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Name motif
Single variable calculus Mathematical study of continuous change of single variable functions wiki
Complex variable calculus Analysis of complex functionals wiki
Calculus of variations Differentiation of functionals wiki
Vector Calculus Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space $\mathbb{R^3}$. wiki
Tensor calculus In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). wiki
Ito Calculus Itô calculus, named after Kiyoshi Itô, extends the methods of calculus to stochastic processes such as Brownian motion. Wiki
Differential forms Differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. Wiki
Discrete calculus Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. wiki
Heaviside's Operator Calculus Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. wiki
Geometric calculus In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories including differential geometry and differential forms wiki

These are all the fields of calculus I've heard of, but are there any more which are significant? Please add a brief introductory description to the field when answering!

J.-E. Pin
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tryst with freedom
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  • See related question (mine) – ə̷̶̸͇̘̜́̍͗̂̄︣͟ Jun 26 '21 at 13:14
  • Oh nice, I had seen that question and that's what inspired me to write this question. There you had asked in sense of optimization, I wanted to know how different calculus fields can be made from different notion of derivative – tryst with freedom Jun 26 '21 at 13:17
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    different notion of derivative --- Possibly relevant is my answer to Is there a garden of derivatives?, which incidentally only deals with functions real-valued functions of a single real variable and (near the end) one type of generality in the case of real-valued functions of a finite number of real variables. I plan on one day (or week or two is more likely the time it'll take!) fleshing out that answer by providing short summaries of many of the types listed there, but this probably won't happen for quite a while. – Dave L. Renfro Jun 26 '21 at 13:33

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