CK12.ORG - Single Variable Calculus

806

[{id:"2276",title:"Functions, Limits, and Continuity"},{id:"2277",title:"Derivatives"},{id:"2278",title:"Applications of Derivatives"},{id:"2279",title:"Integration"},{id:"2280",title:"Applications of Definite Integrals"},{id:"2281",title:"Transcendental Functions"},{id:"2282",title:"Integration Techniques"},{id:"2283",title:"Infinite Series"},]

FlexBook: Single Variable Calculus

Table of Contents

Chapter Title

Creator

Functions, Limits, and Continuity

CK-12 Foundation

Functions, Limits, and Continuity

A review of the basics of functions is given. Students use linear approximations to study the limit...

Created: Oct. 06, 2009 03:51 PM

Last edited: Jun. 16, 2010 02:16 PM

A review of the basics of functions is given. Students use linear approximations to study the limit process, before a more formal treatment of limits is given.

Categories: Calculus , Single Variable , Continuity , Differentiation

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: evaluating limits , finding limits , models , functions

Created: Oct. 06, 2009 03:51 PM

Last Edited: Jun. 16, 2010 02:16 PM

Functions, Limits, and Continuity

Derivatives

CK-12 Foundation

Derivatives

Students explore instantaneous rate of change, and the relationship between continuity and...

Created: Oct. 06, 2009 03:51 PM

Last edited: Jun. 16, 2010 02:16 PM

Students explore instantaneous rate of change, and the relationship between continuity and differentiability. The Chain Rule and implicit differentiation are reviewed.

Categories: Calculus , Single Variable , Continuity , Differentiation

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: techniques of differentiation , rate of change , derivative , tangent lines

Created: Oct. 06, 2009 03:51 PM

Last Edited: Jun. 16, 2010 02:16 PM

Derivatives

Applications of Derivatives

CK-12 Foundation

Applications of Derivatives

Students gain practice with using the derivatives in related rates problems. Additional topics...

Created: Oct. 06, 2009 03:51 PM

Last edited: Jun. 16, 2010 02:16 PM

Students gain practice with using the derivatives in related rates problems. Additional topics include The First Derivative Test, The Second Derivative Test, limits at infinity, optimization, and approximation errors.

Categories: Calculus , Single Variable , Differentiation , Functions

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: approximating errors , optimization , second derivative test , limits at infinity

Created: Oct. 06, 2009 03:51 PM

Last Edited: Jun. 16, 2010 02:16 PM

Applications of Derivatives

Integration

CK-12 Foundation

Integration

Topics in this chapter include: indefinite integrals calculus, initial value problems, definite...

Created: Oct. 06, 2009 03:51 PM

Last edited: Jun. 16, 2010 02:16 PM

Topics in this chapter include: indefinite integrals calculus, initial value problems, definite integrals, the Fundamental Theorem of Calculus, integration by substitution, and numerical integration.

Categories: Calculus , Differential Equations , Ordinary Differential Equations , Single Variable

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: integration by substitution , fundamental theorem of calculus , definite integrals , initial value problems

Created: Oct. 06, 2009 03:51 PM

Last Edited: Jun. 16, 2010 02:16 PM

Integration

Applications of Definite Integrals

CK-12 Foundation

Applications of Definite Integrals

This chapter includes applications of the definite integral, such as calculating areas between two...

Created: Oct. 06, 2009 03:51 PM

Last edited: Jun. 16, 2010 02:16 PM

This chapter includes applications of the definite integral, such as calculating areas between two curves, volumes, length of curves, and other real-world applications in physics and statistics.

Categories: Calculus , Single Variable , Integration , Mathematics

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: applications in physics , surface area of revolution , volume of solid of revolutions , area between two curves

Created: Oct. 06, 2009 03:51 PM

Last Edited: Jun. 16, 2010 02:16 PM

Applications of Definite Integrals

Transcendental Functions

CK-12 Foundation

Transcendental Functions

This chapter includes differentiation and integration of logarithmic and exponential functions,...

Created: Oct. 06, 2009 03:52 PM

Last edited: Jun. 16, 2010 02:16 PM

This chapter includes differentiation and integration of logarithmic and exponential functions, exponential growth and decay, derivatives and integrals involving inverse trigonometric functions, and L’Hospital’s Rule.

Categories: Calculus , Single Variable , Continuity , Differentiation

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: functions , l'hospital's rule , exponential functions , logarithmic functions

Created: Oct. 06, 2009 03:52 PM

Last Edited: Jun. 16, 2010 02:16 PM

Transcendental Functions

Integration Techniques

CK-12 Foundation

Integration Techniques

Topics in this chapter include: integration by substitution, integration by parts, integration by...

Created: Oct. 06, 2009 03:52 PM

Last edited: Jun. 16, 2010 02:16 PM

Topics in this chapter include: integration by substitution, integration by parts, integration by partial fractions, trigonometric integrals, trigonometric substitutions, and improper integrals.

Categories: Calculus , Differential Equations , Ordinary Differential Equations , First Order

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: integration by substitution , integration , trigonometric integrals , improper integrals

Created: Oct. 06, 2009 03:52 PM

Last Edited: Jun. 16, 2010 02:16 PM

Integration Techniques

Infinite Series

CK-12 Foundation

Infinite Series

This chapter introduces the study of sequences and infinite series. The properties presented describ...

Created: Oct. 06, 2009 03:52 PM

Last edited: Jun. 16, 2010 02:16 PM

This chapter introduces the study of sequences and infinite series. The properties presented describe the behavior of a sequence or series, including whether a sequence approaches a number or an infinite series adds to a number.

Categories: Calculus , Several Variables , Taylor Series , Single Variable

Grades: 11 , 12

Organizations: CK-12 Foundation , CK-12 Community

Tags: comparison test , limit comparison test , integral test , alternating series test

Created: Oct. 06, 2009 03:52 PM

Last Edited: Jun. 16, 2010 02:16 PM

Infinite Series

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Single Variable Calculus

Reviewed

Created: Oct. 06, 2009 03:51 PM
Last modified: 2 months, 2 weeks ago

CK-12 Foundation’s Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

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Categories:

Calculus

Continuity

Differentiation

Functions

Integration

Limits

Mathematics

Series

Single Variable

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Reviewed

CK-12 readers should treat this FlexBook as a final draft. This FlexBook underwent a thorough review conducted by practicing teachers, domain experts, copyeditors, technical editors, and has been developed following state and national standards. It can be used in its current form, "flexed" (customized), and/or printed by the user. CK-12 supports feedback on all of its FlexBooks so that they can be continually improved and updated.

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