{"product_id":"two-and-three-dimensional-calculus-with-applications-in-science-and-engineering-hardback-9781119221784","title":"Two and Three Dimensional Calculus; with Applications in Science and Engineering (Hardback) 9781119221784","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTwo and Three Dimensional Calculus\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003ewith Applications in Science and Engineering\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003ePhil Dyke (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781119221784, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 27 April 2018\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e400 pages\u003cbr\u003e23.1 x 15.8 x 2.8 cm, 0.68 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eCovers multivariable calculus, starting from the basics and leading up to the three theorems of Green, Gauss, and Stokes, but always with an eye on practical applications.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWritten for a wide spectrum of undergraduate students by an experienced author, this book provides a very practical approach to advanced calculus—starting from the basics and leading up to the theorems of Green, Gauss, and Stokes. It explains, clearly and concisely, partial differentiation, multiple integration, vectors and vector calculus, and provides end-of-chapter exercises along with their solutions to aid the readers’ understanding.\u003c\/p\u003e \u003cp\u003eWritten in an approachable style and filled with numerous illustrative examples throughout, \u003ci\u003eTwo and Three Dimensional Calculus: with Applications in Science and Engineering\u003c\/i\u003e assumes no prior knowledge of partial differentiation or vectors and explains difficult concepts with easy to follow examples. Rather than concentrating on mathematical structures, the book describes the development of techniques through their use in science and engineering so that students acquire skills that enable them to be used in a wide variety of practical situations. It also has enough rigor to enable those who wish to investigate the more mathematical generalizations found in most mathematics degrees to do so.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eAssumes no prior knowledge of partial differentiation, multiple integration or vectors\u003c\/li\u003e \u003cli\u003eIncludes easy-to-follow examples throughout to help explain difficult concepts\u003c\/li\u003e \u003cli\u003eFeatures end-of-chapter exercises with solutions to exercises in the book.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eTwo and Three Dimensional Calculus: with Applications in Science and Engineering\u003c\/i\u003e is an ideal textbook for undergraduate students of engineering and applied sciences as well as those needing to use these methods for real problems in industry and commerce. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Revision of One-Dimensional Calculus 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Limits and Convergence 1\u003c\/p\u003e \u003cp\u003e1.2 Differentiation 3\u003c\/p\u003e \u003cp\u003e1.2.1 Rules for Differentiation 5\u003c\/p\u003e \u003cp\u003e1.2.2 Mean Value Theorem 7\u003c\/p\u003e \u003cp\u003e1.2.3 Taylor’s Series 8\u003c\/p\u003e \u003cp\u003e1.2.4 Maxima and Minima 12\u003c\/p\u003e \u003cp\u003e1.2.5 Numerical Differentiation 13\u003c\/p\u003e \u003cp\u003e1.3 Integration 16\u003c\/p\u003e \u003cp\u003eExercises 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Partial Differentiation 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 25\u003c\/p\u003e \u003cp\u003e2.2 Differentials 29\u003c\/p\u003e \u003cp\u003e2.2.1 Small Errors 30\u003c\/p\u003e \u003cp\u003e2.3 Total Derivative 33\u003c\/p\u003e \u003cp\u003e2.4 Chain Rule 36\u003c\/p\u003e \u003cp\u003e2.4.1 Leibniz Rule 39\u003c\/p\u003e \u003cp\u003e2.4.2 Chain Rule in n Dimensions 41\u003c\/p\u003e \u003cp\u003e2.4.3 Implicit Functions 42\u003c\/p\u003e \u003cp\u003e2.5 Jacobian 43\u003c\/p\u003e \u003cp\u003e2.6 Higher Derivatives 46\u003c\/p\u003e \u003cp\u003e2.6.1 Higher Differentials 49\u003c\/p\u003e \u003cp\u003e2.7 Taylor’s Theorem 50\u003c\/p\u003e \u003cp\u003e2.8 Conjugate Functions 52\u003c\/p\u003e \u003cp\u003e2.9 Case Study: Thermodynamics 54\u003c\/p\u003e \u003cp\u003eExercises 58\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Maxima and Minima 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 61\u003c\/p\u003e \u003cp\u003e3.2 Maxima, Minima and Saddle Points 63\u003c\/p\u003e \u003cp\u003e3.3 Lagrange Multipliers 74\u003c\/p\u003e \u003cp\u003e3.3.1 Generalisations 77\u003c\/p\u003e \u003cp\u003e3.4 Optimisation 81\u003c\/p\u003e \u003cp\u003e3.4.1 Hill Climbing Techniques 81\u003c\/p\u003e \u003cp\u003eExercises 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Vector Algebra 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 89\u003c\/p\u003e \u003cp\u003e4.2 Vector Addition 90\u003c\/p\u003e \u003cp\u003e4.3 Components 92\u003c\/p\u003e \u003cp\u003e4.4 Scalar Product 94\u003c\/p\u003e \u003cp\u003e4.5 Vector Product 97\u003c\/p\u003e \u003cp\u003e4.5.1 Scalar Triple Product 102\u003c\/p\u003e \u003cp\u003e4.5.2 Vector Triple Product 105\u003c\/p\u003e \u003cp\u003eExercises 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Vector Differentiation 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 109\u003c\/p\u003e \u003cp\u003e5.2 Differential Geometry 111\u003c\/p\u003e \u003cp\u003e5.2.1 Space Curves 112\u003c\/p\u003e \u003cp\u003e5.2.2 Surfaces 120\u003c\/p\u003e \u003cp\u003e5.3 Mechanics 129\u003c\/p\u003e \u003cp\u003eExercises 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Gradient, Divergence, and Curl 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 139\u003c\/p\u003e \u003cp\u003e6.2 Gradient 139\u003c\/p\u003e \u003cp\u003e6.3 Divergence 143\u003c\/p\u003e \u003cp\u003e6.4 Curl 145\u003c\/p\u003e \u003cp\u003e6.5 Vector Identities 146\u003c\/p\u003e \u003cp\u003e6.6 Conjugate Functions 151\u003c\/p\u003e \u003cp\u003eExercises 154\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Curvilinear Co-ordinates 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 157\u003c\/p\u003e \u003cp\u003e7.2 Curved Axes and Scale Factors 157\u003c\/p\u003e \u003cp\u003e7.3 Curvilinear Gradient, Divergence, and Curl 161\u003c\/p\u003e \u003cp\u003e7.3.1 Gradient 161\u003c\/p\u003e \u003cp\u003e7.3.2 Divergence 163\u003c\/p\u003e \u003cp\u003e7.3.3 Curl 165\u003c\/p\u003e \u003cp\u003e7.4 Further Results and Tensors 166\u003c\/p\u003e \u003cp\u003e7.4.1 Tensor Notation 166\u003c\/p\u003e \u003cp\u003e7.4.2 Covariance and Contravariance 168\u003c\/p\u003e \u003cp\u003eExercises 171\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 PathIntegrals 173\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 173\u003c\/p\u003e \u003cp\u003e8.2 Integration Along a Curve 173\u003c\/p\u003e \u003cp\u003e8.3 Practical Applications 181\u003c\/p\u003e \u003cp\u003eExercises 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Multiple Integrals 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 191\u003c\/p\u003e \u003cp\u003e9.2 The Double Integral 191\u003c\/p\u003e \u003cp\u003e9.2.1 Rotation and Translation 199\u003c\/p\u003e \u003cp\u003e9.2.2 Change of Order of Integration 201\u003c\/p\u003e \u003cp\u003e9.2.3 Plane Polar Co-ordinates 203\u003c\/p\u003e \u003cp\u003e9.2.4 Applications of Double Integration 208\u003c\/p\u003e \u003cp\u003e9.3 Triple Integration 213\u003c\/p\u003e \u003cp\u003e9.3.1 Cylindrical and Spherical Polar Co-ordinates 219\u003c\/p\u003e \u003cp\u003e9.3.2 Applications of Triple Integration 227\u003c\/p\u003e \u003cp\u003eExercises 233\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Surface Integrals 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 241\u003c\/p\u003e \u003cp\u003e10.2 Green’s Theorem in the Plane 242\u003c\/p\u003e \u003cp\u003e10.3 Integration over a Curved Surface 246\u003c\/p\u003e \u003cp\u003e10.4 Applications of Surface Integration 253\u003c\/p\u003e \u003cp\u003eExercises 256\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Integral Theorems 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 259\u003c\/p\u003e \u003cp\u003e11.2 Stokes’ Theorem 260\u003c\/p\u003e \u003cp\u003e11.3 Gauss’ Divergence Theorem 268\u003c\/p\u003e \u003cp\u003e11.3.1 Green’s Second Identity 275\u003c\/p\u003e \u003cp\u003e11.4 Co-ordinate-Free Definitions 277\u003c\/p\u003e \u003cp\u003e11.5 Applications of Integral Theorems 279\u003c\/p\u003e \u003cp\u003e11.5.1 Electromagnetic Theory 279\u003c\/p\u003e \u003cp\u003e11.5.1.1 Maxwell’s Equations 279\u003c\/p\u003e \u003cp\u003e11.5.2 Fluid Mechanics 283\u003c\/p\u003e \u003cp\u003e11.5.3 Elasticity Theory 287\u003c\/p\u003e \u003cp\u003e11.5.4 Heat Transfer 297\u003c\/p\u003e \u003cp\u003eExercises 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Solutions and Answers to Exercises 301\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 375\u003c\/p\u003e \u003cp\u003eIndex 377\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52174331379992,"sku":"9781119221784","price":47.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781119221784.jpg?v=1781174041","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/two-and-three-dimensional-calculus-with-applications-in-science-and-engineering-hardback-9781119221784","provider":"Freshly Printed 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