Multivariable Calculus, Linear Algebra, and Differential Equations

¿Preface1 Vectors In The Plane 1.1 Vectors and Vector Operations 1.2 The Dot Product 1.3 Some Applications of Vectors (Optional) Review Exercises for Chapter One2 Vector Functions, Vector Differentiation, And Parametric Equations In R2 2.1 Vector Functions and Parametric Equations 2.2 The Equation of the Tangent Line to a Parametric Curve 2.3 The Differentiation and Integration of a Vector Function 2.4 Some Differentiation Formulas 2.5 Arc Length Revisited 2.6 Arc Length as a Parameter 2.7 Velocity, Acceleration, Force, and Momentum 2.8 Curvature and the Acceleration Vector (Optional) Review Exercises for Chapter Two3 Vectors In Space 3.1 The Rectangular Coordinate System in Space 3.2 Vectors in R3 3.3 Lines in R3 3.4 The Cross Product of Two Vectors 3.5 Planes 3.6 Quadric Surfaces 3.7 The Space Rn and the Scalar Product 3.8 Vector Functions and Parametric Equations in R3 3.9 Cylindrical and Spherical Coordinates Review Exercises for Chapter Three4 Differentiation Of Functions Of Two Or More Variables 4.1 Functions of Two or More Variables 4.2 Limits and Continuity 4.3 Partial Derivatives 4.4 Higher-Order Partial Derivatives 4.5 Differentiability and the Gradient 4.6 The Chain Rules 4.7 Tangent Planes, Normal Lines, and Gradients 4.8 Directional Derivatives and the Gradient 4.9 Conservative Vector Fields and the Gradient (Optional) 4.10 The Total Differential and Approximation 4.11 Exact Vector Fields or How to Obtain a Function from Its Gradient 4.12 Maxima and Minima for a Function of Two Variables 4.13 Constrained Maxima and Minima-Lagrange Multipliers Review Exercises for Chapter Four5 Multiple Integration 5.1 Volume Under a Surface and the Double Integral 5.2 The Calculation of Double Integrals 5.3 Density, Mass, and Center of Mass (Optional) 5.4 Double Integrals in Polar Coordinates 5.5 Surface Area 5.6 The Triple Integral 5.7 The Triple Integral in Cylindrical and Spherical Coordinates Review Exercises for Chapter Five6 Introduction To Vector Analysis 6.1 Vector Fields 6.2 Work, Line Integrals in the Plane, and Independence of Path 6.3 Green's Theorem in the Plane 6.4 Line Integrals in Space 6.5 Surface Integrals 6.6 Divergence and Curl of a Vector Field in R3 6.7 Stokes's Theorem 6.8 The Divergence Theorem 6.9 Changing Variables in Multiple Integrals and the Jacobian Review Exercises for Chapter Six7 Matrices And Linear Systems Of Equations 7.1 Matrices 7.2 Matrix Products 7.3 Linear Systems of Equations 7.4 Matrices and Linear Systems of Equations 7.5 The Inverse of a Square Matrix 7.6 The Transpose of a Matrix Review Exercises for Chapter Seven8 Determinants 8.1 Definitions 8.2 Properties of Determinants 8.3 Determinants and Inverses 8.4 Cramer's Rule (Optional) Review Exercises for Chapter Eight9 Vector Spaces And Linear Transformations 9.1 Vector Spaces 9.2 Subspaces 9.3 Linear Independence, Linear Combination and Span 9.4 Basis and Dimension 9.5 Change of Basis (Optional) 9.6 Linear Transformations 9.7 Properties of Linear Transformations: Range and Kernel 9.8 The Rank and Nullity of a Matrix 9.9 The Matrix Representation of a Linear Transformation 9.10 Eigenvalues and Eigenvectors 9.11 If Time Permits: A Model of Population Growth 9.12 Similar Matrices and Diagonalization Review Exercises for Chapter Nine10 Calculus In Rn 10.1 Taylor's Theorem in n Variables 10.2 Inverse Functions and the Implicit Function Theorem: I 10.3 Functions from Rn to Rm 10.4 Derivatives and the Jacobian Matrix 10.5 Inverse Functions and the Implicit Function Theorem: II Review Exercises for Chapter Ten11 Ordinary Differential Equations 11.1 Introduction 11.