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 + 4ay3 + 3xy2
2. (Integrals) Compute the following inde¯nite integrals
(a) R xndx
(b) R sin(x)dx
(c) R tan(x)dx
(d) R sec(x)dx
(e) R dx
x2+a2
3. (Solution veri¯cation) State the order of the ODE. Verify that the given
function is a solution (a, b and c are arbitrary constants).
(a) y00 + 2y0 + 10y = 0; y = 4e¡x sin(3x)
(b) y000 = cos(x); y = ¡sin(x) + ax2 + bx + c
1
(c) y0 + 2xy = 0; y = ce¡x2
(d) y0 = 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 o®?
(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
(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 + 4ay3 + 3xy2
2. (Integrals) Compute the following inde¯nite integrals
(a) R xndx
(b) R sin(x)dx
(c) R tan(x)dx
(d) R sec(x)dx
(e) R dx
x2+a2
3. (Solution veri¯cation) State the order of the ODE. Verify that the given
function is a solution (a, b and c are arbitrary constants).
(a) y00 + 2y0 + 10y = 0; y = 4e¡x sin(3x)
(b) y000 = cos(x); y = ¡sin(x) + ax2 + bx + c
1
(c) y0 + 2xy = 0; y = ce¡x2
(d) y0 = 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 o®?
(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
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