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书名：CALCULUS CALCU LUS Ⅲ
作者：Paul Dawkins
文件格式：PDF
文件大小：1.94M
页数：286
资料类别：微积分
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目录：
Preface .......................................................................................................................................... iii Outline .......................................................................................................................................... iv Three Dimensional Space.............................................................................................................. 1 Introduction ............................................................................................................................................... 1 The 3-D Coordinate System ....................................................................................................................... 3 Equations of Lines .................................................................................................................................... 9 Equations of Planes ................................................................................................................................. 15 Quadric Surfaces ..................................................................................................................................... 18 Functions of Several Variables ................................................................................................................ 24 Vector Functions ..................................................................................................................................... 31 Calculus with Vector Functions ............................................................................................................... 40 Tangent, Normal and Binormal Vectors .................................................................................................. 43 Arc Length with Vector Functions ........................................................................................................... 46 Curvature ................................................................................................................................................. 49 Velocity and Acceleration ........................................................................................................................ 51 Cylindrical Coordinates ........................................................................................................................... 54 Spherical Coordinates .............................................................................................................................. 56 Partial Derivatives ....................................................................................................................... 62 Introduction ............................................................................................................................................. 62 Limits ...................................................................................................................................................... 63 Partial Derivatives ................................................................................................................................... 68 Interpretations of Partial Derivatives ....................................................................................................... 77 Higher Order Partial Derivatives .............................................................................................................. 81 Differentials ............................................................................................................................................ 85 Chain Rule .............................................................................................................................................. 86 Directional Derivatives ............................................................................................................................ 96 Applications of Partial Derivatives .......................................................................................... 105 Introduction ............................................................................................................................................105 Tangent Planes and Linear Approximations ...........................................................................................106 Gradient Vector, Tangent Planes and Normal Lines ...............................................................................110 Relative Minimums and Maximums .......................................................................................................112 Absolute Minimums and Maximums ......................................................................................................121 Lagrange Multipliers ...............................................................................................................................129 Multiple Integrals ...................................................................................................................... 139 Introduction ............................................................................................................................................139 Double Integrals .....................................................................................................................................140 Iterated Integrals ....................................................................................................................................144 Double Integrals Over General Regions .................................................................................................151 Double Integrals in Polar Coordinates ....................................................................................................162 Triple Integrals .......................................................................................................................................173 Triple Integrals in Cylindrical Coordinates .............................................................................................181 Triple Integrals in Spherical Coordinates ................................................................................................184 Change of Variables ...............................................................................................................................188 Surface Area ...........................................................................................................................................197 Area and Volume Revisited ....................................................................................................................200 Line Integrals ............................................................................................................................. 201 Introduction ............................................................................................................................................201 Vector Fields ..........................................................................................................................................202 Line Integrals – Part I ..............................................................................................................................207 Line Integrals – Part II ............................................................................................................................218 Line Integrals of Vector Fields................................................................................................................221 Fundamental Theorem for Line Integrals ................................................................................................224 Conservative Vector Fields .....................................................................................................................228 Calculus III © 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx Green’s Theorem ....................................................................................................................................235 Curl and Divergence ...............................................................................................................................243 Surface Integrals ........................................................................................................................ 247 Introduction ............................................................................................................................................247 Parametric Surfaces ................................................................................................................................248 Surface Integrals ....................................................................................................................................254 Surface Integrals of Vector Fields ...........................................................................................................263 Stokes’ Theorem ....................................................................................................................................273 Divergence Theorem ...............................................................................................................................278
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