. This 12-month, full-time programme is a business qualification with impact. In 2010, our MiM employment rate was 95% within 3 months of graduation*; the majority of graduates choosing to work in consulting or financial services. As well as a renowned qualification from a world-class business school, you also gain access to the School’s network of more than 34,000 global alumni – a community that offers support and opportunities throughout your career. For more information visit www.london.edu/mm, email mim@london.edu or give us a call on +44 (0)20 7000 7573. * Figures taken from London Business School’s Masters in Management 2010 employment report Download free ebooks at bookboon.com 4 Real Functions in Several Variables 8. Improper integrals 9. Vector analysis Contents 95 111 9.1 Tangential line integral; gradient fi eld 111 9.2 Flux and divergence of a vector field; Gauss’s theorem 118 9.3 Rotation of a vector field; Stokes’s theorem 142 9.4 Potentials 151 A Formulæ 155 A.1 Squares etc. 155 A.2 Powers etc. 155 A.3 Differentiation 156 A.4 Special derivatives 157 A.5 Integration 158 A.6 Special antiderivatives 160 A.7 Trigonometric formulæ 162 A.8 Hyperbolic formulæ 164 A.9 Complex transformation formulæ 166 A.10 Taylor expansions 166 A.11 Magnitudes of functions 167 Teach with the Best. Learn with the Best. Agilent offers a wide variety of affordable, industry-leading electronic test equipment as well as knowledge-rich, on-line resources —for professors and students. We have 100’s of comprehensive web-based teaching tools, lab experiments, application notes, brochures, DVDs/ CDs, posters, and more. © Agilent Technologies, Inc. 2012 See what Agilent can do for you. www.agilent.com/find/EDUstudents www.agilent.com/find/EDUeducators u.s. 1-800-829-4444 canada: 1-877-894-4414 Download free ebooks at bookboon.com 5 ... - tailieumienphi.vn
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