Calculus Definition and 1000 Threads

Part A) For part A I forgo breaking down the identity into it's component x, y, and z parts, and just take the r derivative treating r' as a constant vector. This seems to give the right answer, but to be entirely honest I'm not sure how I'd go about doing this component by component. I figure...

Hi, PF I've got a translation into spanish of the sixth edition of "Calculus", by Robert A. Adams. At the second chapter, "Differentiation", eleventh section, I would like to know: the title of the section (Could it be "Velocity and Acceleration"?); and a sentence of the Example 2 ("A point P...

Let $F = (P(x,y),Q(x,y))$ a field of vector class 1 in the ring $A={(x,y): 4<x²+y²<9}$ and $x,y$ reals. I am having trouble to understand why this alternative is wrong: If $ \partial P /\partial y = \partial Q /\partial x$ for every x,y inside A, so $\int_{C} Pdx + Qdy = 0$ for every...

Hi! I was looking for a Calculus textbook to buy and was debating between Courant and Apostol. I was planning on reading Spivak parallel to one of these. My question is does Apostol cover more material than Courant does or are they practically the same. Sorry if this has already been asked, I...

Hello everyone, Last year I took pre calc and that was the highest math I was required to take for my biology degree. I’ve recently became interested in learning calculus. Does anyone have a good online course recommendation I could buy in order to learn all of calc 1? I was looking on udemy...

Hey guys ! I just need a little help on a integral I was trying to solve using feyman's technique. This is the integral from 0 to 1 of (sin(ln(x))/ln(x) dx, which has been solved in one of the videos of bprp, but I'm trying to solve it using a different technique, and I end up with a different...

I have the following definition: $$ \lim_{x\to p^+}f(x)=+\infty\iff \forall\,\,\varepsilon>0,\,\exists\,\,\delta>0,\,\,\text{with}\,\,p+\delta< b: p< x < p+\delta \implies f(x) > \varepsilon$$ From this, how can I get the definition of $$\lim_{x\to p^-}=-\infty? $$

How would you go about finding maximum value for this function without Calculus? You can draw in it a CAS tool like Geogebra, NSpire or Maple. And use the maximise ability. But is possible to do it by hand? Pre-Calculus?

Hey guys, so I was on this thread on tips for self studding physics as a high schooler with the aim to become a theoretical (quantum) physicist in the future. I myself am a 15 year old who wants to become a theoretical physicist in the future. A lot of people in the thread were saying that...

How would I determine the following limit without substitution of large values of x to see what value is approached by the complex function? ## \lim_{x \rightarrow +\infty} {\dfrac {2^{x}} {x^{2} } } ## where ## x\in \mathbb{R}##

Hi all, Over the last few weeks I've been catching back up with High School Algebra, Trigonometry, along with some Geometry. I'm now looking for the next challenge and unsure where to start. Due to studying Astrophysics/Physics topics, I'm assuming studying applied mathematics topics is the...

I know the formula profit = (price-cost)quantity. but when ı applied the numbers ı can not substitute them profit = ((30-2q-2-(40/q)) but don't know what ı need to do ? would appreciate any help given please.

Since the question asks for Cartesian coordinates, I wrote dV as 2pi(x^2+y^2+z^2)dxdydz and did the integral over the left hand side of the equation with x, y, z from 0 to R. My integral returned (0, 2*pi*R^5, 5/3*pi*R^6) which doesn't seem right. I also tried to compute the right-hand side of...

I failed to become a mechanical engineer because I could not learn how to do sequences and series in Calculus II. I could get Cs and Bs on all the concepts of Calculus II until I got to Sequences and Series. Then I would get F minuses on any tests involving series problems such as Infinite...

please I need solve of this question very quickly

Hi I'm having troubles with integration specially by substitution, I'm going to read a calculus textbook and i need recommendations of books with a good treatment on the different techniques of integration. I'd like a book with good exercises for self study and a exposure to integration of...

Question: Diagram: So the common approach to this problem is using polar coordinates. The definition of infinitesimal rotational inertia at O is ##dI_O=r^2\sigma\, dA##. Therefore the r. inertia of the triangle is $$I_O=\int_{0}^{\pi/3}\int_{0}^{\sec\theta}r^2r\,drd\theta$$ whose value is...

I was walking around with my head in the clouds and suddenly I wondered if a smart person, say, a philosopher, could start at the full monster of real analysis instead of elementary calculus. Would there be any hope for this unfortunate soul? What are your opinions and why? Or if you feel this...

Hi, I'm reading the volume 1 of "Introduction to calculus and analysis" by Courant and Fritz but the problems are hard for me, i understand what he say but i can't solve many problems of the chapter one. It's normal or should i try with other book?

Hello everyone. I'm about to take Calc 3 next semester and am looking for a rigorous book to work with on multivariable calculus. I've gone through Spivak's "Calculus" from cover to cover and am hoping to find something with the same degree of rigor, if possible, and preferably with a solution...

Majoring in electrical engineering imply studying Griffiths book on electrodynamics, so I have begun reading its first chapter, which is a review of vector calculus. A list of vector calculus identities is given, and I would like to derive each one, with one of them being ##\nabla \cdot (A...

I have a question : If we consider the change in g due to distance from the Earth core; then y=distance from earth’s core t=time G=gravitation constant M=Earth’s mass k=GM $$y^2(t)=\frac{k}{y(t)^2}$$ If we consider air resistive force as proportional to speed squared, then: m=falling object...

I was recently studying the pressure gradient force, and I found it interesting (though this may be incorrect) that you can use a Taylor expansion to pretend that the value of the internal pressure of the fluid does not matter at all, because the internal pressure forces that are a part of the...

Clearly, ##x_{n+1}>x_n \because x_n + \sqrt{x_n} > x_n## $$ \begin{align*} x_{n+1} &= x_n+ \sqrt{x_n} \\ &= x_1 + \sqrt{x_1} + \sqrt{x_2} + \cdots \sqrt{x_n} \\ &>n+1 \end{align*} $$ ##\because \sqrt{x_n}>\sqrt{x_1}=1## In fact, $$x_{n+1} > 1+ \sqrt{1} + \sqrt{2}+ \sqrt{3} + \cdots \sqrt{n}$$...

Hi, I have a course on calculus of variations and Sturm Liouville theory and was wondering if anyone had any good textbook suggestions? If they had questions and solutions it would be a bonus! I have put all the subtopics of the course below. Calculus of variations Variation subject to...

Hello.Questions: How tensor operations are done?Like addition, contraction,tensor product, lowering and raising indices. Why do we need lower and upper indices if we want and not only lower? Is a tensor a multilinear mapping?Or a generalisation of a vector and a matrix? Could a tensor be...

I've been studying calculus A and B on and off over the last ten years, and I'm starting to learn calculus again for fun as soon as I can get my hands on a textbook. I was wondering if multivariable calc is as fun as A and B have been so far.

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...

Up and Atom gives a look at some Calculus tools which a layman can follow.

i think solution with récurrence for n=1 then 1=2¨¨^0(2x0 +1) true suppose that n=2¨^p(2q+1) is true shows that n+1=2^p( 2q +1)? n+1=2¨^p(2q+1) +1 ⇒ ??

From Wikipedia: "In 1727, [Euler] first entered the Paris Academy Prize Problem competition; the problem that year was to find the best way to place the masts on a ship." Does anyone know how he did this? Is there an on-line paper? (But what that is accessible with today's knowledge). And by...

I know some multivariable calculus, I just want someone to walk me through the integration deriving the mass element dM and the integration of thin rings composing the hollow sphere. It would also be nice if you could show me doing it one way using the solid angle and one way without using the...

If f'(x) were a simpler function like f'(x) = cos(x) I would say f(x) = sin(x) + C and then evaluate C by knowing that 2 = sin(1) + C and then C would equal 2-sin(1) the f(x) = sin(x) + 2 - sin(1), f(0) = sin(0) + 2 - sin(1) = 0 + 2 -.841 = 1.58 However the more complicated problem has f'(x) -...

Hi, In $\mathbb{R^3} || v-w ||^2=||v||^2 + ||w||^2 - 2||v||\cdot ||w||\cos{\theta}$ But can we say $||v+w||^2=||v||^2 +||w||^2 + 2||v|| \cdot||w|| \cos{\theta}$ where v and w are any two vectors in $\mathbb{R}^3$

Hi PF, Can you tell me about an alternative, substitute for "Calculus", written by Robert A. Adams, from University of British Columbia?. It's good, but I need more bibliography; I find this one too implicit: suggested but not communicated directly. I am now asking doubts to a lot of forums each...

Details of Question: ds/dt= v which becomes ds=v dt, where s=displacement, t =time, and v=velocity Then we can integrate both sides of this equation, and do a little algebra, and turn the above equation into: s − s0 = v0t + ½at2 My main question is about the integration of...

Kindly help me with: Iterated integrals Q1, 2,3 Double integrals in polar coordinates Q1, 2,3 Triple integrals Q1, 2,3 Triple integrals in cylindrical coordinates Q1, 2,3 Triple integrals in spherical coordinates Q1, 2,3 Change of variables Q7,8,9 Green's theorem Q1,2 Surface integrals...

Doing R=|r-r'|, i get the expected result: \nabla \frac{1}{|r-r'|} = -\frac{1}{R^2}\hat r=-\frac{(r-r')}{|r-r'|^3} But doing it this way seems extremely wrong, as I seem to be disregarding the module. So I tried to do it by the chain rule, and I got: \nabla...

Hello, I am a very experienced Mathematician with a BSc Honours degree in Mathematics and one year MSc studies in Operational Research in Sussex and London Universities respectively. I am interested in Advanced Calculus, Algebras, Positivity in Algebraic Geometry, The standard Model, and many...

If say we have a scalar function ##T(x,y,z)## (say the temperature in a room). then the rate at which T changes in a particular direction is given by the above equation) say You move in the ##Y##direction then ##T## does not change in the ##x## and ##z## directions hence ##dT = \frac{\partial...

The Attempt at a Solution I know the answer is supposed to be ##(-1,0)##. However when I differentiate the above expression I get. $$ 2x+{\frac 5 2} $$ Then the shortest distance would be when the expression equates to 0. $$ 2x+{\frac 5 2}=0 $$ I should be getting ##x=-1## but solving for ##x##...

screen shot to avoid typos OK the key said it was D I surfed for about half hour trying to find a solution to this but $f'(0)$ doesn't equal any of these numbers $e^0=\pm 1$ from the $e^{(x^2-1)^2}$ kinda ?

ok I thot this was just observation to get b. but maybe not I saw some rather hefty substations to get different answers

$\tiny{4.2.5}$ $\displaystyle\int^1_0{xe^x\ dx}$ is equal to $A.\ \ {1}\quad B. \ \ {-1}\quad C. \ \ {2-e}\quad D.\ \ {\dfrac{e^2}{2}}\quad E.\ \ {e-1}$ ok I think this is ok possible typos but curious if this could be solve not using IBP since the only variable is x

Hello! I am a 'mature' learner and am fascinated by all kinds of physics and math ideas. Learning is the key to enjoying science and keeping an open mind. I must admit, I am not very sharp on my physics skills and my calculus is pretty rusty now (I don't work in the science field, per se) so I...

I have the following function $$f^{(0)}\left(x\right)=f\left(x\right)=e^{x}$$ And want to approximate it using Taylor at the point ##\frac{1}{\sqrt e} ## I also want to decide (without calculator)whether the error in the approximation is smaller than ##\frac{1}{25} ## The Taylor polynomial is...

Hi! Some time ago I came across a series and never solved it, I tried to give a new go because I was genuinely curious how to tackle it, which I thought would work, because it looks innocent, but there is something about the beast making it hard to approach for me. So need some help! Maybe this...

I got a polar function. $$ \psi = P(\theta )R(r) $$ When I calculate the Laplacian: $$ \ \vec \nabla^2 \psi = P(\theta)R^{\prime\prime}(r) + \frac{P(\theta)R^{\prime}(r)}{r} + \frac{R(r)P^{\prime\prime}(\theta)}{r^{2}} $$ Now I need to convert this one into cartesian coordinates and then...