26Axx Functions of one variable
This subtopic studies functions of one variable, covering continuity, differentiability, variation, and the analytic behavior of real or complex-valued functions.
Specific topics
26A03 Foundations: limits, continuity, and related questions
Overview
26A03 studies foundations: limits, continuity, and related questions in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for foundations: limits, continuity, and related questions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A06 One-variable calculus
Overview
26A06 studies one-variable calculus in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for one-variable calculus
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A09 Elementary functions
Overview
26A09 studies elementary functions in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for elementary functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A12 Rate of growth of functions, orders of infinity
Overview
26A12 studies rate of growth of functions, orders of infinity in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for rate of growth of functions, orders of infinity
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A15 Continuity and related questions
Overview
26A15 studies continuity and related questions in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for continuity and related questions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A16 Lipschitz (Hölder) classes
Overview
26A16 studies lipschitz (hã¶lder) classes in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for lipschitz (hã¶lder) classes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A21 Classification of real functions; Baire classification
Overview
26A21 studies classification of real functions; baire classification in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for classification of real functions; baire classification
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A24 Differentiation (functions of one variable)
Overview
26A24 studies differentiation (functions of one variable) in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for differentiation (functions of one variable)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A27 Nondifferentiable functions
Overview
26A27 studies nondifferentiable functions in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for nondifferentiable functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A30 Singular functions, Cantor functions, functions with other special properties
Overview
26A30 studies singular functions, cantor functions, functions with other special properties in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for singular functions, cantor functions, functions with other special properties
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A33 Fractional derivatives and integrals
Overview
26A33 studies fractional derivatives and integrals in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fractional derivatives and integrals
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A36 Antidifferentiation
Overview
26A36 studies antidifferentiation in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for antidifferentiation
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A39 Denjoy and Perron integrals, other special integrals
Overview
26A39 studies denjoy and perron integrals, other special integrals in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for denjoy and perron integrals, other special integrals
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
Overview
26A42 studies integrals of riemann, stieltjes and lebesgue type in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integrals of riemann, stieltjes and lebesgue type
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A45 Functions of bounded variation, generalizations
Overview
26A45 studies functions of bounded variation, generalizations in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for functions of bounded variation, generalizations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A46 Absolutely continuous real functions of one variable
Overview
26A46 studies absolutely continuous real functions of one variable in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for absolutely continuous real functions of one variable
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A48 Monotonic functions; generalizations
Overview
26A48 studies monotonic functions; generalizations in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for monotonic functions; generalizations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks
26A51 Convexity of real functions of one variable
Overview
26A51 studies convexity of real functions of one variable in functions of one variable. It studies real-valued and complex-valued functions of a single variable, including smoothness, convexity, approximation, and asymptotic behavior.
Related Wikipedia Page
Functions Of One Variable (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for convexity of real functions of one variable
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize differentiation, integration, approximation, and analytic inequalities.
Applications
- Real and complex analysis of one variable
- Approximation and asymptotic methods
- Smoothness and convexity
References
Recommended Textbooks