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Malham, Simon J.A. - Department of Mathematics, Heriot-Watt University
Question 1 (17 Marks) (a) Suppose we wish to derive the EulerLagrange equation that results from extrem-
Commun. Math. Phys. 193, 287 316 (1998) Communications in
BIT 0006-3835/00/4004-0001 $15.00 2003, Vol. **, No. *, pp. 00*00* c Swets & Zeitlinger
Review notes Introductory Schubert calculus
Review notes Introductory Fredholm theory and computation
An introduction to asymptotic analysis
Differential Equations and Linear Algebra Supplementary Notes
Chapter 3 (Non-homogeneouslinear ODEs): Solutions Solution 3.1(a).
Chapter 4 (Laplace transforms): Solutions (The table of Laplace transforms is used throughout.)
Question 1 (15 Marks) Find the general solution of the following differential equations
Question 1 (10 Marks) Consider the following linear second order ODE
Question 1 (15 Marks) Each of the differential equations below represents the position of a one gram mass oscil-
Final exam 2006: solutions Solution 1 (10 marks)
Question 1 (20 Marks) A soap film is stretched between two rings of radius a which lie in parallel planes a distance
Question 1 (20 Marks) A cone of semi-angle has its axis vertical and vertex downwards, as in Figure 1 (overleaf).
Chapter 5 (Linear algebraic equations): Solutions Solution 5.1
Final exam 2005: solutions Solution 1 (10 marks)
Nonlinearity 6 (1993)549-568. Printed in the UK Lengthscalesin solutionsof the NavierStokes equations
Final exam 2004: solutions Solution 1(a)
Chapter 7 (Systems of differential equations): Solutions Solution 7.1.
An introduction to Lagrangian and Hamiltonian mechanics
An introduction to Lagrangian and Hamiltonian mechanics
Question 1 (15 Marks) Find the general solution of the following differential equations
l(1993) 79-91. Printed in the UK Lattice methodsand the pressurefieldfor solutionsof the
Differential Equations and Linear Algebra Lecture Notes
Question 1 (10 Marks) Consider the following linear second order ODE
Review: Schubert calculus Simon J.A. Malham
Lecture notes Ideal fluid mechanics
Question 1 (10 Marks) Consider the following linear second order ODE
Question 1 (20 Marks) The goal of this problem is to find the path on the surface of the sphere of radius r that