Recent content by AfterSunShine

Hi, Are there calculus books that lie between Stewart (or Thomas) level and Spivak (Courant/Apostol) level? Thanks.

Thank you. What about algebra and trigonometry (Stage 1)? Go for separated gelfand books or do you have other rigorous recommendations? Am really interested in rigorous books for algebra & trig. Any recommendation is appreciated to start plan instead of just thinking about book & waste time.

Hello everyone, I'm planning to review learned mathematics from high school & start leaning pure math. You can reply to red colored text if you don't want to read full thread. My math level : Graduates as engineer 10 years ago. Got A in Calculus 1 & 2 (Those were single variable calculus), Got...

@TheBill Thank you for your detailed reply. Appreciated. @fresh_24 Thank you for your reply. My request is specific. Basically a book considered as an introduction to advanced mathematics. In other words, a book considered as introduction to abstract math including logic, proof methods...

Hi, For an engineer who graduated and finished typical Cal A,B,C + Linear Algebra + ODE, what book do you recommend to start reading to be a transition to advanced pure math subjects like abstract algebra and number theory? I did deep google search & concluded that that book supposed to include...

If I plug a number for t i will get vector not point! Still confuses me. Put t=k, then i will get <x1,x2,x3> + <ka,kb,kc>=< x1+ka , x2+kb , x3+kc > which a vector going from origin to the line. Vector not a point.

I will get the vector <x1,x2,x3>

Hi, In my calculus book,I found this vector form of line equation in space (bold means vector): Given point (x1,x2,x3) lies on line L & v=<a,b,c>, then equation of line is : r = <x1,x2,x3> + t <a,b,c> with t any number. Now, my question if I plug any number for t, then result will be vector...

So i substitute pi with 180. And yes you are correct, while calculating final answer i forget to include the "-" sign I have negative sign in my v(t), and there will (cos(something) - 1) which will give minus for sure as maximum value for cosine is 1, with the negative in v(t), answer must be...

Homework Statement The current through a 100 microfarad is i(t) = 50 sin(120*pi*t) mA Calculate the voltage across it at t = 1 ms. Consider zero initial voltage. Homework Equations v(t) = (1/c) integral of i(t) from t = 0 to t = t The Attempt at a Solution Am getting v(t) = - 1.326 (...

Finally i got it! Oh god the headache gone. Thank you sir.

Thanks for you reply, I solved it using two different ways. (1) First solution : Taking 2 parallel with 6 & redraw circuit, solve it as shown in attach file. I redraw the circuit as our instructor said : " When taking two resistors in parallel, replace one of the resistors by the equivalent R...

"Ignore the dependent current source which will just feed into the short circuit for the time being." Am not following you ! So whenever I have current source parallel with short circuit, I just kill the source i.e. making it open circuit? Explain pelase. Edit: Let me generalize my question ...

Homework Statement The problem ask for Thevenin Equivalent for the circuit attached. Homework Equations Vth = Vab Rth = Req Rth = Vth / Isc Rth = 1 / It The Attempt at a Solution Already calculated Vth = 166.67 V. I've no problem with that. Already confirmed by textbook answer. However, my...

What about differentiating arcos(-x) and arcos(x) separately and noting that the derivatives are the equal?