Everything about Vector calculus
Calculus of vector-valued functions
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Vector calculusA 5-minute orientation
- Skim a recent paper: Vector-valued fractal functions: Fractal dimension and fractional calculusInfluential work since 2022
- Pick up a classic book: Schaum's outline of theory and problems of vector analysisThe most-reprinted book on the subject
- Read the landmark paper: Fractional vector calculus and fractional Maxwell’s equationsCited 265 times
- Go sideways: Curl (mathematics)A closely related topic
- Go sideways: Vector fieldA closely related topic
đź“– Definitions
Noun The branch of mathematics that covers the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Fractional vector calculus and fractional Maxwell’s equations
Fractional vector calculus for fractional advection–dispersion
Students’ difficulties with vector calculus in electrodynamics
Vector logics: The matrix-vector representation of logical calculus
General Fractional Vector Calculus
Toward lattice fractional vector calculus
Fractional vector calculus and fluid mechanics
Vector Differential Calculus in Statistics
🆕 Influential since 2022
Vector-valued fractal functions: Fractal dimension and fractional calculus
A vector calculus for neural computation in the cerebellum
AN INSIGHT ON THE FRACTAL POWER LAW FLOW: FROM A HAUSDORFF VECTOR CALCULUS PERSPECTIVE
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
ChatGPT-4 with Code Interpreter can be used to solve introductory college-level vector calculus and electromagnetism problems
đź“š Books worth reading
Schaum's outline of theory and problems of vector analysisMurray R. Spiegel · 1959
Calculus&MathematicaBill Davis, William Davis · 1994
TensoranalysisHeinz Schade · 1996
Vector analysis and Cartesian tensorsDonald Edward Bourne · 1977
Vector and tensor analysisEutiquio C. Young · 1978
Mathematics ApplicableSchools Council Sixth Form Mathematics Project · 1975
Vector calculus, linear algebra, and differential formsHubbard, John H., John H. Hubbard · 1999
Vector calculusJerrold E. Marsden · 1976
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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