Recent content by Rescy

Thanks for your detailed reply! I think I want to learn mathematical methods to a level which will enable me to understand graduate level physics. My current backgrounds are multivariable calculus, linear algebra and a bit of differential equation. I do not have understanding with regard to...

May I ask if you are applying to UK or US?

You are absolutely right, and it is embarrassing to know that I forgot to add the dots! As I punishment, I've written out the full procedures for Gracie.

Of course! Lagrangian is equivalent to Newton's second law of motion in Cartesian coordinates. $$L={1\over 2}m({\dot x}^2+{\dot y}^2)-mgy$$ Now apply Euler-Lagrange equation for x and y, we get $$m\ddot x=0 \tag{1}$$ $$m\ddot y=-mg \tag{2}$$ From (1), $$\dot x =v_x= \text{constant}$$ From...

Of course! Lagrangian is equivalent to Newton's second law of motion in Cartesian coordinates. $$L= {1\over 2}m(x^2+y^2)-mgy$$ apply Euler-Lagrange equation for x and y and you derive a differential equation whose solutions are SUVAT. It is a waste for Lagrangian Mechanics to be applied on SUVAT!

Think of Carnot's Engine in terms of a state diagram (P-V). Then you understand that every closed transformation would necessarily waste some energy (energy is represented as area).

Sorry, I will add the authors Yes, Morse and Feshbach. Is the book too advanced?

Use 'Vector Calculus' by Matthews if you are not learning it as part of the analysis course. I recommend this book from my heart, the clearest I have ever seen.

Would you recommend this book as a first exposure to mathematical methods? How high a lever is this book of? Is it out-of-date or still quiet useful?

The application of Newton's laws should be well understood while you are in high school! Try University Physics by Freedman, it has very detailed explanation and plenty of exercise.

How important is advisor's connection with professors at other universities?

What is the most important factors that determine if a candidate can be admitted into top theoretical physics PHD program? Since undergraduate students are most likely not able to produce significant research paper, will universities put more emphasis on GRE and GPA?

You are right, perhaps I should spend my time focusing on developing my skills instead of worrying. Complaining and worrying are just wasting precious time. Thank you for the reply! These are the best words for me today, thank you so much! I really can't imagine myself working in fields other...

I often wonder people's life in developed countries, not for the recreational activities or big houses, but that the people there are encouraged to pursue what they want and to turn their individual dreams into reality. I have long been fascinated by physics, and maths, and have been dreaming...

This seems to be not so satisfactory if you plan to do theory, because it delays your exposure to quantum physics, and the mathematics study is not intense.There is an emphasis for astrophysics, which I suppose is one of the strong points of your university. I think the forth year is good...