LEADER 03738nam 22005295 450 001 9910337569803321 005 20200705163611.0 010 $a3-030-11376-0 024 7 $a10.1007/978-3-030-11376-6 035 $a(CKB)4100000007761761 035 $a(DE-He213)978-3-030-11376-6 035 $a(MiAaPQ)EBC5919236 035 $a(PPN)235234486 035 $a(EXLCZ)994100000007761761 100 $a20190312d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCalculus for Computer Graphics /$fby John Vince 205 $a2nd ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVII, 303 p. 179 illus., 178 illus. in color.) 311 $a3-030-11375-2 327 $aIntroduction -- Functions -- Limits and Derivatives -- Derivatives and Antiderivatives -- Higher Derivatives -- Partial Derivatives -- Integral Calculus -- Area Under a Graph -- Are Length and Parameterisation of Curves -- Surface Area -- Volume -- Vector-Valued Functions -- Tangent and Normal Vectors -- Continuity -- Curvature -- Conclusion. . 330 $aStudents studying different branches of computer graphics have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems. In this 2nd edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function?s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples, and over a hundred and seventy colour illustrations. This book complements the author?s other books on mathematics for computer graphics, and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer graphics, games and animation. 606 $aComputer graphics 606 $aComputer science?Mathematics 606 $aComputer mathematics 606 $aComputer Graphics$3https://scigraph.springernature.com/ontologies/product-market-codes/I22013 606 $aMathematical Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M13110 615 0$aComputer graphics. 615 0$aComputer science?Mathematics. 615 0$aComputer mathematics. 615 14$aComputer Graphics. 615 24$aMathematical Applications in Computer Science. 676 $a006.60151 676 $a006.60151 700 $aVince$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut$0564065 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910337569803321 996 $aCalculus for Computer Graphics$92499602 997 $aUNINA