# 数学物理方程代考，美国代考，加拿大代考，澳洲代考，英国代考

Question 1)
(a) Show that, by choosing suitable values for P and Q, Green’s Theorem in the
plane leads to the formula for the area enclosed by a loop i.e.,
Area =
1
2 ˛loop
xdy − ydx
[2 marks]
(b) Use this to find the area of the closed curve defined by
x = cos 
y = 3 sin 
where 0 ≤  ≤ 2. [4 marks]
Question 2)
Consider the vector field, F = x2yz i+xy2z j+xyz2 k. Use the divergence theorem
to evaluate
” F · ds
over the surface of the unit cube defined by the ranges x = [0, 1]; y = [0, 1]; z = [0, 1].
[4 marks]
Question 3)
Consider the vector field F = (2x+yz) i+(2y+xz) j+xyk. Using Stokes’ theorem,
show that ¸ F · dr = 0 around any closed curve. [2 marks]
Question 4)
Consider the vector field, F = y i+x k. Use Stokes’ theorem to find ¸ F·dr around
the circular loop in the xy-plane defined by x2 + y2 = a2. [4 marks]
Question 5)
For gravity, g, we can define the divergence as, ∇ · g = −4G, where G is the
gravitational constant and  is the mass density. The divergence theorem states that,
“S
g · ds = °V
∇ · g dV.
By applying the divergence theorem to a point within the Earth’s radius, a distance
r from the centre:
(a) Draw a sketch showing a suitable choice of surface, S. [2 marks]
(b) Show that the magnitude of g is given by:
g(r) = −
4
3
Gr
(Assume that the Earth has a constant density.) [2 marks]
Question 6)
The square OABC lies in the xy-plane and is defined by the points:
O = (0, 0, 0);A = (1, 0, 0);B = (1, 1, 0);C = (0, 1, 0). The vector field, b, is given by,
b = 2yz i + (x2 − y2) j + (y + x2 − z2) k.
(a) Evaluate the line integral, I1 = ¸ b · dr, following the path O-A-B-C-O.
[4 marks]
(b) Determine ∇ × b. [2 marks]
(c) Evaluate, I2 = ˜OABC(∇ × b) · ds, over the square OABC. [4 marks]

# 数学代写|Real analysis实变分析代考，Complex analysis复变分析代考,数学代考

analysis是数学专业代数方向学生的必修课程，简单来说，复分析是描述解析函数性质的，实分析是描述解析函数性质的。

1. Let D  C be the intersection of the half planes y < 2x and y > 􀀀2x, where z = x +
iy 2 C. Find a conformal mapping of D onto the following domains:
a) Find a conformal mapping of D onto the right half plane.
b) Find a conformal mapping of D onto the unit disk D = fjzj < 1g.
c) Determine the automorphism group for D.
2. Given a 2 (􀀀1; 1) we wish to find a conformal map  of the slit disk D n (􀀀1; a]
onto the unit disk D such that (i=2) = 0. In order to do this proceed as follows:
a) Find a conformal map of D n (􀀀1; a] onto D n (􀀀1; 0].
b) Find a conformal map of D n (􀀀1; 0] onto D.
3. Let D = D n fjz + 1=2j  1=2g. Find a conformal map from D to D.
4. Consider the unit disk
a) Show that D is not conformally equivalent to C.
b) Find an analytic mapping f : D ! C such that f(D) = C.
5. Prove that the only entire functions f : C ! C which are injective (one to one) are the
linear functions f(z) = az + b.
6. Let Dj ; j = 1; 2; : : : ; be a sequence of simply connected domains such that Dj+1 
Dj  C for all j = 1; 2; : : : , and such that the interior D of \jDj is nonempty and
connected.
a) Prove that D is simply connected.
b) Pick any point z0 2 \jDj . Let gj : D ! Dj be a conformal map, normalized so that
gj (0) = z0 and g0
j (0) 2 (0; 1). Prove that the sequence gj ; j = 1; 2; : : : ; converges
locally uniformly on D to an analytic function g with the properties: if z0 2= D then g
 z0; if z0 2 D then g : D ! D is a conformal map.

# Final代考｜澳洲大学代考｜UNSW代考｜悉尼大学代考｜墨尔本大学代考

• LECTURE NOTES-救命稻草

• 按时上课

• 整理知识点与例题总结

• 制订学习时间表

• 多做各种模拟考试

• 注意劳逸结合