Two and Three Dimensional Calculus

with Applications in Science and Engineering

Inbunden, Engelska, 2018

819 kr

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Covers 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.Written 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.Written in an approachable style and filled with numerous illustrative examples throughout, Two and Three Dimensional Calculus: with Applications in Science and Engineering 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. Assumes no prior knowledge of partial differentiation, multiple integration or vectorsIncludes easy-to-follow examples throughout to help explain difficult conceptsFeatures end-of-chapter exercises with solutions to exercises in the book.Two and Three Dimensional Calculus: with Applications in Science and Engineering 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.

Produktinformation

Utgivningsdatum2018-04-27
Mått158 x 231 x 28 mm
Vikt680 g
FormatInbunden
SpråkEngelska
Antal sidor400
FörlagJohn Wiley & Sons Inc
ISBN9781119221784

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Preface xi1 Revision of One-Dimensional Calculus 11.1 Limits and Convergence 11.2 Differentiation 31.2.1 Rules for Differentiation 51.2.2 Mean Value Theorem 71.2.3 Taylor’s Series 81.2.4 Maxima and Minima 121.2.5 Numerical Differentiation 131.3 Integration 16Exercises 222 Partial Differentiation 252.1 Introduction 252.2 Differentials 292.2.1 Small Errors 302.3 Total Derivative 332.4 Chain Rule 362.4.1 Leibniz Rule 392.4.2 Chain Rule in n Dimensions 412.4.3 Implicit Functions 422.5 Jacobian 432.6 Higher Derivatives 462.6.1 Higher Differentials 492.7 Taylor’s Theorem 502.8 Conjugate Functions 522.9 Case Study: Thermodynamics 54Exercises 583 Maxima and Minima 613.1 Introduction 613.2 Maxima, Minima and Saddle Points 633.3 Lagrange Multipliers 743.3.1 Generalisations 773.4 Optimisation 813.4.1 Hill Climbing Techniques 81Exercises 854 Vector Algebra 894.1 Introduction 894.2 Vector Addition 904.3 Components 924.4 Scalar Product 944.5 Vector Product 974.5.1 Scalar Triple Product 1024.5.2 Vector Triple Product 105Exercises 1065 Vector Differentiation 1095.1 Introduction 1095.2 Differential Geometry 1115.2.1 Space Curves 1125.2.2 Surfaces 1205.3 Mechanics 129Exercises 1356 Gradient, Divergence, and Curl 1396.1 Introduction 1396.2 Gradient 1396.3 Divergence 1436.4 Curl 1456.5 Vector Identities 1466.6 Conjugate Functions 151Exercises 1547 Curvilinear Co-ordinates 1577.1 Introduction 1577.2 Curved Axes and Scale Factors 1577.3 Curvilinear Gradient, Divergence, and Curl 1617.3.1 Gradient 1617.3.2 Divergence 1637.3.3 Curl 1657.4 Further Results and Tensors 1667.4.1 Tensor Notation 1667.4.2 Covariance and Contravariance 168Exercises 1718 PathIntegrals 1738.1 Introduction 1738.2 Integration Along a Curve 1738.3 Practical Applications 181Exercises 1869 Multiple Integrals 1919.1 Introduction 1919.2 The Double Integral 1919.2.1 Rotation and Translation 1999.2.2 Change of Order of Integration 2019.2.3 Plane Polar Co-ordinates 2039.2.4 Applications of Double Integration 2089.3 Triple Integration 2139.3.1 Cylindrical and Spherical Polar Co-ordinates 2199.3.2 Applications of Triple Integration 227Exercises 23310 Surface Integrals 24110.1 Introduction 24110.2 Green’s Theorem in the Plane 24210.3 Integration over a Curved Surface 24610.4 Applications of Surface Integration 253Exercises 25611 Integral Theorems 25911.1 Introduction 25911.2 Stokes’ Theorem 26011.3 Gauss’ Divergence Theorem 26811.3.1 Green’s Second Identity 27511.4 Co-ordinate-Free Definitions 27711.5 Applications of Integral Theorems 27911.5.1 Electromagnetic Theory 27911.5.1.1 Maxwell’s Equations 27911.5.2 Fluid Mechanics 28311.5.3 Elasticity Theory 28711.5.4 Heat Transfer 297Exercises 29812 Solutions and Answers to Exercises 301References 375Index 377