Calculus volume 3

OpenStax

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0.1 About openstax

0.2 About openstax's resources

0.3 Customization

0.6 About Calculus Volume 3

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

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

4 Area and arc length in polar coordinates

5 Conic sections

Vectors in space

1 Vectors in the plane

2 Vectors in three dimensions

3 The dot product

4 The cross product

5 Equations of lines and planes in space

5.1 Equations for a line in space

5.2 Distance between a point and a line

5.3 Relationships between lines

5.4 Equations for a plane

5.5 Parallel and intersecting planes

5.6 Key concepts

5.7 Key equations

6 Quadric surfaces

7 Cylindrical and spherical coordinates

Vector-valued functions

1 Vector-valued functions and space curves

2 Calculus of vector-valued functions

3 Arc length and curvature

4 Motion in space

Differentiation of functions of several variables

1 Functions of several variables

2 Limits and continuity

3 Partial derivatives

3.1 Derivatives of a function of two variables

3.2 Functions of more than two variables

3.3 Higher-order partial derivatives

3.4 Partial differential equations

3.5 Key concepts

3.6 Key equations

4 Tangent planes and linear approximations

5 The chain rule

6 Directional derivatives and the gradient

7 Maxima/minima problems

7.1 Critical points

7.2 Second derivative test

7.3 Absolute maxima and minima

7.4 Key concepts

7.5 Key equations

8 Lagrange multipliers

Multiple integration

1 Double integrals over rectangular regions

2 Double integrals over general regions

3 Double integrals in polar coordinates

4 Triple integrals

4.1 Integrable functions of three variables

4.2 Triple integrals over a general bounded region

4.3 Changing the order of integration

4.4 Average value of a function of three variables

4.5 Key concepts

4.6 Key equations

5 Triple integrals in cylindrical and spherical coordinates

6 Calculating centers of mass and moments of inertia

7 Change of variables in multiple integrals

7.1 Planar transformations

7.3 Change of variables for double integrals

7.4 Change of variables for triple integrals

7.5 Key concepts

7.6 Chapter review exercises

Vector calculus

1 Vector fields

2 Line integrals

3 Conservative vector fields

4 Green’s theorem

5 Divergence and curl

5.4 Using divergence and curl

5.8 Key concepts

5.9 Key equations

6 Surface integrals

7 Stokes’ theorem

8 The divergence theorem

Second-order differential equations

1 Second-order linear equations

2 Nonhomogeneous linear equations

4 Series solutions of differential equations

Source: OpenStax, Calculus volume 3. OpenStax CNX. Feb 05, 2016 Download for free at http://legacy.cnx.org/content/col11966/1.2

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