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Phyman1109
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Just started multivariate course, can't figure out this simple question. If f(u,v,w) is a function of 3 variables. And u, v and w are themselves function of t. Then does f(u,v,w)=0 implies df/dt=0 or df/du=0. or both.
Multivariate calculus is a branch of mathematics that deals with the study of functions of several variables. It involves the application of differential and integral calculus to functions with multiple independent variables.
Multivariate calculus has many practical applications, including in physics, engineering, economics, and statistics. Some specific examples include calculating the trajectory of a projectile, optimizing the design of a bridge, analyzing economic models, and determining the probability distribution of a random variable.
In single variable calculus, functions have only one independent variable, while in multivariate calculus, functions have multiple independent variables. This means that in multivariate calculus, we must consider the effects of changes in multiple variables on the function, whereas in single variable calculus, we only consider the effect of changes in one variable at a time.
Some key concepts in multivariate calculus include partial derivatives, multiple integrals, gradients, and optimization. These concepts are used to analyze and solve problems involving functions with multiple variables.
There are many books, online courses, and instructional videos available for learning multivariate calculus. Some popular resources include "Calculus: Early Transcendentals" by James Stewart, the Khan Academy multivariate calculus course, and MIT's OpenCourseWare lectures on multivariate calculus.