What is the difference between single and multivariable calculus

Physics Help. Chemistry Help. Single Variable Versus Multivariable Calculus. Thread starter nycmath Start date Aug 18, Tags calculus multivariable single variable versus. JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Jan 7 New York City. This is a silly question but I really want to know the answer. I need a basic answer. I want to know what is the main difference between single variable and multivariable calculus?

In other words, why is calculus 1 and 2 called single variable and calculus 3 called multivariable? Jun 1, Illinois. As the names imply - single variable calculus deals with one variable at a time.

For example you might work a problem having to do with an object's position versus time - here time is the variable. Multivariable calculus usually called "multivariate calculus" involves two or more variables. Even when the functions are continuous. As demonstrated by Fubini's theorem. It seems to me that an important difference is that while in one-variable calculus one only deals with one derivative, in multi-variable calculus there are infinitely many derivatives, the directional derivatives , a particular case of which are the partial derivatives.

There are still the total derivatives for functions whose variables depend on another variable. Though all these derivatives are a generalization of the derivative of a single variable function. This matters because simple connectivity enters as a hypothesis in several theorems.

Since the fundamental theorem of calculus requires integrating over a boundary, the theorem is more complicated in several variables. Integration over a manifold is more subtle and requires a large amount of machinery to do formally. In two variables there are infinitely lines through a point, hence there are infinitely many directions to narrow a point and moreover you might get different results on different other kind of curves.

The key differences are the single variable calculus is one dimensional, and deals with scalars, while multivariate calculus is multidimensional, and deals with mapping relations using vectors and matrices. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Difference between one-variable calculus and multi-variable calculus? Ask Question. Asked 10 years, 11 months ago.

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