دانلود کتاب Multivariable Calculus

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Preface\nI Preliminaries\n Rn\n Vector arithmetic\n Linear transformations\n The matrix of a linear transformation\n Matrix multiplication\n The geometry of the dot product\n Determinants\n Exercises for Chapter 1\nII Vector-valued functions of one variable\n Paths and curves\n Parametrizations\n Velocity, acceleration, speed, arclength\n Integrals with respect to arclength\n The geometry of curves: tangent and normal vectors\n The cross product\n The geometry of space curves: Frenet vectors\n Curvature and torsion\n The Frenet-Serret formulas\n The classification of space curves\n Exercises for Chapter 2\nIII Real-valued functions\n Real-valued functions: preliminaries\n Graphs and level sets\n More surfaces in R3\n The equation of a plane in R3\n Open sets\n Continuity\n Some properties of continuous functions\n The Cauchy-Schwarz and triangle inequalities\n Limits\n Exercises for Chapter 3\n Real-valued functions: differentiation\n The first-order approximation\n Conditions for differentiability\n The mean value theorem\n The C1 test\n The Little Chain Rule\n Directional derivatives\n f as normal vector\n Higher-order partial derivatives\n Smooth functions\n Max/min: critical points\n Classifying nondegenerate critical points\n The second-order approximation\n Sums and differences of squares\n Max/min: Lagrange multipliers\n Exercises for Chapter 4\n Real-valued functions: integration\n Volume and iterated integrals\n The double integral\n Interpretations of the double integral\n Parametrizations of surfaces\n Polar coordinates (r, ) in R2\n Cylindrical coordinates (r, , z) in R3\n Spherical coordinates (, , ) in R3\n Integrals with respect to surface area\n Triple integrals and beyond\n Exercises for Chapter 5\nIV Vector-valued functions\n Differentiability and the chain rule\n Continuity revisited\n Differentiability revisited\n The chain rule: a conceptual approach\n The chain rule: a computational approach\n Exercises for Chapter 6\n Change of variables\n Change of variables for double integrals\n A word about substitution\n Examples: linear changes of variables, symmetry\n Change of variables for n-fold integrals\n Exercises for Chapter 7\nV Integrals of vector fields\n Vector fields\n Examples of vector fields\n Exercises for Chapter 8\n Line integrals\n Definitions and examples\n Another word about substitution\n Conservative fields\n Green\'s theorem\n The vector field W\n The converse of the mixed partials theorem\n Exercises for Chapter 9\n Surface integrals\n What the surface integral measures\n The definition of the surface integral\n Stokes\'s theorem\n Curl fields\n Gauss\'s theorem\n The inverse square field\n A more substitution-friendly notation for surface integrals\n Independence of parametrization\n Exercises for Chapter 10\n Working with differential forms\n Integrals of differential forms\n Derivatives of differential forms\n A look back at the theorems of multivariable calculus\n Exercises for Chapter 11\n Answers to selected exercises\n Index