Calculus volume 1

OpenStax

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0.1 About openstax

0.2 About openstax's resources

0.3 Customization

0.6 About Calculus Volume 1

0.7 Coverage and scope

0.8 Pedagogical foundation

0.9 Assessments that reinforce key concepts

0.10 Early or late transcendentals

0.11 Comprehensive art program

0.12 Assessments that reinforce key concepts

0.13 Ancillaries

0.15 About our team

0.16 Senior contributing authors

0.17 Contributing authors

1 Table of integrals

2 Table of derivatives

3 Review of pre-calculus

Functions and graphs

1 Review of functions

1.2 Representing functions

1.5 Algebraic formulas

1.6 Combining functions

1.7 Combining functions with mathematical operators

1.8 Function composition

1.9 Symmetry of functions

1.10 Key concepts

1.11 Key equations

2 Basic classes of functions

2.1 Linear functions and slope

2.2 Polynomials

2.3 Power functions

2.4 Behavior at infinity

2.5 Zeros of polynomial functions

2.6 Mathematical models

2.7 Algebraic functions

2.8 Transcendental functions

2.9 Piecewise-defined functions

2.10 Transformations of functions

2.11 Key concepts

2.12 Key equations

3 Trigonometric functions

4 Inverse functions

5 Exponential and logarithmic functions

1 A preview of calculus

2 The limit of a function

3 The limit laws

4.1 Continuity at a point

4.3 Types of discontinuities

4.4 Continuity over an interval

4.6 The intermediate value theorem

4.7 Key concepts

5 The precise definition of a limit

1 Defining the derivative

1.1 Tangent lines

1.2 The derivative of a function at a point

1.3 Velocities and rates of change

1.4 Key concepts

1.5 Key equations

2 The derivative as a function

3 Differentiation rules

4 Derivatives as rates of change

5 Derivatives of trigonometric functions

6 The chain rule

7 Derivatives of inverse functions

8 Implicit differentiation

9 Derivatives of exponential and logarithmic functions

Applications of derivatives

1 Related rates

2 Linear approximations and differentials

2.1 Linear approximation of a function at a point

2.2 Differentials

2.3 Calculating the amount of error

2.4 Key concepts

2.5 Key equations

3 Maxima and minima

3.1 Absolute extrema

3.2 Local extrema and critical points

3.4 Locating absolute extrema

3.5 Key concepts

4 The mean value theorem

4.1 Rolle’s theorem

4.3 The mean value theorem and its meaning

4.5 Corollaries of the mean value theorem

4.9 Key concepts

5 Derivatives and the shape of a graph

6 Limits at infinity and asymptotes

7 Applied optimization problems

7.1 Solving optimization problems over a closed, bounded interval

7.2 Solving optimization problems when the interval is not closed or is

7.3 Key concepts

8 L’hôpital’s rule

9 Newton’s method

10 Antiderivatives

10.1 The reverse of differentiation

10.2 Indefinite integrals

10.3 Initial-value problems

10.4 Key concepts

10.5 Chapter review exercises

1 Approximating areas

1.1 Sigma (summation) notation

1.3 Approximating area

1.4 Forming riemann sums

1.5 Key concepts

1.6 Key equations

2 The definite integral

3 The fundamental theorem of calculus

4 Integration formulas and the net change theorem

5.2 Substitution for definite integrals

5.3 Key concepts

5.4 Key equations

6 Integrals involving exponential and logarithmic functions

7 Integrals resulting in inverse trigonometric functions

7.1 Integrals that result in inverse sine functions

7.3 Integrals resulting in other inverse trigonometric functions

7.4 Key concepts

7.5 Key equations

7.6 Chapter review exercises

Applications of integration

1 Areas between curves

2 Determining volumes by slicing

2.1 Volume and the slicing method

2.2 Solids of revolution

2.3 The disk method

2.4 The washer method

2.5 Key concepts

2.6 Key equations

3 Volumes of revolution: cylindrical shells

4 Arc length of a curve and surface area

5 Physical applications

6 Moments and centers of mass

7 Integrals, exponential functions, and logarithms

8 Exponential growth and decay

9 Calculus of the hyperbolic functions

9.1 Derivatives and integrals of the hyperbolic functions

9.2 Calculus of inverse hyperbolic functions

9.3 Applications

9.4 Key concepts

9.5 Chapter review exercises

Source: OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2

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