Calculus Definition and 1000 Threads

This is my first year in college, and I am currently taking calculus 1, and physics w/ calculus. My academic adviser told me that I would be okay taking the two together since I'd be learning the calculus as i went. This doesn't seem to be the case because for a lot of my problems we are already...

I am at the stage of my education where I am seeing calculus (mainly differential equations) popping up in my engineering courses. However, I have just started multi-variable calculus, so I have not taken differential equations yet. My professors basically show us how certain equations are...

Homework Statement Let P be a point on the sphere with center O, the origin, diameter AB, and radius r. Prove the triangle APB is a right triangle Homework Equations |AB|^2 = |AP|^2 + |PB|^2 |AB}^2 = 4r^2 The Attempt at a Solution Not sure if showing the above equations are true is the...

Hi! First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was...

I have a question regarding the usage of notation on problem 2-11. Find ##f'(x, y)## where ## f(x,y) = \int ^{x + y} _{a} g = [h \circ (\pi _1 + \pi _2 )] (x, y)## where ##h = \int ^t _a g## and ##g : R \rightarrow R## Since no differential is given, what exactly are we integrating with...

So I have a quick question that will hopefully yield some clarification. So the divergence of a dyadic ##\bf{AB}## can be written as, $$\nabla \cdot (\textbf{AB}) = (\nabla \cdot \textbf{A}) \textbf{B} + \textbf{A} \cdot (\nabla \textbf{B})$$ where ##\textbf{A} = [a_1, a_2, a_3]## and...

What's the difference between f(x)=3 and f(x)=3x^0 ? and why Limit of the second function when x\rightarrow0 exists ? and is the second function continuous at x=0 ?

Hey everyone, I've been stuck on this one piece of HW for days and was hoping someone could help me. It reads: The surface area, A, of a sphere with radius R is given by A=4πR^2 Re-derive this formula and write down the 3 essential steps. This formula is usually derived from a double...

I saw the topic and have given it a lot of thought over the past few years, and my take is so different from the other thread I'm starting another. Problems with the beginning math curriculum: 1. Too abstract and difficult 2. Totally unmotivated These problems were unavoidable 50 years ago...

Hello, do you know of any books similar in style to Callahan's Advanced Calculus book(a book that explains the geometrical intuition behind the math)? This goes for any subject in mathematics(but especially for subjects like vector calculus, differential geometry, topology). Thanks in advance!

Good afternoon, I'm looking to complete a Mathematics Calculus Exploration for my course, before starting to write up my project I was hoping to find someone that could offer some advice or comments to make my project more successful. First of all my project seems very simple at first glance...

I've seen the terms tensor calculus and tensor analysis both being used - what is the difference?

This is an exercise from the textbook Apostol Vol 1 (page 525, second edition), and I do not know how to prove it: Suppose a curve C is described by two equivalent functions X and Y, where Y(t) = X[u(t)]. Prove that at each point of C the velocity vectors associated with X and Y are parallel...

Which skill is more important for Physics in the modern era? From what I know, Newton (along with some other fellows) developed Calculus in order to solve problems in Physics. Because of this, it's safe to say that Calculus is an essential branch of mathematics to understand when it comes to...

Hi everyone, I will be junior next year in my high school and take Calculus BC. However, I also take Calculus 1&2 Honor in the community college which is known as Orange Coast College ( If anyone has studied here before, please tell me the difference between the content of this course and...

Homework Statement Section 11-2, Page 651, Example 3 Homework Equations y = sin^3t and dy = 3cos^2t sint dt. Shouldn't there be a Minus Sign there? The Attempt at a Solution Answer is correct. But isn't there a missing Minus Sign?

I am linearizing a vector equation using the first order taylor series expansion. I would like to linearize the equation with respect to both the magnitude of the vector and the direction of the vector. Does that mean I will have to treat it as a Taylor expansion about two variables...

Hello everyone, Im currently taking my first semester of College Physics with Calculus and i need a good book to help me study concepts and maybe have example problems that have step by step analysis. Any Suggestions?

Is there a website that anyone can suggest to practice Algebra, and/ or Calculus?

Hi, there is a book of dg of surfaces that is also about tensor calculus ? Currently i study with Do Carmo, but i am looking for a text that there is also the tensor calculus! Thank you in advance

A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. Two ratios are proportional if they change equally and are related by a constant of proportionality? Not sure about this definition, but please correct it if you can...

Homework Statement You have been employed but(sic) the Mathematics Football League (MFL) to design a football. Using the volume of revolution technique, your football design must have a capacity of 5L ± 100mL. You must present a statement considering the brief below. Just a quick side note, I...

Do I substitute A_\mu + \partial_\mu \lambda everywhere A_\mu appears, then expand out? Do I substitute a contravariant form of the substitution for A^\mu as well? (If so, do I use a metric to convert it first?) I’m new to Ricci calculus; an explanation as to the meaning of raised and lowered...

Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I...

Homework Statement Let A be a dense set**. Prove that if f is continuous and f(x) = 0 for all x in A, then f(x) = 0 for all x. **A dense set is defined, in the book, as a set which contains a point in every open interval, such as the set of all irrational or all rational numbers.Homework...

Homework Statement X and Y 2 real numbers / |x| <1 and |y|<1 Prove that |x+y|<|xy+1|Homework EquationsThe Attempt at a Solution |x+y|<2 I couldn't prove that |xy+1| >2 And couldn't find a way to solve the problem Please help

Homework Statement Decide whether the given function is bounded above or below on the given interval, and which take on their maximum or minimum value. (Notice that ƒ might have these properties even if ƒ is not continuous, and even if the interval** isn't closed) **The interval is (-a-1...

Can someone help me with this? (dA/dt)=1cm/s (cm^2 whatever...leave out trivial corrections). A=pir^2 (dA/dt)=2pir(dR/dt) Multiply through by (1/2pir) (dA/dt)/(2pir)=dR/Dt What is the rate of change of the radius for a circumfrance of 2 I just used the related rates formula that I derived for...

Homework Statement : the question wants me to prove that the limit of f(x,y) as x approaches 1.3 and y approaches -1 is (3.3, 4.4, 0.3). f(x,y) is defined as (2y2+x, -2x+7, x+y). [/B] The attempt at a solution: This is the solution my lecturer has given. it's not very neat, sorry...

Hi, i am looking for a good textbook for someone who knows nothing about calculus.

Pappus's centroid theorems were discovered 17 centuries ago, when calculus wasn't invented yet. How are these theorems proved without using calculus? "The first theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C...

I was reading this book yesterday and looking at this proof/justification. I was thinking it is possibly incorrect, but wanted to get some other opinions. Here is the example they gave in the book with the work attached.

Homework Statement I worked on this question and I made it so far, and now I am stuck on how to finish it. Here is the problem and below I will explain what I attempted. Homework EquationsThe Attempt at a Solution I know looking at the last part about using previous homework, I want to...

lim_(h->0^-) (e^(x+h)/((x+h)^2-1)-e^(x+h)/(x^2-1))/h = -(2 e^x x)/(x^2-1)^2 I know how to differentiate the expression using the quotient rule; however, I want to use the limit definition of a derivative to practice it more.This desire to practice led me into a trap! Now I just can't simplify...

For $$P=P_0\times e^{G(t)}$$ and $$G'(t) = a+bt$$ Show $$G(0)=0$$ I get $$G(t) = \int a+bt ~dt = at+\frac{1}{2} b t^2+C$$ therefore $$G(0)=C $$

Homework Statement Homework EquationsThe Attempt at a Solution I know I will just have to show this by one example. I thought about using f(x) = x2 but I am not sure if this satisfies the last part dealing with the absolute value of the derivative. It is just the last part on which I am stuck.

Homework Statement Homework EquationsThe Attempt at a Solution I started looking at this problem and I think I am going to have to use the intermediate value theorem for this proof, but I am not quite sure. I started looking at possible examples of these functions, but I know this is not good...

I want to start learning calculus I. But, I don't know what courses I need to finish before starting precalculus. any help would be appreciated.

While trying to study textbooks on analytical mechanics or QFT I realized that I simply cannot operate with variations of functions in the same way I can operate with derivatives and integrals. I have never learned calculus of variations in university and, frankly, I am not much interested in...

Homework Statement I have been working with researching and writing a paper on the Freshman Dream Quotient Rule. This rule states , and I was wondering if anyone can come up with an example of 2 functions which make this work. Homework EquationsThe Attempt at a Solution I have looked at...

Homework Statement ' Here is the given problem Homework EquationsThe Attempt at a Solution a. For part a, I felt it was not continuous because of the sin(1/x) as it gets closer to 0, the graph switches between 1 and -1. Then I felt it might be continuous, therefore I am not sure. b. For part...

Homework Statement I am posting this for another student who I noticed did not have the proof in the problem. Here is what she said. Let's try and help her out. I have been working on the problem below and I am stuck. I am stuck primarily because of the part where is says x=0. If x-0, it...

Hi, I want to know about some books that can help me to clear my concepts of calculus.I know the basics of differentiation and integration,but don't have clear idea about it.Well,I would like to buy such a book that has explained the rules and methods of calculus properly.Also,I want to know...

Hi, I want to re-learn multivariable calculus, after I have learned it, not in the best possible way... and feel bad about it. I have seen the recommendations here about Hubbard/Shifrin/Fleming/Edwards. I have also seen the books by Munkres/Spivak/Apostol. I didn't really like Hubbard's book...

My name is Amit Gupta and I am a teacher of physics and calculus, I have experienced in physics last several years, I love to solve physics equations, Anyone who have problems in physics and calculus subjects, I will provide you a right solution through problems practice. We are working towards...

In English grammar, we typically refer to specific branches of mathematics without a prefixed article; e.g., solve using algebra, trig., etc.. By contrast, we often prefix calculus with the definite article, "the". For instance, "solve via the calculus". Can anyone explain this exception to...

1. The problem: Ive been all afternoon struggling with this doubt. Its a bit more teoric than the rest of the exercices i did and i just can't seem to get around it so here it goes ...

Homework Statement Statement:[/B] Let y = u(x)v(x). a) Find y' , y'', and y''' b) The general formula for yn, the n-th derivative, is called Leibniz’ formula: it uses the same coefficients as the binomial theorem , and looks like https://i.gyazo.com/53728964c6b3ef142fd70f600c29e037.png Use...

Question : General solution of dy/dt = -ay + b My solution : dy/dt = -a(y-b/a) (dy/dt)/(y-(b/a)) = -a Integrating both sides : ln | y-(b/a) | = -at + C e(-at+C) = y-(b/a) Ce(-at) = y-(b/a)

Hello, I am want to prove that: $$ \sum_{1}^{\infty} \frac{1}{n^{2} + 1} < \frac{1}{2} + \frac{1}{4}\pi $$ Cauchy's Convergence Integral If a function decreases as n tends to get large, say f(x), we can obtain decreasing functions of x, such that: $$ f(\nu - 1) \geqslant f(x) \geqslant...