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Учебные пособия

Calculus Volume 1

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Main Body

Linear Approximations and Differentials
Page 1
Maxima and Minima

Functions and Graphs

The Mean Value Theorem
Review of Functions
Derivatives and the Shape of a Graph
Basic Classes of Functions
Limits at Infinity and Asymptotes
Trigonometric Functions
Applied Optimization Problems
Inverse Functions
L’Hôpital’s Rule
Exponential and Logarithmic Functions
Newton’s Method
Chapter 1
Antiderivatives

Limits

Integration

A Preview of Calculus
Introduction
The Limit of a Function
Approximating Areas
The Limit Laws
The Definite Integral
Continuity
The Fundamental Theorem of Calculus
The Precise Definition of a Limit
Integration Formulas and the Net Change Theorem

Derivatives

Substitution
Introduction
Integrals Involving Exponential and Logarithmic Functions
Defining the Derivative
Integrals Resulting in Inverse Trigonometric Functions
The Derivative as a Function

Applications of Integration

Differentiation Rules
Introduction
Derivatives as Rates of Change
Areas between Curves
Derivatives of Trigonometric Functions
Determining Volumes by Slicing
The Chain Rule
Volumes of Revolution: Cylindrical Shells
Derivatives of Inverse Functions
Arc Length of a Curve and Surface Area
Implicit Differentiation
Physical Applications
Derivatives of Exponential and Logarithmic Functions
Moments and Centers of Mass

Applications of Derivatives

Integrals, Exponential Functions, and Logarithms
Introduction
Exponential Growth and Decay
Related Rates
Calculus of the Hyperbolic Functions