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Unformatted text preview: MATH 2070U/2072U Test 7
Instructor: D.A. Aruliah Week 13, 2008
Name (last name, ﬁrst name): Student Number: Teaching Assistant: Instructions
• Before starting, read over the entire test carefully. • Please verify that the test has 5 pages. • You may use a calculator and a pen or pencil. • Test written in pencil are not elegible for regrading. • Laptops, cellphones, and pagers are not permitted. • Have your student card on your desk. • There are 4 questions on this test and a total of 20 marks. • There are 45 minutes for the test. • Questions do not carry equal weight so use your time wisely. • Show as much work as needed to fully answer the questions. • Write your answers as neatly as possible in the test itself. • You are expected to comply with the UOIT rules for academic conduct. Q: Mks: 1 4 2 6 3 6 4 4 Total 20 MATH 2070U/2072U Test 7 Page 2 of 5 1. [4 marks] Reduce the fourthorder initialvalue problem x(0) = x− 1 sin(xx ) − t = 0, 2 1 , 4 1 x (0) = − , 2 x (0) = 4 to an equivalent ﬁrstorder system of ODEs MATH 2070U/2072U 2. [6 marks] Consider the initialvalue problem Test 7 Page 3 of 5 y y =1+ , ˙ t y (1) = 0.5. Carry out two steps of the modiﬁed Euler method with stepsize h = 0.1 to determine an approximate value y2 y (t2 ) = y (1.2). WXIT W !J X W! ] !] ! X! WXIT W !J X ! W! ]! L ! W W X ! !J MATH 2070U/2072U Test 7 Page 4 of 5 3. [6 marks] Consider the initialvalue problem for the system of ODEs dF 1 FC =− , dt 8 F +1 dC 2F C C = −, dt F +1 2 F (0) = 0.1, C (0) = 0.24 Carry out one step of Euler’s method with stepsize h = 0.1 to determine approximate values for F1 F (t1 ) = F (0.1) and C1 C (t1 ) = C (0.1). MATH 2070U/2072U Test 7 Page 5 of 5 4. [4 marks] Consider the initialvalue problem for the system of ODEs dX = −3.6X + 1.2 Y (1 − Y 2 ) − 1 , dt 2 dY = −1.2Y + 6 X + , dt Z +1 dZ = −0.12Z + 12X dt X (0) = 0.1, Y (0) = 0.15, Z (0) = 0.125. Write out the M ATLAB commands required to produce a numerical solution of the given IVP on the interval 0 ≤ t ≤ 15. Use ode23 and an anonymous function. J!$ X] ? XWTER !? A ] !? ?8 = A!SHI ] ] A J XWTER ] ] ] ] A B ...
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 Spring '10
 aruliahdhavidhe
 Math, Numerical Analysis, Teaching assistant, 45 minutes, initialvalue problem

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