Torrent details for "Ghergu M. Differential Calculus in Several Variables. A Learning-by-Doing 2024 [andryold1]"    Log in to bookmark

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Preface
Foreword to the Student
Vectors and Sets in Rm
Vectors in Rm
Lines and Planes in R3
Points or Vectors?
Convergent Sequences in Rm
Sets in Rm
Functions of Several Variables
Functions, Domains and Codomains
The Graph of a Function
Level Sets
Quadric Surfaces
Curves
Limits and Continuity
Limit of a Function
Two-Path Test for the Nonexistence of a Limit
Functions with Limit at a Point
Continuous Functions
Continuous Extensions
Differentiable Functions
Partial Derivatives
The Tangent Plane to a Surface
Differentiable Functions
A Criterion for Differentiability
Differentiability of Vector-Valued Functions
Chain Rule
Chain Rule for Several Variable Functions
Implicit Differentiation
Mean Value Theorem in Several Variables
Directional Derivative
Directional Derivative
A Geometric Insight
The Gradient and the Level Sets
Second-Order Derivatives
Second-Order Derivatives
Chain Rule for Second-Order Derivatives
The Laplace Operator
Taylor’s Theorem
Higher Order Derivatives
Taylor’s Theorem
Linear and Quadratic Approximation
Implicit Function Theorem
Preliminaries
Two-Variable Case
Three-Variable Case
The General Case
Local and Global Extrema
Extreme Values and Critical Points
Second-Order Derivative Test
The Inconclusive Case
Constrained Optimization
Motivation
Lagrange Multipliers Method, Part I
Lagrange Multipliers Method, Part II
Extrema of Functions on General Compact Sets
Some Applications to Business and Economics
Solutions
Useful Facts in Linear Algebra
Bibliography

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