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Supervision Times (Easter Term)
Mondays
6.00-7.00pm Neeloy Banerjee, Charles Emerton & Joaquim d'Souza
7.00-8.00pm Mark Fisher & Jirawat Tangpanitanon
Supervisions this term will be held in the Drawing Room in the
Fisher Building. Please make sure that
work is handed in to my pigeonhole in the Forecourt Porter's Lodge by
6.00pm the night before.
Easter Supervisions
Supervision 1 (May 9)
Example Sheet 1: 1, 4, 7, 9, 12, 14, 15, 18
Supervision 2 (May 16)
Example Sheet 1: 21, 27, 29, 30, 32, 33
Review: 2008 Paper 2: 10Y, 11X, 16S
Supervision 3 (May 16)
Example Sheet 2: 1, 3, 6
Review: 2009 Paper 1: 11S, 17T, 18X, 19Z
Lent Supervisions
Supervision 1 (Jan. 24)
Review of timed exams. (Postponed)
Supervision 2 (Jan. 31)
Example Sheet 1: S1(b,j), S3b, S4b, 6b, 7, 8a,b, 11
Supervision 3 (Feb. 7)
Example Sheet 1: 9c,e,g, 10, 13
Practice ODEs (y' = dy/dx):
y' = y/x - tan(y/x)
y'' + y' - 2y = 4sin(2x)
y''' + y = 0
Supervision 4 (Feb. 14)
Example Sheet 2: 4, 5, 7, 8, 10(i,ii,iv,v), 12
Supervision 5 (Feb. 21)
Example Sheet 2: 13, 15, 16c, 17a, 18, 20 21
Supervision 6 (Feb. 28)
Example Sheet 2: 21
Example Sheet 3: 3, 6, 8, 9
Lagrange Multiplier Review: What proportions (r:l:s) will maximize
the volume of a projectile in the form of a circular cylinder (length
l) with one flat end (radius r) and one conical end (length from edge
of cylinder to tip of cone is s), if the surface area is given?
Supervision 7 (March 7)
Example Sheet 3: 12, 13, 15, 17, 19
Review Sheet: 2, 3, 4
Supervision 8 (March 17)
Example Sheet 3: 14, 20
Past Exam, 2008, Paper 2: 15Z, 19T
Review Sheet: 5
Compute the surface integral of the vector, curl(V), over the surface consisting of the four slanting faces of a pyramid whose base is the square in the (x,y) plane with corners at (0,0), (),2), (2,0), (2,2) and whose top vertex is at (1,1,2). The vector V is given by V = ( 3x-yz , z^2-y^2 , 2yz + x^2 ).
Michaelmas Supervisions
Supervision 1 (Oct. 18)
A4, A6, A9, B6, B7, B10, B13, C3, C5, C7, C10
Supervision 2 (Oct. 24)
D1, E4, F2, F5, F7(b,e,h,k), F8, F11, F12, F15
Supervision 3 (Nov. 1)
F17(a,c,e), F18, F20(b,d), F21, G4(a,c,e,g), H1, I1
Supervision 4 (Nov. 7)
J1(iii,iv,v), K1, K2, L1, L2, M2(b,c)
One last review of complex numbers! Write the following in the form
x+iy (^ means to the power of, i.e. 2*2 = 2^2):
( 2i )^( 1+i )
( i-1 )^( i+1 )
( 1-sqrt(2i) )^i
arcsin(2)
arccos(i*sqrt(8))
artanh(i*sqrt(3)) (artanh is the inverse tanh)
Find the modulus of (2*exp(ia)-i)/(i*exp(ia)+2), where a is a real number, 0< a
<2*pi.
Supervision 5 (Nov. 15)
M3, N1, N2, N3, P4, P6, P8
For N1 and N2, please find the first three non-zero terms.
Bonus problem(!): Find the approximation of [sin(pi/2 + x +
x^2)]/[(2-x^3}^(1/2)] for x<<1 accurate to O(x^3).
Supervision 6 (Nov. 22)
P10, P11, P12, P15, Q1, Q3, Q4, Q6, Q8
For those looking for more review of approximations, work through N4
and the following problem:
Evaluate the limit of the expression, lim x-->pi/2, ln( 2 - sin(x) )/ln( 1+cos(x) ). Then by introducing a variable z = x - pi/2, find the leading order (first term) correction to the limit. You can leave your answer in terms of z.
Supervision 7 (Nov. 29)
R2, R5, R7, R8, R10, R12, R14
Review of multiple integrals:
i) Find the volume in the first octant (i.e. x, y, z > 0) bounded by the coordinate planes and the plane x + 2y + z = 4. You can check your answer by changing the order of integration and recovering the same answer.
ii) (more difficult) Find the volume that is inside the two cylinders x^2 + z^2 = a^2 and x^2 + y^2 = a^2. Hint: Work in the first octant to start and draw a careful picture!
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