Advanced Calculus of Several Variables (1973)
Part I. Euclidean Space and Linear Mappings
Chapter 1. THE VECTOR SPACE Rn
Chapter 3. INNER PRODUCTS AND ORTHOGONALITY
Chapter 4. LINEAR MAPPINGS AND MATRICES
Chapter 5. THE KERNEL AND IMAGE OF A LINEAR MAPPING
Chapter 7. LIMITS AND CONTINUITY
Chapter 8. ELEMENTARY TOPOLOGY OF Rn
Part II. Multivariable Differential Calculus
Chapter 2. DIRECTIONAL DERIVATIVES AND THE DIFFERENTIAL
Chapter 5. MAXIMA AND MINIMA, MANIFOLDS, AND LAGRANGE MULTIPLIERS
Chapter 6. TAYLOR'S FORMULA FOR SINGLE-VARIABLE FUNCTIONS
Chapter 7. TAYLOR'S FORMULA IN SEVERAL VARIABLES
Chapter 8. THE CLASSIFICATION OF CRITICAL POINTS
Part III. Successive Approximations and Implicit Functions
Chapter 1. NEWTON'S METHOD AND CONTRACTION MAPPINGS
Chapter 2. THE MULTIVARIABLE MEAN VALUE THEOREM
Chapter 3. THE INVERSE AND IMPLICIT MAPPING THEOREMS/a>
Part IV. Multiple Integrals
Chapter 1. AREA AND THE 1-DIMENSIONAL INTEGRAL
Chapter 2. VOLUME AND THE n-DIMENSIONAL INTEGRAL
Chapter 3. STEP FUNCTIONS AND RIEMANN SUMS
Chapter 4. ITERATED INTEGRALS AND FUBINI'S THEOREM
Chapter 5. CHANGE OF VARIABLES
Chapter 6. IMPROPER INTEGRALS AND ABSOLUTELY INTEGRABLE FUNCTIONS
Part V. Line and Surface Integrals; Differential Forms and Stokes' Theorem
Chapter 1. PATHLENGTH AND LINE INTEGRALS
Chapter 3. MULTILINEAR FUNCTIONS AND THE AREA OF A PARALLELEPIPED
Chapter 7. THE CLASSICAL THEOREMS OF VECTOR ANALYSIS
Chapter 8. CLOSED AND EXACT FORMS
Part VI. The Calculus of Variations
Chapter 1. NORMED VECTOR SPACES AND UNIFORM CONVERGENCE
Chapter 2. CONTINUOUS LINEAR MAPPINGS AND DIFFERENTIALS
Chapter 3. THE SIMPLEST VARIATIONAL PROBLEM
Chapter 4. THE ISOPERIMETRIC PROBLEM