26Bxx Functions of several variables
This subtopic studies functions of several variables, emphasizing partial derivatives, multivariable continuity, and geometric aspects of mappings between Euclidean spaces.
Specific topics
26B05 Continuity and differentiation questions
Overview
26B05 studies continuity and differentiation questions in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for continuity and differentiation questions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B10 Implicit function theorems, Jacobians, transformations
Overview
26B10 studies implicit function theorems, jacobians, transformations in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for implicit function theorems, jacobians, transformations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B12 Calculus of vector functions
Overview
26B12 studies calculus of vector functions in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for calculus of vector functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B15 Integration: length, area, volume
Overview
26B15 studies integration: length, area, volume in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integration: length, area, volume
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B20 Integral formulas (Stokes, Gauss, Green, etc.)
Overview
26B20 studies integral formulas (stokes, gauss, green, etc.) in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integral formulas (stokes, gauss, green, etc.)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B25 Convexity of real functions of several variables
Overview
26B25 studies convexity of real functions of several variables in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for convexity of real functions of several variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B30 Absolutely continuous real functions of several variables
Overview
26B30 studies absolutely continuous real functions of several variables in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for absolutely continuous real functions of several variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B35 Special properties of functions of several variables
Overview
26B35 studies special properties of functions of several variables in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special properties of functions of several variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks
26B40 Representation and superposition of functions
Overview
26B40 studies representation and superposition of functions in functions of several variables. It studies functions of several real or complex variables, including differentiability, Jacobians, and geometric behavior of level sets.
Related Wikipedia Page
Functions Of Several Variables (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representation and superposition of functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in multivariable calculus, optimization, and local geometric analysis.
Applications
- Optimization and critical point theory
- Multivariable differential calculus
- Local geometry of level sets
References
Recommended Textbooks