Document Sample

```					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.

2

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 54 posted: 4/30/2010 language: German pages: 2