A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2006 To book contents

6. Limits and Derivatives

• 6.1. Basic Concepts of Mathematical Analysis
  • 6.1.1. Number Sets. Functions of Real Variable
  • 6.1.2. Limit of a Sequence
  • 6.1.3. Limit of a Function. Asymptotes
  • 6.1.4. Infinitely Small and Infinitely Large Functions
  • 6.1.5. Continuous Functions. Discontinuities of the First and the Second Kind
  • 6.1.6. Convex and Concave Functions
  • 6.1.7. Functions of Bounded Variation
  • 6.1.8. Convergence of Functions
• 6.2. Differential Calculus for Functions of a Single Variable
  • 6.2.1. Derivative and Differential, Their Geometrical and Physical Meaning
  • 6.2.2. Table of Derivatives and Differentiation Rules
  • 6.2.3. Theorems about Differentiable Functions. L'Hospital Rule
  • 6.2.4. Higher-Order Derivatives and Differentials. Taylor's Formula
  • 6.2.5. Extremal Points. Points of Inflection
  • 6.2.6. Qualitative Analysis of Functions and Construction of Graphs
  • 6.2.7. Approximate Solution of Equations (Root-Finding Algorithms for Continuous Functions)
• 6.3. Functions of Several Variables. Partial Derivatives
  • 6.3.1. Point Sets. Functions. Limits and Continuity
  • 6.3.2. Differentiation of Functions of Several Variables
  • 6.3.3. Directional Derivative. Gradient. Geometrical Applications
  • 6.3.4. Extremal Points of Functions of Several Variables
  • 6.3.5. Differential Operators of the Field Theory
• References for Chapter 6

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