Calculus Definition and 1000 Threads

Homework Statement By relative velocity, we mean velocity with respect to a specified coordinate system. (The term velocity, alone, is understood to be relative to the observer’s coordinate system.) (a) A point is observed to have velocity Va relative to coordinate system A.What is its...

Hello! Let ##I## be an interval of size ##L##, suppose we divide it into bits of ##dx## then ##L=dx+dx+... =\alpha.dx## Since ##dx## is by definition infinitesimally small is it correct to imply that for each ##x## there's a corresponding ##dx## hence, here, ##\alpha## would be, theoretically...

Hello everyone. This was originally a homework problem but I realized my misunderstanding stems from the explanation given before the problem so here we are. The thread deals with these 3 pages from Spivak's Calculus: https://ibb.co/kAKyVU https://ibb.co/jXVSPp https://ibb.co/kwRdVU I'm pretty...

Homework Statement "Consider a cylinder with a generator perpendicular to the horizontal plane; the only requirement for a point ##(x,y,z)## to lie on this cylinder is that ##(x,y## lies on a circle: ##x^2+y^2=C^2##. Show that the intersection of a plane with this cylinder can be described by...

I am confused when I should use the ∂ notation and the d notation. For example, on http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx, in Case 1, the author wrote dz/dt while in Case 2, the author wrote ∂z/∂t. Could anyone please explain to me when I should use the ∂ notation and the...

Homework Statement Find k so that y - 36x = k is a normal to the curve y = 1 / abs(x-2). Homework EquationsThe Attempt at a Solution My problem is regarding the absolute value. I know that the tangent to the curve must be (-1/36). In the solutions manual, it is said that by knowing the sign...

What is the difference between: THOMAS' CALCULUS, media UPGRADE (11TH EDITION) [ISBN-13 9780321489876] and THOMAS' CALCULUS (11TH EDITION) [ISBN-13 9780321185587]? could you provide detailed answer please? what does the title-addition "Media Upgrade" mean and what changes does it make on the...

Section 1 Indices and Logarithms 1) Solve Ln(e6x−4+7)=7 for x. The answer (correct to 3 decimal places) is x = Marks : 1 Section 2 Functions 2) Let f(x) = −4x+72x−2, find f-1(x). Answer: (Correct to 3 decimal places) f-1(x) = (-2 x + ) / ( x + ). Section 3 Roots of Equations 3) Solve...

Hey guys, I am working on a school project and have fired some water rockets at different angles. I am now trying to compare theoretical results vs experimental results. But I am struggling to produce an accurate mathematical model. I have attached my attempt to this post. It is quite long and...

Homework Statement Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong. Homework...

Hello, I'm new to the language of calculus. I am learning about Newtons second law and I'm trying to understand it's forms in calculus. Excuse my notation, just trying to keep it as simple as possible. F=m * dV/dt I know V= dx/dt My textbook says you can 'apply chain rule' to obtain the...

Homework Statement https://www.physicsforums.com/attachments/229290 Homework Equations The Attempt at a Solution I am not sure what equation to use for the volume[/B]

hello, Some background I transfer to SUNY Albany in Fall 2017 and took the following courses Organic chemistry 1: C+ Calculus 2: B- A PHY 140 Physics I: Mechanics (3): E (like F) An introduction to the fundamentals of physics: Classical Mechanics. Topics include the concepts of force, energy...

Hi PF! Given a functional ##J[y]##, if the first variation is $$\delta J[y] = \int_D(ay+y'')y \, dV + \int_{\partial D} (y'+by)y\,dS$$ am I correct to think that when finding stationary points of ##J[y]##, I would solve ##ay+y''=0## on ##D## subject to boundary conditions, which would either...

Hi, I'd like to compute the de Rham cohomology of the 3 following objects : -A connected sum of ##g \in \mathbb{N}## reals projectives plans ##P_{2}(\mathbb{R})##. -A connected sum of ##g \in \mathbb{N}## torus without ##n## points ##\mathbb{T}^{2} - \{x_{1}, x_{2}, ..., x_{n}\}##. - A...

Greg Bernhardt submitted a new PF Insights post The 10 Commandments of Index Expressions and Tensor Calculus Continue reading the Original PF Insights Post.

I am doing a problem from Schutz, Introduction to general relativity.The question asks you to find a coordinate transformation to a local inertial frame from a weak field Newtonian metric tensor ##(ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2))##. I looked at the solution from a manual and it...

Since the two functions touch at $\displaystyle \begin{align*} A\left( 0, \frac{15}{2} \right) \end{align*}$ that means that this point lies on the cubic function. Thus $\displaystyle \begin{align*} \frac{15}{2} &= a\left( 0 \right) ^3 + b\left( 0 \right) ^2 + c\left( 0 \right) + d \\...

Hey, I have been told to study calculus following Spivak's book. I was in an Engineering program and I have moved to a Physics one, and I want to retake calculus to really get good at it. The problem is, Spivak's seems to me like it's very proof based, and I'm having a hard time even with the...

Which calculus book self contains experiences in order, and is stable to the max, for all the problems known in the subject? --------------------------------------------------------- I have got confused now. Math history seems to allow knowing all the data on how math formed, for any of a...

I’ve always been confused by the formula for the Total Derivative of a function. $$\frac{df(u,v)}{dx}= \frac{\partial f}{\partial x}+\frac{\partial f }{\partial u}\frac{\mathrm{d}u }{\mathrm{d} x}+\frac{\partial f}{\partial v}\frac{\mathrm{d}v }{\mathrm{d} x}$$ Any insight would be greatly...

I am currently self learning high school level AP Calculus BC over the summer. From a mathematical perspective, I have heard that high school level calculus is just pure and shallow computational work. For this reason, I seek a deeper understanding in calculus. So far, the BC curriculum has been...

Homework Statement I have to construct 8 concrete right cylinders for hurricane protection on windows, but I need to know the height to fit the given criteria. Each has a 4 inch radius and each weighs 1200 pounds. Concrete weighs 150 pounds per cubic foot. V= volume of right cylinder r=radius...

Homework Statement If ##x\sqrt{1+y} + y\sqrt{1+x } = 0##, then prove that ##\frac {dy} {dx} = \frac {-1}{(x-1)^2}##. 2.Relevant Equations: $$ \frac {dy} {dx} = - \frac {\left (\frac {\partial f}{\partial x} \right)} {\left( \frac {\partial f} {\partial y} \right)}.$$ 3...

Homework Statement My problem is in integral calculus (I'm new to it). I know what it is and how it works (basically. I'm not too advanced right now). The problem is as following: (I will be posting comments/reasons along with what I've done and with what logic/understanding I've done it...

What are the best book to study Calculus? And there is a academic book with History of Calculus? I would like recommendations. I appreciate all.

Okay. So I'm new to calculus. And this is the first time I'm solving a physics problem using integration. I understood that ∫dt (or ∫1dt) will be equal to just 't+C.' (Just like f ' (t+C) = 1). Though, that's not the problem. The problem is when I apply it this way: Question: The expression for...

Could someone explain to me how from this graph you can deduce that ##\tan(\theta) = \frac {df} {dx}##. Thanks

Homework Statement The path integral from (0,0,0) to (1,1,1) of $$<x^2,2yz,y^2>$$. I am a little confused about the setup.Homework Equations $$\int_{a}^{b} v.dl$$The Attempt at a Solution Here is how I set it up. $$\int_{0}^{1}x^2 dx + \int_{0}^{1}2yz dy + \int_{0}^{1}y^2 dz$$ Since the...

i have one question concerning measure theory and this...could we map the natural numbers to the positive rationals...then observe the measure between the rationals being mapped ,as a value giving us a sense of how many irrationals are between them...then generate a function where we take the...

Homework Statement The problem is stated as follows: "The result in Problem 1-7 has an important generalization: If ##a_1,...,a_n≥0##, then the "arithmetic mean" ##A_n=\frac {a_1+...+a_n} {n}## and "geometric mean" ##G_n=\sqrt[n] {a_1...a_n}## Satisfy ##G_n≤A_n## Suppose that ##a_1\lt A_n##...

I have been teaching undergrad students informally, and one of the math problems that I have always enjoyed introducing them to is how to compute the area under a gaussian curve, or to keep it simple, the area under the curve ##z=e^{-x^2}## One of my students asked me a question that has...

Hey everyone 1. Homework Statement I want to compute the Taylor expansion (the first four terms) of $$f(x) =x/sin(ax)$$ around $$x_0 = 0$$. I am working in the space of complex numbers here. Homework Equations function: $$f(x) = \frac{x}{\sin (ax)}$$ Taylor expansion: $$ f(x) = \sum...

Why is this way of thinking wrong?. can't I assume that when Δx tends to zero is a sufficient approximation of what I want to get? It confuses me with the basic idea of integrating a function to get the area beneath a curve of a function (which isn't also as perfect) . PD: I put Δx tends to...

I have a question. If you're given a force of 20 N and its 60 degrees to the horizontal, how could you find two perpendicular forces?

i'm trying to review calculus and look a little deeper into proofs/derivations/etc. I'm doing this both for fun and to review before i go back to school. am i the only one who has difficulty understanding the "rigorous" definition of the limit? i found this web page...

Homework Statement Is it possible to accurately approximate the speed of a passing car while standing in the protected front hall of the school? Task: Determine how fast cars are passing the front of the school. You may only go outside to measure the distance from where you are standing to the...

Homework Statement Please help me solve the calc problem pictured! Homework Equations y=3-x^2 and y=x+1 The Attempt at a Solution My attempt is in one of the photos!

The current community college I'm at offers courses titled analytical geometry and calculus and only transfer to the universities in my state as calculus courses. I'm looking to move outside of South Carolina and going to a school like WSU. Should I wait to take calculus courses when I transfer...

Homework Statement Please look at the photo! Homework Equations -x^2+4x=x^2-6x+5 The Attempt at a Solution I got 2x^2-10x+5 but it says it's wrong

Homework Statement determine the center of mass of a thin plate of density 12 and whose shape is the triangle of vertices (1,0), (0,0), (1,1). Then, using the appropriate pappus theorem, calculate the volume of the solid obtained by rotating this region around the line x = -2. Homework...

Homework Statement A carriage is mounted on a spring, as shown in the diagram. The bottom of the spring is fixed to the ground. The carriage (loaded with its passenger) has a mass of 150kg. The carriage can only move vertically. The natural length of the spring is 10m and its spring...

Given : $$p\wedge\neg (q\vee r)$$ then prove whether this formula implies:!) $$(p\wedge\neg q)\vee (p\wedge\neg r)$$ OR 2) $$(p\wedge\neg q)\wedge (p\wedge\neg r)$$

Homework Statement I don't understand how to form an equation using the knowledge that, 'When ##t=4##, ##P## is moving parallel to the vector ##\mathbf {j}##'. I've seen the solution, and not a single part of it makes sense. I haven't attempted any question like this before, so I have no idea...

Homework Statement Homework EquationsThe Attempt at a Solution I have attached the problem and solution. I don’t know how to do part b even I have looked at the solution. How to transform the original cartesian equation to the semi cylindral coordinate equation? Is there is systematical...

Just a quick question. Can you really teach economics without calculus? Reviewing it now just to refresh my memory since we have a budget being delivered tomorrow here in Aus. I have reached the point where it is proven that maximizing overall profit is different from profit per unit of...

Hello. My problem is as follows: Suppose x^4+y^2+y-3=0. a) Compute dy/dx by implicit differentiation. b) What is dy/dx when x=1 and y=1? c) Solve for y in terms of x (by the quadratic formula) and compute dy/dx directly. Compare with your answer in part a). I solved a) and b). a)=-4x^3/2y+1, and...

I have just started to learn calculus.Can you suggest the best book to grasp the concepts and to teach myself the true calculus.

I wanted to go through Calculus and then Linear Algebra following either of two paths: a) Keisler's Infinitesmal approach>>>Nitecki Deconstructing Calculus>>>Nitecki Calculus in 3D>>>Freidberg's Linear Algebra OR b) Simmons Calculus with analytic geometry>>>Apostol Vol 1>>>>Apostol Vol...

1. At the instant of the figure, a 6.70 kg particle P has a position vector of magnitude 4.30 m and angle θ1 = 43.0° and a velocity vector of magnitude 3.40 m/s and angle θ2 = 32.0°. Force , of magnitude 7.40 N and angle θ3 = 32.0° acts on P. All three vectors lie in the xy plane. About the...