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Bibliografická citace

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0 (hodnocen0 x )
BK
New York : Springer, c2010
xvi, 526 s. : il. ; 26 cm

objednat
ISBN 978-1-4419-7331-3 (váz.)
Undergraduate texts in mathematics
Obsahuje bibliografické odkazy a rejstřík
000195584
Contents // 1 Starting Points... 1 // 1.1 Substitution... 1 // 1.2 Work and path integrals... 6 // 1.3 Polar coordinates... 20 // Exercises... 22 // 2 Geometry of Linear Maps... 29 // 2.1 Maps from R2 to R2... 29 // 2.2 Maps from R" to R"... 42 // 2.3 Maps from Rn to Rp, n / p... 46 // Exercises... 57 // 3 Approximations... 71 // 3.1 Mean-value theorems... 71 // 3.2 Taylor polynomials in one variable... 77 // 3.3 Taylor polynomials in several variables... 90 // Exercises...100 // 4 The Derivative...105 // 4.1 Differentiability...105 // 4.2 Maps of the plane...112 // 4.3 Parametrized surfaces...121 // 4.4 The chain rule...129 // Exercises...141 // 5 Inverses...151 // 5.1 Solving equations...151 // 5.2 Coordinate changes...158 // 5.3 The inverse function theorem...165 // Exercises...176 // XV // xvi Contents // 6 Implicit Functions...185 // 6.1 A single equation...185 // 6.2 A pair of equations...198 // 6.3 The general case...205 // Exercises...215 // 7 Critical Points...219 // 7.1 Functions of one variable...219 // 7.2 Functions of two variables...224 // 7.3 Morse’s lemma...243 // Exercises...265 // 8 Double Integrals...269 // 8.1 Example: gravitational attraction...269 // 8.2 Area and Jordan content...276 // 8.3 Riemann and Darbou integrals...295 // Exercises...313 // 9 Evaluating Double Integrals...317 // 9.1 Iterated integrals...317 // 9.2 Improper integrals...326 // 9.3 The change of variables formula...337 // 9.4 Orientation...353 // 9.5 Green’s theorem ...364 // Exercises...378
// 10 Surface Integrals...387 // 10.1 Measuring flux...387 // 10.2 Surface area and scalar integrals...405 // 10.3 Differential forms...423 // Exercises...443 // 11 Stokes’ Theorem...449 // 11.1 Divergence...449 // 11.2 Circulation and vorticity...460 // 11.3 Stokes’ theorem...482 // 11.4 Closed and exact forms...492 // Exercises...509 // References...515 // Index // 517

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