- Page 1: 1 0.8 0.6 0.4 z 0.2 0 -0.2 -0.4 -10
- Page 5 and 6: Preface This book covers calculus i
- Page 7 and 8: Contents Preface iii 1 Vectors in E
- Page 9 and 10: 1 Vectors in Euclidean Space 1.1 In
- Page 11 and 12: 1.1 Introduction 3 You have already
- Page 13 and 14: 1.1 Introduction 5 Unless otherwise
- Page 15 and 16: 1.1 Introduction 7 Finding the magn
- Page 17 and 18: 1.2 Vector Algebra 9 1.2 Vector Alg
- Page 19 and 20: 1.2 Vector Algebra 11 Theorem 1.3.
- Page 21 and 22: 1.2 Vector Algebra 13 2 z z v=(a,b,
- Page 23 and 24: 1.3 Dot Product 15 1.3 Dot Product
- Page 25 and 26: 1.3 Dot Product 17 Since cosθ>0for
- Page 27 and 28: 1.3 Dot Product 19 3. v=(5,1,−2),
- Page 29 and 30: 1.4 Cross Product 21 The span of an
- Page 31 and 32: 1.4 Cross Product 23 It may seem at
- Page 33 and 34: 1.4 Cross Product 25 Example 1.12.
- Page 35 and 36: 1.4 Cross Product 27 A 2×2 matrix
- Page 37 and 38: 1.4 Cross Product 29 Interchanging
- Page 39 and 40: 1.5 Lines and Planes 31 1.5 Lines a
- Page 41 and 42: 1.5 Lines and Planes 33 Line throug
- Page 43 and 44: 1.5 Lines and Planes 35 We will now
- Page 45 and 46: 1.5 Lines and Planes 37 Distance be
- Page 47 and 48: 1.5 Lines and Planes 39 ☛ ✟ ✡
- Page 49 and 50: 1.6 Surfaces 41 Example 1.27. Find
- Page 51 and 52: 1.6 Surfaces 43 The equations of sp
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1.6 Surfaces 45 The hyperbolic para
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1.7 Curvilinear Coordinates 47 1.7
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1.7 Curvilinear Coordinates 49 Some
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1.8 Vector-Valued Functions 51 1.8
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1.8 Vector-Valued Functions 53 A sc
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1.8 Vector-Valued Functions 55 Just
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1.8 Vector-Valued Functions 57 In g
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1.9 Arc Length 59 1.9 Arc Length Le
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1.9 Arc Length 61 A curve can have
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1.9 Arc Length 63 and so x ′ (t)
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2 Functions of Several Variables 2.
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2.1 Functions of Two or Three Varia
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2.1 Functions of Two or Three Varia
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2.2 Partial Derivatives 71 2.2 Part
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2.2 Partial Derivatives 73 Solution
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2.3 Tangent Plane to a Surface 75 2
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2.3 Tangent Plane to a Surface 77 E
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2.4 Directional Derivatives and the
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2.4 Directional Derivatives and the
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2.5 Maxima and Minima 83 2.5 Maxima
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2.5 Maxima and Minima 85 If conditi
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2.5 Maxima and Minima 87 So D= ∂2
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2.6 Unconstrained Optimization: Num
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2.6 Unconstrained Optimization: Num
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2.6 Unconstrained Optimization: Num
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2.6 Unconstrained Optimization: Num
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2.7 Constrained Optimization: Lagra
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2.7 Constrained Optimization: Lagra
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3 Multiple Integrals 3.1 Double Int
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3.1 Double Integrals 103 Solution:
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3.2 Double Integrals Over a General
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3.2 Double Integrals Over a General
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3.2 Double Integrals Over a General
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3.3 Triple Integrals 111 double int
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3.4 Numerical Approximation of Mult
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3.4 Numerical Approximation of Mult
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3.5 Change of Variables in Multiple
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3.5 Change of Variables in Multiple
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3.5 Change of Variables in Multiple
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3.5 Change of Variables in Multiple
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3.6 Application: Center of Mass 125
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3.6 Application: Center of Mass 127
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3.7 Application: Probability and Ex
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3.7 Application: Probability and Ex
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3.7 Application: Probability and Ex
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4 Line and Surface Integrals 4.1 Li
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4.1 Line Integrals 137 whichyoumayr
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4.1 Line Integrals 139 be the posit
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4.1 Line Integrals 141 So in both c
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4.2 Properties of Line Integrals 14
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4.2 Properties of Line Integrals 14
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4.2 Properties of Line Integrals 14
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4.2 Properties of Line Integrals 14
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4.3 Green’s Theorem 151 (4.24). S
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4.3 Green’s Theorem 153 If we mod
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4.3 Green’s Theorem 155 ☛ ✟
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4.4 Surface Integrals and the Diver
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4.4 Surface Integrals and the Diver
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4.4 Surface Integrals and the Diver
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4.4 Surface Integrals and the Diver
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4.5 Stokes’ Theorem 165 4.5 Stoke
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4.5 Stokes’ Theorem 167 Example 4
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4.5 Stokes’ Theorem 169 along tha
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4.5 Stokes’ Theorem 171 Thus, ∂
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4.5 Stokes’ Theorem 173 The bound
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4.5 Stokes’ Theorem 175 Finally,b
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4.6 Gradient, Divergence, Curl and
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4.6 Gradient, Divergence, Curl and
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4.6 Gradient, Divergence, Curl and
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4.6 Gradient, Divergence, Curl and
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4.6 Gradient, Divergence, Curl and
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Bibliography Abbott, E.A., Flatland
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Appendix A Answers and Hints to Sel
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191 Section 2.7 (p. 100) ( ( ) −4
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193 In this case, n(av,bw) must be
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195 n(v,w)=n(v 1 i+v 2 j+v 3 k,w 1
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197 For a function z= f(x,y), is t
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199 2*(x**2) + y**2 654321 25 20 ex
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GNU Free Documentation License Vers
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203 means the text near the most pr
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205 G. Preserve in that license not
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207 7. AGGREGATION WITH INDEPENDENT
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History Thissectioncontainstherevis
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Index 211 right-handed ............
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Index 213 right-hand rule..........