Hello there! I will be studying Mathematics and Physics in University in approximately 2 months. I really enjoy Mathematics and have done some introductory Calculus. I have looked into Spivak's book "Calculus" and, although written very well, I just tent to find Calculus boring. However, when...
1. Homework Statement
I am using Spivak's Calculus and just finished the third exercise in part 1.
It was a very easy exercise but it seems that Spivak makes some assumptions.
The problem is as stated:
If x^{2}=y^{2}, then either x=y or x=-y. Prove it.
The proof was relatively simple (by...
Hello there. I have been reading G.H. Hardy's book "A Course of Pure Mathematics". It is a fantastic introduction to Analysis. I have no problems with the book so far, however, it does assume some knowledge in number theory. I just want to make sure that the following proofs for properties of...
Hello there physicists! I am here to ask a few straightforward questions regarding nuclear fusion accomplished here on Earth.
Question 1: How does a magnetic field contain the heat produced by nuclear fusion in the reactor? If we look at the example of Deuterium fusing with Tritium, a high...
Hi there! My question involves the area of a parallelogram. Now, I know how to prove the commonly used formula (b*h) very easily, however, there is a formula given on Wikipedia as an alternative that states....Given two sides B and C with angle (theta), B*C*sin(theta)=Area of a parallelogram...
1. Homework Statement
Hello there! I have a couple of questions regarding light(EMR) and how it behaves when moving from one medium to another. From what I understand, the frequency of any light wave, when it moves from one medium to another, stays the same. As a consequence of this, the...
1. Homework Statement
Hi there! I am currently taking physics and we are in the process of learning about electromagnetic radiation. I am a bit confused as to how exactly an electromagnetic wave is produced. I understand that a periodically oscillating charge produces and oscillating magnetic...
Hi there! I have been reading Apostol's "Calculus: Volume 1" and have been trying to prove a few theorems using specific field axioms(note that this is not a "homework" question since I have not been assigned it, but instead, chosen to attempt it out of curiosity). Although I am not a math...
Can someone help me prove that if ab=ac and a does not equal 0, then b=c. You can only use the field axioms. Here is my attempt( I am not sure about the final result).
ab=ac
then,
ab-ac=0
a(b-c)=0
a(0)=0 (Already proved this)
since a cannot equal 0, (b-c) must equal zero and we are left...
1. Homework Statement
Hi there. I am currently taking physics 30(algebra physics course) and we are in the electrostatics unit. I am curious as to why, when trying to find the force acting on a charged particle moving perpendicular to a magnetic field, the force results in a direction that is...
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Hi there! We are currently studying forces and fields in physics and we are in the electrostatics chapter. I am having a bit of trouble fully understanding electric potential energy. The book states that electric potential energy is defined as the work required to move a...
1. Homework Statement
The problem is that I don't understand what causes an object to become positively or negatively charged. I know that, in chemistry, ions represent charges in voltaic cells. For example, cations become reduced and their electrons travel to the anode. This creates a negative...
1. Homework Statement
As I was relearning some concepts in calculus, I came across a section on ellipses. What I don't understand is why a and b in the standard equation of an ellipse govern the length of the minor/major axes. Can anyone shed some light? Thank you very much!
2. Homework...
1. Homework Statement
Euclid's proof
Euclid offered the following proof published in his work Elements (Book IX, Proposition 20)[1] and paraphrased here.
Take any finite list of prime numbers p1, p2, ..., pn. It will be shown that some additional prime numbers not in this list exist. Let P be...
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2. Homework Equations
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3. The Attempt at a Solution
I guess I will start here. My question does not necessarily involve equations. In the Calculus book I am currently studying from, I am reviewing some pre-calculus and I came across a section that...