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

1.1 Area of a region between two curves

1.2 Areas of compound regions

1.3 Regions defined with respect to y

1.4 Key concepts

1.5 Key equations

2 Determining volumes by slicing

3 Volumes of revolution: cylindrical shells

3.1 The method of cylindrical shells

3.2 Which method should we use?

3.3 Key concepts

3.4 Key equations

4 Arc length of a curve and surface area

5 Physical applications

5.1 Mass and density

5.2 Work done by a force

5.3 Work done in pumping

5.4 Hydrostatic force and pressure

5.5 Key concepts

5.6 Key equations

6 Moments and centers of mass

7 Integrals, exponential functions, and logarithms

8 Exponential growth and decay

8.1 Exponential growth model

8.2 Exponential decay model

8.3 Key concepts

9 Calculus of the hyperbolic functions

Techniques of integration

1 Integration by parts

1.1 The integration-by-parts formula

1.2 Integration by parts for definite integrals

1.3 Key concepts

1.4 Key equations

2 Trigonometric integrals

3 Trigonometric substitution

3.1 Integrals involving a 2 − x 2

3.2 Integrating expressions involving a 2 + x 2

3.3 Integrating expressions involving x 2 − a 2

3.4 Key concepts

4 Partial fractions

5 Other strategies for integration

6 Numerical integration

7 Improper integrals

7.1 Integrating over an infinite interval

7.2 Integrating a discontinuous integrand

7.3 A comparison theorem

7.4 Key concepts

7.5 Key equations

7.6 Chapter review exercises

Introduction to differential equations

1 Basics of differential equations

2 Direction fields and numerical methods

2.1 Creating direction fields

2.2 Using direction fields

2.3 Euler’s method

2.4 Key concepts

2.5 Key equations

3 Separable equations

4 The logistic equation

5 First-order linear equations

Sequences and series

2 Infinite series

3 The divergence and integral tests

3.1 Divergence test

3.2 Integral test

3.3 The p -series

3.4 Estimating the value of a series

3.5 Key concepts

3.6 Key equations

4 Comparison tests

5 Alternating series

6 Ratio and root tests

1 Power series and functions

1.1 Form of a power series

1.2 Convergence of a power series

1.4 Representing functions as power series

1.5 Key concepts

1.6 Key equations

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

2.1 Derivatives of parametric equations

2.3 Second-order derivatives

2.4 Integrals involving parametric equations

2.5 Arc length of a parametric curve

2.6 Surface area generated by a parametric curve

2.7 Key concepts

2.8 Key equations

3 Polar coordinates

3.1 Defining polar coordinates

3.2 Polar curves

3.3 Symmetry in polar coordinates

3.4 Key concepts

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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