Calculus volume 2

OpenStax

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0.1 About openstax

0.2 About openstax's resources

0.3 Customization

0.6 About Calculus Volume 2

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

1 Approximating areas

2 The definite integral

3 The fundamental theorem of calculus

4 Integration formulas and the net change theorem

6 Integrals involving exponential and logarithmic functions

7 Integrals resulting in inverse trigonometric functions

Applications of integration

1 Areas between curves

2 Determining volumes by slicing

3 Volumes of revolution: cylindrical shells

4 Arc length of a curve and surface area

5 Physical applications

6 Moments and centers of mass

6.1 Center of mass and moments

6.2 Center of mass of thin plates

6.3 The symmetry principle

6.4 Theorem of pappus

6.6 Key concepts

6.7 Key equations

7 Integrals, exponential functions, and logarithms

8 Exponential growth and decay

9 Calculus of the hyperbolic functions

Techniques of integration

1 Integration by parts

2 Trigonometric integrals

3 Trigonometric substitution

4 Partial fractions

5 Other strategies for integration

6 Numerical integration

6.1 The midpoint rule

6.2 The trapezoidal rule

6.3 Absolute and relative error

6.4 Simpson’s rule

6.5 Key concepts

6.6 Key equations

7 Improper integrals

Introduction to differential equations

1 Basics of differential equations

2 Direction fields and numerical methods

3 Separable equations

4 The logistic equation

5 First-order linear equations

Sequences and series

2 Infinite series

3 The divergence and integral tests

4 Comparison tests

5 Alternating series

6 Ratio and root tests

1 Power series and functions

2 Properties of power series

3 Taylor and maclaurin series

3.1 Overview of taylor/maclaurin series

3.2 Taylor polynomials

3.3 Taylor’s theorem with remainder

3.5 Representing functions with taylor and maclaurin series

3.6 Key concepts

3.7 Key equations

4 Working with taylor series

Parametric equations and polar coordinates

1 Parametric equations

2 Calculus of parametric curves

3 Polar coordinates

4 Area and arc length in polar coordinates

5 Conic sections

Source: OpenStax, Calculus volume 2. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11965/1.2

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