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n-Dimensional Euclidean Space Review Exercises for Chapter 1 2.1 The Geometry of Real-Valued Functions 2.2 Limits and Continuity 2.3 Differentiation 2.4 Introduction to Paths and Curves 2.5 Properties of the Derivative 2.6 Gradients and Directional Derivatives Review Exercises for Chapter 2 3.1 Iterated Partial Derivatives 3.2 Taylor's Theorem 3.3 Extrema of Real-Valued Functions 3.4 Constrained Extrema and Lagrange Multipliers 3.5 The Implicit Function Theorem Review Exercises for Chapter 3 4.1 Acceleration and Newton's Second Law 4.2 Arc Length 4.3 Vector Fields 4.4 Divergence and Curl Review Exercises for Chapter 4 5.1 Introduction 5.2 The Double Integral Over a Rectangle 5.3 The Double Integral Over More General Regions 5.4 Changing the Order of Integration 5.5 The Triple Integral Review Exercises for Chapter 5 6.1 The Geometry of Maps from R^2 to R^2 6.2 The Change of Variables Theorem 6.3 Applications 6.4 Improper Integrals Review Exercises for Chapter 6 7.1 The Path Integral 7.2 Line Integrals 7.3 Parametrized Surfaces 7.4 Area of a Surface 7.5 Integrals of Scalar Functions Over Surfaces 7.6 Surface Integrals of Vector Fields 7.7 Applications to Differential Geometry, Physics, and Forms of Life Review Exercises for Chapter 7 8.1 Green's Theorem 8.2 Stokes' Theorem 8.3 Conservative Fields 8.4 Gauss' Theorem 8.Simple and minimal line s reddit icon summary
1.1 Vectors in Two- and Three-Dimensional Space 1.2 The Inner Product, Length, and Distance 1.3 Matrices, Determinants, and the Cross Product 1.4 Cylindrical and Spherical Coordinates 1.5.
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