# What is Multivariate calculus: Definition and 31 Discussions

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather than just one.

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1. ### Calculus Does Apostol Calculus Volume 2 cover sufficient multivariate calculus?

Hello. I am currently doing a high school univariate calculus book, but I would like to go through Apostol's two volumes to get a strong foundation in calculus. His first volume seems great, and I've heard great things about his series, but I am not sure if his second volume contains sufficient...
2. ### I Self-Study General Relativity: After Multivariate Calc in HS

I just finished multivariate calculus (without any linear algebra experience yet) and I am seeking out a path to understanding General Relativity. I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR, and what...
3. ### Verify Stokes' Theorem for this vector field on a surface

I do not understand how can I parameterize the surface and area and line differentials.

17. ### How do you know a function is well defined?

Homework Statement I was given the following function f(x,y) = \begin{cases} \frac{x^2y}{x^4+y^2} & (x,y) \neq 0 \\ 0 & (x,y) = 0 \end{cases} Which of the following are true? (I) f is not continuous at (0, 0). (II) f is differentiable everywhere (III) f as a well defined partial...
18. ### Proof of ||∇h||^2 when h=fog

Homework Statement Let f:R2−>R be a differentiable function at any point, and g be the function g:R3−>R2defined by: g(u,v,w)=(g1,g2)=(u2+v2+w2,u+v+w) consider the function h=fog and prove that ||∇h||^2 = 4(∂f/∂x)^2*g1 + 4(∂f/∂x)(∂f/∂y)*g2 + 3(∂f/∂y)^2.The Attempt at a Solution...
19. ### Express Langrange constraint that an expression*cannot* equal a value

I have an optimization where I'd like to express the idea that some of my parameters cannot equal a certain value e.g... max \ f(x) = ... s.t. x_3 \neq 1 Is there a standard method to solve this using lagrangian optimization? Thanks.
20. ### General question on multivariate calculus

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.
21. ### Multivariate Calculus

A firm has the following total-cost and demand functions: C = aQ^3 - bQ^2 + cQ + d Q = e - P (d) Find optimizing level of Q. (e) Chooses a,b,c,d and e such that there is only one profit-maximizing level of output Q. I found 2 solutions for question d, but in a very long and messy...
22. ### Multivariate Calculus Text Recommendation

It has been awhile since I've posted. :rolleyes: Anyways... I'd like to start learning multivariate calculus along with linear algebra. However, I have a little problem in choosing a suitable text. I'd like to have a text with more theory and less applications. Some people have recommend...
23. ### Multivariate calculus, find the normal vector

Homework Statement Consider the surface x^2 / 4 + y^2 + z^2 = 3 (a) what type of quadric surface is this? (a spheroid...) (b) find the outward unit normal vector to this surface at the point (2,1,1). Homework Equations How do we find a normal vector? Does one just take grad(f(2,1,1))...
24. ### Multivariate Calculus Chain Rule.

Homework Statement Apply the two cases of th change rule. For example: The voltage V in an electrical circuit is slowly decreasing as a battery wears out and the resistance R is slowly increasing as the resistor heats up Use Ohm's law V=IR to find how the current is changing (with respect to...
25. ### Suggestions for a Rigorous Multivariate Calculus Book

I've spent a lot of time soul searching after having some academic "failures" in the previous semesters, and what I found is that often when I'm not studying, it's not because I can't study, but it's because the book we're using is unreadable to me. For example, after sailing through Calculus...
26. ### Multivariate Calculus & Linear Algebra In 3 Weeks

I wish to master Multivariate Calculus(to the extent required to get an A with a ridiculously difficult professor) and Linear Algebra in 3 weeks so I can breeze through both classes in the Fall semester. I've self studied both of my textbooks that I will be using for the two courses, but I'd...
27. ### Good source of problems for multivariate calculus

Hi, I have this qualifying exam coming up in about a month for my Ph.D. program in math. I just noticed that my European undergraduate education covered nothing about actually calculating any tricky integrals. It was only about Riemann sums and proving properties of the integral which I know...
28. ### Help with multivariate Calculus

Homework Statement Show that: max{a,b}=1/2*(a+b+|a-b|) Hence or otherwise, show that if f,g:R ----> R are continuous, then the function h:R ----> R defined by h(x) = max{f(x),g(x)} is also continuos. Suppose the f:(0,inf) ---> R is differentiable and f(x) ---> 0 as x---> inf. Set...
29. ### Multivariate Calculus question

Hi, could anyone tell me the steps to solve the following question: Find the solution of x'=Ax with the initial value -------1---------2 0 0 x(0)=( 0 ), if A=( 0 1 -1 ) -------1---------1 1 1
30. ### Textbook recommendation for multivariate calculus?

I am currently studying multivariate calculus, and quite frankly, I'm not doing well. I am currently using Thomas' Calculus, 11/e media upgrade by Pearson. I don't like this book. The text is 75% theory and 25% simple examples, too few exercise problems, and the explanation is just too difficult...
31. ### Constraint Equation? Multivariate calculus

Homework Statement This is a second (university) year calculus problem dealing with calculus of multiple variables. In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of goods. A utility function u = u(a,b) gives the utility from consuming...