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ERG2011A Advanced Engineering Ma

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					ERG2011A Advanced Engineering Mathematics
                 (Syllabus A)
                Problem Set 1
 Kreyszig 9th edition – 1.1 − 1.3, 8th edition –
                    1.1 − 1.4


1. (Derivatives) Compute the derivatives of the following functions with re-
   spect to x.
   (a) xn
   (b) sin(x) cos(x)
    (c) tan(x)
   (d) tan−1 (x)
    (e) sin−1 (x) cos−1 (x)
    (f) ln(3/x)
   (g) log2 (4x)
   (h) e3x
    (i) 5(245x )
    (j) 3x2 + 4ay 3 + 3xy 2
2. (Integrals) Compute the following indefinite integrals
        R
    (a) xn dx
        R
    (b) sin(x)dx
        R
    (c) tan(x)dx
        R
    (d) sec(x)dx
        R
    (e) x2dx 2
             +a

3. (Solution verification) State the order of the ODE. Verify that the given
   function is a solution (a, b and c are arbitrary constants).
   (a) y + 2y + 10y = 0, y = 4e−x sin(3x)
   (b) y     = cos(x), y = − sin(x) + ax2 + bx + c

                                     1
                             2
   (c) y + 2xy = 0, y = ce−x
   (d) y = y tan(x), y = c sec(x)
4. (Modeling)
   (a) If an airplane has a run of 3 km, starts with a speed of 6 m/sec,
       moves with constant accelaration, and makes the run in 1 minute,
       with what speed does it take off?
   (b) Kreyszig 9th edition Problem Set 1.1, problem 19 = Kreyszig 8th
       edition Problem Set 1.1, problem 26
   (c) Kreyszig 9th Edition Section 1.3, examples 2, 4, 5.
   (d) Kreyszig 9th Edition Problem Set 1.3, problems 25, 28, 29 (Hint: use
       the forms of the solutions of examples 2 and 4 of Section 1.2).
5. (Geometric method) Kreyszig 9th Edition Problem Set 1.2, problems 4, 8,
   12, 13.
6. (Solving Degree 1 ODEs) Kreyszig 9th Edition Problem Set 1.3, problems
   5, 7, 10, 12, 14.




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