Calculus Definition and 1000 Threads

This is a question I'v got about calculus after doing my bachelors in engineering degree. So you can integrate an acceleration graph to get velocity, and integrate a velocity graph to get distance. Integrating a graph can be done by easily finding the area under the graph. This applies to all...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 7: The Riemann Integral ... I need help in fully understanding yet another aspect of the proof of Theorem 7.3.5 ...Theorem 7.3.5 and its proof ... ... read as...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 7: The Riemann Integral ... I need help in fully understanding an aspect of the proof of Theorem 7.3.5 ...Theorem 7.3.5 and its proof ... ... read as follows: In...

Homework Statement [/B] $$\int \left ( \frac{-1}{2*\sinh(x)*\sqrt{1-e^{2x}})} \right ) dx$$ or http://www.HostMath.com/Show.aspx?Code=\int \left ( \frac{-1}{2*\sinh(x)*\sqrt{1-e^{2x}})} \right ) dx Homework Equations the sinh identity, which is (e^x-e^-x)/2 The Attempt at a Solution Tried...

hey everyone just started university and the jump i feel is huge from a level and was just wondering if you guys knew of any books that had linear algebra and/or several variable calculus in them but displayed and explained stuff in a clear simple way? or if anyone has any websites that do the...

So My Question Is Simple, But It confuse me too much! What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?

Homework Statement Solve from x = 0 to x = ∞, ∫xe-axcos(x)dx Homework EquationsThe Attempt at a Solution I have a solution for the integral ∫e-axcos(x)dx at the same limits, and I feel that the result might be of use, but have no idea how to manipulate the integral above such that I can use...

I'm wondering if and how to establish an online community of people who would like to self-teach physics from the bottom-up without direct involvement in academic institutions. The idea is to structure it in a flipped teaching classroom format where students first follow a video course and/or...

1. Find if the limit exist: sin (x^3 + y^3) / (x + y) (x,y)-> (0,0) So I am starting solving this by using polar coordinates form and I get to lim= sin r^3 ( cos^3θ + sin^3θ) / r ( cosθ + sinθ) = lim r^2 ( cos^2Θ + sin^2Θ) My question is ok so far and how...

Homework Statement Let f(x) be the function whose graph is shown below (I'll upload the image) Determine f'(a) for a = 1,2,4,7. f'(1) = f'(2) = f'(4) = f'(7) = Use one decimal. Homework Equations f(x+h)-f(x)/h The Attempt at a Solution Hi everybody I was trying to do this function...

Show that y≈∆φ×secφ in the jpeg attached. or ∆y = sec φ A and B are points on curved surface, two lines are extended through origin to a line that is tangent to the circle, these points are A' and B', change in Angle will bring a change in length between A' and B'. I need to know how is this...

I tried to derivate pi using calculus but i just found a quite different result. Can you spot my wrong please?First i started with equlation of a circle which is: $$x^2+y^2=r^2$$ I am assuming circle's center stands on the center of origin. To reach pi we shoud consider the situation that...

So I am in calculus 3 this year and have passed both calc 1 and 2 with a B and C+ respectively. I could have gotten a better grade but was lazy. I was lazy by using calculators and not actually learning the arithmetic and algebra. Now one serious issue I have is Trig. I can never remember trig...

1. Problem Recall that we defined linear equations as those whose solutions can be superposed to find more solutions. Which of the following differential/integral equations are linear equations for the function u(x,t)? Below, a and b are constants, c is the speed of light, and f(x,t) is an...

Homework Statement A quadrangular pyramid OABCD with square ABCD as the bottom. OA = 1, AB = 2, BC = 2 Also, OA perpendicular to AB, OA perpendicular to AD. Question 1 : Find the inner product \overrightarrow {OA}.\overrightarrow {OB} and the size of the cross product |\overrightarrow...

<Moderator's note: Moved from a technical forum and therefore no template.> Hi everybody I've been trying to solve this problem all the afternoon but I haven't been able to do it, I've written what I think the answers are even though I don't know if they're correct, so I've come here in order...

Hi! Can anyone help me? If a constant number h of fish are harvested from a fishery per unit time, then a model for the population P(t) of the fishery at time t is given by: dP/dt = P(5-P) - h, P(0) = P0. a. Solve for the IVP if h = 4. b. Determine the value of P0 such that the fish...

Homework Statement This is a chain rule problem that I can't seem to get right no matter what I do. It wants me to find the derivative of y=sqrt(x+sqrt(x+sqrt(x))) Homework Equations dy/dx=(dy/du)*(du/dx) d/dx sqrtx=1/(2sqrtx) d/dx x=1 (f(x)+g(x))'=f'(x)+g'(x) The Attempt at a Solution My...

Homework Statement i want to find limit value using riemann sum \lim_{n\to\infty}\sum_{i = 1}^{2n} f(a+\frac{(b-a)k}{n})\cdot\frac{(b-a)}{n}= \int_a^b f(x)dx<br> question : <br> \lim_{h \to \infty} =\frac{1}{2n+1}+\frac{1}{2n+3}+...+\frac{1}{2n+(2n-1)}<br> Homework EquationsThe Attempt at a...

Hello. The textbook that was assigned to my class is not a good fit for my professor. The textbook simplifies the basic force equations so that there are no general equations with integrals or vector calculus calculations. Can anybody recommend a Fluid Mechanics book or books that deal only...

How much would time pass between watching the sun set from ground level and then watching it set again from the top of a sky scraper? I heard once that this could be done using one of the towers of the World Trade Center. So I assume one could also do this using the Sears / Willis Tower in...

Homework Statement question : find the value of \iint_D \frac{x}{(x^2 + y^2)}dxdy domain : 0≤x≤1,x2≤y≤x Homework Equations The Attempt at a Solution so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x and i decided to convert...

I thought Differentiation is all about understanding it in a graph. Every time I solve a question on differentiation I visualise it as a graph so it's more logical. After all, that IS what the whole topic is about, right? Or am I just wrong? But when you look at these questions...

I'm currently struggling a lot in self-studying Spivak's Calculus; I've tried numerous online resources including math stackexchange, I'm currently about half-way through How To Prove It as many people have suggested. I'm only in high school, so the calculus class I'm taking barely coincides...

Homework Statement I have 2 thin rods of length L in the axial plane(x axis), they're of the same uniform linear charge distribution and are separated by a distance a . Homework Equations $$E = \frac{kq} {R^2}$$ $$F = qE$$ The Attempt at a Solution [/B] Let 0 be one at one end of the two rod...

Homework Statement Solve the following heat Eq. using FFCT: A metal bar of length L is at constant temperature of Uo, at t=0 the end x=L is suddenly given the constant temperature U1, and the end x=0 is insulated. Assuming that the surface of the bar is insulated, find the temperature at any...

Homework Statement am trying to solve this PDE (as in the attached picture) https://i.imgur.com/JDSY4HA.jpg also my attempt is included, but i stopped in step, can you help me with it? appreciated, Homework EquationsThe Attempt at a Solution my attempt is the same as in the attached picture...

I was talking to my friend and she told me how she was taking Calculus 1 over the summer in 5 weeks. Everyone else averaging a 30 percent as their overall grade. The teacher was planning to raise the grade. So if you get a 30%, you'll get a C. However, my question is that is it okay to pass...

when inducing that the cycloid is the least time-taking course between the two points in the two dimension, we have to use calculus of variations. Then is it possible to induce the parameter of the least time-taking course between two points in the three dimension?

Homework Statement How does one show that q(t) is indeed a solution? Homework EquationsThe Attempt at a Solution My current idea is that i should come up with any form of solution, like q = Acos(ωt), and slot it in the RHS. Reason being that if q is indeed a solution, the result of the...

Hey, I have a theorem I cannot prove. We have a function x^* that maximizes or minimizes the integral: \int^{t_1}_{t_0} F(t,x(t),\dot{x}(t))dt Our end point conditions are: x(t_0) = x_0, x(t_1) \geq x_1 I am told that x^* has to satisfy the Euler equation. That I can fully understand since...

So here is a problem (more of a dilemma) I encountered in my mandatory physics class [(high school level) i say mandatory since I take an other optional calculus based one], many students are often mislead for example in kinematics the equations are very clunkily derived and when you finish...

particles in plane polar coordinates r = rcosθ i + rsinθ k F = Fer + Feθ ∂r/∂r =|∂r/∂r|er = (cos2θ + sin2θ)½er = er why ∂r/∂θ =|∂r/∂θ|eθ = (r2cos2θ + r2sin2θ)½eθ = reθ I understand that ∂r/∂θ = -rsinθ + rcosθ but why ∂r/∂θ = (r2cos2θ + r2sin2θ)½eθ

I am an engineering major at Los Angeles Pierce community college. I have been for the last years working 40 hours a week in order to sustain and put myself through community college. After I transfer, I don't plan on working. Now, each semester due to my work schedule and life happening, I can...

I have learned an adequate amount of calculus including implicit, parametric differentiation as well as Upton second order differential equations in high school math course. It was really abstract and we were taught only how to solve mathematical problems. Now, I need to model those problems in...

Homework Statement Calculating the area of equilateral triangle using calculus. Homework EquationsThe Attempt at a Solution The area of the triangle is the area of the circle minus 3 times the area of the sector shown in (light blue). So, the target is to calculate the pink area first...

Oh wait, I am not supposed to ask questions here, sorry. I can't find where i should post questions though

Hello and thank you for trying to help. In spite of the fact that this seems a very simple problem, I do not find myself able to get a solution. Here it goes: Let $$f(x)=\displaystyle \sum_{k=3}^\infty a_k \frac{x^k}{k(k-1)(k-2)}$$ and $$g(x)=\displaystyle \sum_{k=0}^\infty a_k x^k$$. Express...

Homework Statement I am working on a project dealing with the velocity and acceleration of satellites based on their distance from Earth. I was recommended to include some calculus in this project. Originally I thought I could just take the derivative of the orbital speed equation to find...

Hi, In next semester, I am going to take vector calculus. Here is the course description: Vector fields, line and surface integrals, Green's Theorem, Stokes' Theorem, Divergence Theorem and advanced topics such as differential forms or applications to mechanics, fluid mechanics, or...

I work full-time, so evening or online classes are all I can do. I need to take calculus from the community college I've been attending, but it is not offered in the evening. In fact, none of the local colleges or universities offer it in the evening, so I must do it online. So I go to register...

I started studying calculus last week and in 2 weeks I start my double degree in: Science (Physics) / Engineering (Honours) My 4 classes will be: FUNDAMENTALS OF PHYSICS B MATHEMATICS 2: SERIES AND INTEGRAL CALCULUS ELECTRICAL SYSTEMS ENGINEERING COMPUTING AND ANALYSIS So, what tips do you...

Books on multivariable calculus that I often see get good recommendations are, Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard Vector Calculus by Colley What are other good books with some material on differential forms like Hubbard and Colley? Books by Edwards...

Homework Statement I understand the derivation it showed that included the sin (15.7 in the image) I just don't understand the following (15.8 in the image). Does "t" get pulled out of the equation? If so what do we derive for then? Does it become 0? If so, it would remain 0 and sin(0) is just...

So, i am currently studying physics in a brazilian university. I am going to have a Calculus 2 course which, in Brazil, covers Ordinary Differential Equations and multi-variable differential calculus. So which challenging and rigourous books would you guys recommend for that? Thanks for the...

I don't understand why grad(1/r)= (-1/r^2)ê_r. I know its derivate, but in cero the function is not definite and you can't find its derivative in cero.And, why div [grad(1/r)]=-4πδ(r vec) ?

so df/dy' is yy'/ √(1+y'^2) then we are supposed to do y' . [ yy'/ √(1+y'^2) ] - y√(1+y'^2) how does this bring equation 2 in the image ?

Homework Statement Find the interval for a so that (3-a)x+ay+(a^2-1)=0 is normal to the curve xy=4Homework Equations If two curves intersect each other orthogonally (at right angles) m1×m2=-1 Slope of a curve y=f(x) at a point(x1,y1) is equal to value of (dy/dx) at x1,y1 The Attempt at a...

I am going to be a freshman in college and I intend to major in astrophysics. This past year I took AP calculus AB, and I got an A and I believe I did well on the AP test (results haven't come back yet though). This morning I took my school's math placement test, and I was placed into...