110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:工程數學(B)#100598

(a) in which H is a Heaviside unit step function. (6%)

(b) (6%)

(C) in which δ is a Dirac delta function. (6%)

(d)(6%)

2. (10%) If f(x) =|x| -I ≤x ≤I, find and write out explicitly the beginning (or lower) four terms of its Fourier series.

4. (16%) Use Laplace transform to solve the following partial differential equation of vibration:

5. (15%) Evaluate the integral

6. (18%) Using the following relation, namely
where A is the surface enclosing the volume △V, expand and explicitly write out ∇• B in spherical r-θ-Φ coordinates. Note that . Show all details to get full credit.