Recent content by Math100

Thank you very much for the suggestion/recommendation, guys!

I've taken Linear Algebra before but haven't taken classes/courses for group theory nor field theory. I think I have to buy/purchase these books then. Thank you for the suggestion/recommendation.

May anyone/someone please suggest/recommend some books on learning Galois Theory? Before learning this pure mathematics subject, is the knowledge of group theory required in order to study Galois Theory? I have the e-textbook of Galois Theory by Ian Stewart, 4th edition but was wondering if...

I wouldn't claim that there exists a 'right' way to study any subject, not just physics, but watching lecture videos on YouTube won't suffice in order to truly understand advanced physics. Textbooks can be boring but they provide formulas, derivations and practice problems. It's very important...

I have taken all of those courses/classes you've listed above, except the last one, 'Introduction to Numerical Methods'. I just wanted to know the quality of the online math classes/courses that are offered from this online college/university, but now, I think I know what I should do.

Hello, I want to know if anyone has taken an 'Introduction to Partial Differential Equations" class/course via UIUC (University of Illinois Urbana-Champaign) through NetMath. I am planning to take this course given the fact that I have taken ODE (Ordinary Differential Equations) and Nonlinear...

Thank you!

But what's ## \dot\theta ## from the integral?

From the original equation of ## \ddot{x}+x+\frac{3}{2}\beta x\lvert x\rvert=0 ##, I've got ## \ddot{x}\dot{x}+x\dot{x}+\frac{3}{2}\beta x\lvert x\rvert\dot{x}=0 \implies \frac{d}{dt}(\frac{1}{2}\dot{x}^2+\frac{1}{2}x^2+\frac{\beta}{2}x^2\lvert x\rvert)=0 \implies...

Is this really a math problem for eight-year old students? How come I have doubts?

That's all the work I have so far.

Proof: Let ## \epsilon=0 ##. Then the unperturbed equation is ## \ddot{x}+x=0 ## and the general solution is ## x(t)=A\sin\omega t+B\cos\omega t ## where ## \omega=1 ## is the angular frequency with the constants ## A ## and ## B ##. With the initial condition ## x(0)=0 ##, we have that ##...

Thank you for the help!

So far, I've got that ## g(a)=(c-1)a+\frac{3}{4}a^3\implies g'(a)=c-1+\frac{9}{4}a^2 ##. I know that if the first derivative of a function is positive (greater than ## 0 ##), then that function is always/strictly increasing. However, how should I construct this proof in order to show that...

Sorry, I think I've made some huge mistakes above from my initial/first post. The equation of the phase paths should be ## y=\pm\sqrt{2(C-V(x))} ## where ## \dot{x}=y, \dot{y}=f(x) ##. So I have ## y=\pm\sqrt{2(C-(\frac{x^2}{2}+\frac{\beta}{2}x^3\operatorname{sgn}(x)))} ## and ## y=0 ## for ##...