Calculus Definition and 1000 Threads

Hi. I have the Marsden an Tromba vector calculus book 6th edition. I was wondering which software was used to create the books graphs. I attach two graphs as an example. Thanks

Summary:: What calculus books do you recommend? Does Thomas Calculus include all the calculus topics? Hi! I'm a 10th grader and preparing for physics olympiads. I'm planning to learn calculus this summer, i self learned prior required topics before calculus (trigonometry, logarithm etc.) ...

How to represent this system in state space form? where: $$ x' = Ax + Bu \text{ and }y = Cx + Du$$ I am trying to create a state space model based on these equations on simulink, need to find A, B, C and D but like I mentioned, i cannot find the solution when the differentials are not of...

Hi, Hi, Author said If we look at the graph of $ f (x, y)= (x^2 +y^2)*e^{-(x^2+y^2)},$ as shown in the following Figure it looks like we might have a local maximum for (x, y) on the unit circle $ x^2 + y^2 = 1.$ But when I read this graph, I couldn't guess that the stated function have a...

Question: Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone. Answer: Let r and h be the radius and height of the right circular cylinder inscribed in a given cone of radius R and height H. Let...

Hi PF, stucked with this proof: Taylor's Formula The following theorem provides a formula for the error in a Taylor approximation ##f(x)\approx{P_{n} (x)}## similar to that provided for linear approximation (...) Taylor's Theorem If the ##(n+1)##st-order derivative, ##f^{(n+1)} (t)##, exists...

Taking the variation w.r.t f(x) of the integral over some x domain of F[f(x), f'(x), df(x)/dt], why doesn't df(x)/dt need to be taken a variational derivative and is treated as if it were constant?

In Keisler Elementary Calculus page 39, example 4 it shows how to compute the standard parts of the following expression: Example 4: If ##\epsilon## is infinitesimal but non zero, find the standard part of ##b=\frac {\epsilon} {5-\sqrt{25+ε}}## Before calculating the standard parts the...

Anyone know of an online course or set of video lectures on John Hubbard's textbook on Vector Calculus, Linear Algebra, and Differential Forms?

This is the question, Now to my question, supposing the vectors were not given, can we let ##V=\vec {RQ}## and ##W=\vec {RP}##? i tried using this and i was not getting the required area. Thanks...

Hello all! I was thinking about strengthening my knowledge of Calculus after I finish the course I am taking in Multivariable Calculus. I am in a particularly unique situation, as I am only going to enter high school next year. I took the AP Calculus BC Exam last year and got a 5. The course I...

Hey! I have to show that the integral of the area of a sphere ##\int \frac{d\vec{a}}{d} = \frac{4}{3}\pi \vec{r}##, with ##d = |\vec{r} - \vec{R}|## and ##\vec{r} = r \hat{z}## This is what I did. ##d\vec{a} = R^2sin\theta d\theta d\phi \hat{r}##, ##\hat{r} = sin \theta cos \phi \hat{x} + sin...

I am about to start a physics with theoretical physics major, I've taken calculus before but I've not been satisfied with the "memorization of formulas" type books. I started to read Spivak and found it enjoyable, but since it's a major undertaking I am also concerned for the practical value...

how does the first step use mean value theorem? I don't get it , can anyone explain , thanks.

A set is nothing more than a collection. To determine whether or not an object belongs to the set , we test it against one or more conditions. If it satisfies these conditions then it belongs to the set, otherwise it doesn't. The geometric point of view of sets- a set can be viewed as being...

c) Why is the assertion ##\lim\limits_{x \to 0} f(x) = \lim\limits_{x \to 0} f(x^3)## obvious? First of all I don't think it is obvious but here is an explanation of why the limits are the same. ##\lim\limits_{x\to0} f(x^3)=l_2## means we are looking at points with ##x## close to zero and...

I believe the x-axis is vertical here. The graph is composed of i) an infinite number of intervals that start on the ##y=x## line and finish at some ##x## with a decimal expansion ending in ##7\bar{9}##. E.g., from ##0.67## to ##0.67\bar{9}## which is considered ##0.68##. Other examples of...

Pending

Consider item ##vii##, which specifies the function ##f(x)=\sqrt{|x|}## with ##a=0## Case 1: ##\forall \epsilon: 0<\epsilon<1## $$\implies \epsilon^2<\epsilon<1$$ $$|x|<\epsilon^2\implies \sqrt{|x|}<\epsilon$$ Case 2: ##\forall \epsilon: 1\leq \epsilon < \infty## $$\epsilon\leq\epsilon^2...

I've started reading up on tensors. Since this lies well outside my usual area, I need some clarifications on some tensor calculus issues. Let ##A## be a tensor of order ##j > 1##. Suppose that the tensor is cubical, i.e., every mode is of the same size. So for example, if ##A## is of order 3...

Good Morning all Yesterday, as I was trying to formulate my confusion properly, I had a series of posts as I circled around the issue. I can now state it clearly: something is wrong :-) and I am so confused :-( Here is the issue: I formulate the Lagrangian for a simple mechanical system...

I'm doing 2 years at a community college before transferring to a university for the last 2 years to become a Civil engineer. I was looking at the courses at the university, granted these are for all 8 semesters not simply post transfer courses. One thing I saw was that the 3 calculus classes...

Hello, Can someone explain how to sketch the flow profile in detail. Also, I solved for curl, but I'm getting a zero while the answer is the differentiation of the function f(y). Pls do help me out!

Please Solve this, I am unable. This problem requires you to read the following scientific article: http://math.colgate.edu/~integers/u76/u76.pdf These answers should be related to this paper. Questions are attached in the image; please answer mainly d, e and f Those are the main problems I...

I tried using hamilton method but i don't think that's correct

Is someone has already heard about this book wrote by Andre I. Khuri (Professor emeritus in science at university of Florida) ? By the table of contents the book seems to cover a lot of things in calculus/multivariable calculus and in a rigourous way according to the preface (they argue that...

Are there any good introductory texts aimed at students with only a working knowledge of High School Algebra? I currently have: Probability: An Introduction by Samuel Goldberg I do plan on eventually learning Calculus, but I would like to start learning probability sooner.

I really don't know how to proceed if I'm not using an specific coordinate system, Is there a way of doing this using only indices, in general form?

Hi everyone! I just bought the courant John calculus volume-1 from uni bookstore. I need some tips like errors, topics which are not explained well and topics which are really important and need to focus more on etc.. My background:- have Spivak as a supplement. Knows how to prove and read...

Hey! :giggle: Give for the following expressions of relation algebra the equivalent expression in relational calculus. 1. $\sigma_{B=A}(R(A,B,C))$ 2. $\pi_{B,C}(R(A,B,C))$ 3. $R(A,B,C)\cup S(A,B,C)$ 4. $R(A,B,C)\cap S(A,B,C)$ 5. $R(A,B,C)\setminus S(A,B,C)$ 6. $R(A,B,C)\times S(D,C,E)$ 7...

Hi, there. I have not systematically learned the calculus of variations. I would like to learn it now. Are there simple materials for the purpose of learning how to do the calculation in physics? No need for deeper consideration in mathematics. Is Mathematical methods for physicists by Arfken...

Hi, This isn't a homework question, but a side task given in a machine learning class I am taking. Question: Using variational calculus, prove that one can minimize the KL-divergence by choosing ##q## to be equal to ##p##, given a fixed ##p##. Attempt: Unfortunately, I have never seen...

I tried to solve it by integrating force from 0 to L dF=dm.g where dm=λdx And then I multiplied it with velocity to get power because velocity is constant ∫(vdF)=v ∫(dF) But the book used integration to find work done and divided it by time for power My answer was λlgv(Option B) Giving...

Preceding Problem. Let ##y=f(x)## be a continuous function defined on a closed interval ##[0, b]## with the property that ##0 < f(x) < b## for all ##x## in ##[0, b]##. Show that there exist a point ##c## in ##[0, b]## with the property that ##f(c) = c##. This problem can be solved by letting...

##f_x=3*x^2+y## ##f_y=2*y+x## ##(3*(t^2)^2+e^{t-1})*2*t+(2*e^{t-1}+t^2)*e^{t-1}## Well, I am not sure how to evaluate it. I got a wrong result by multiplying by 0.1, i.e. ##((3*(t^2)^2+e^{t-1})*2*t+(2*e^{t-1}+t^2)*e^{t-1})*0.1## I guess it is trivial but I am lost. :(

Summary:: I want to teach myself physics and was wondering if Thomas' Calculus is a good book to learn the Calculus I need to learn introductory physics. Hi, I am following a guide by Susan Rigetti (https://www.susanrigetti.com/physics) which aims to help and give sort of structured learning...

Hi,PF I've got "Cálculo", Spanish 6th edition, by Robert A. Adams. At Chapter 4.2, would like to read an updated (guess it might be better) 1st. paragraph of the section I translate "Test of the first derivate". Regards

Hi, I have to find the real and imaginary parts and then using Cauchy Riemann calculate ##\frac{df}{dz}## First, ##\frac{df}{dz} = \frac{1}{(1+z)^2}## Then, ##f(z)= \frac{1}{1+z} = \frac{1}{1+ x +iy} => \frac{1+x}{(1+x)^2 +y^2} - \frac{-iy}{(1+x^2) + y^2}## thus, ##\frac{df}{dz} =...

Hello PF, After thinking, googling, and reading many threads here, I decided that I'm going to start learning calculus using Stewart. The problem is that the book puts too many exercises after each section, in addition to those at the end of each chapter. What's the difference between these...

Solving integrals by hand is difficult and prone to errors, and the techniques such as integration by parts, partial fraction decomposition, and trig substitutions only work for a small subset of integrals and I do not see the point of avoiding technology like Wolfram Mathematica for...

But, If I use chain rule than, I get that. ##\vec v_i = \frac{dr_i}{dt}=\sum_k \frac{\partial r_i}{\partial q_k} \cdot \frac{\partial q_k}{\partial t}## But, they found that?

Homework Statement:: Book suggestion Relevant Equations:: Calculus Book suggestion for tensor calculus.

I would like to know what is the utility or purpose for which the elements below were defined in the Tensor Calculus. They are things that I think I understand how they work, but whose purpose I do not see clearly, so I would appreciate if someone could give me some clue about it. Tensors. As...

I tried to use a Taylor series expanded at 3 and set to 3.01: https://www.wolframalpha.com/input/?i=27+++9+(-3+++x)^2+++(-3+++x)^3+++3+y^2+++y^3+++(-3+++x)+(27+++y^2)=3.01 I got the vector ## (\Delta x, \Delta y)= (0.37887, -0.54038)## It does give a desired result but it is marked as wrong...

Question about the differential in Calculus. Assume a function y = f(x) , differentiable everywhere. Now we have for some Δx Δy = f(x + Δx) - f(x) The differential of x, is defined as “dx”, can be any real number, and dx = Δx The differential of y, is defined by “dy” and dy = f’(x)...

Intersecting the graph of the surface z=f(x,y) with the yz -plane. This is the option I have chosen, but it's wrong. I don't understand why. x is fixed so I thought the coordinates: y and z are left. I thought this source may be helpful...

We've a functional ##J(\alpha)=\int_{x_{1}}^{x_{2}} f\left\{y(\alpha, x), y^{\prime}(\alpha, x) ; x\right\} d x## It's derivative with respect to the parameter ##\alpha## is given in textbook Thornton Marion as ##\frac{\partial J}{\partial \alpha}## Shouldn't it have been ##\frac{d J}{d...

Hi, PF I've got the spanish sixth edition of "Calculus", by Robert A. Adams. When it comes to introduce the exponential function properties, calls it "TEOREMA 2", but could it be a typo?. Just a page before, there is another TEOREMA 2: Natural logarithm properties. Greetings

I self-studied Calculus 1 (AP Calc AB) in my sophomore year of high school and I got a 4 on the AP exam. I took the class Calculus 2 (AP Calc BC) in my junior year of high school. I did not take the exam at the end of the year. I didn't take any math in my senior year of high school. Because...