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.

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

Fall 2009
Assignment # 1 Total Marks: 15
Due Date: 21/10/2009


Objectives:
To asses students’ knowledge of the subject and to motivate them towards conceptual knowledge and practical application of the subject.

Instructions

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Question No.1 (5)

Which theory of communication do you prefer from three theories of communication present in your course and why?

Question No.2

(a)

Describe the traits of a good communicator. (5)

(b)

What is the role of proximity and artifacts in non verbal communication? (5)

Mr. A purchased some grocery items from a departmental store. At the time of payment, he offered his credit card to the seller. The seller allowed Mr. A to leave with the goods. Why? Has Mr. A made the final payment?

Ans.

As Mr. A gives the credit card to the seller, he gets the payment from the bank after verifying the card and allow Mr. A to leave with things. But Mr. A has not paid the final payment as he is using the credit card and bank has paid the payment on his behalf at this time. Final payment will be done when Mr. A paid the credit amount to the bank.

Analyze the following transactions and fill the boxes given below in front of each transaction with appropriate answers.

An example is also given in Sr. No. 1 for reference and guidance.

Sr. No


Transactions


Account to be Debited


Account to be Credited


Increase or decrease (affect on accounts due to transactions)

1


Mr. A invested in business Rs.50,000




Cash




Mr. A’s Capital


Increase in asset

Increase in Owner’s Equity

2


Purchased furniture for cash Rs.15,000 for office use






?






?






?



3


Paid salaries of Rs.4,000 to office staff




?






?






?



4


Received commission on sale of goods worth Rs.1,000




?






?






?



5


Received cash of Rs.1,000 from Mr.Bilal who owed him Rs. 2,000 for last 30 days on account of goods sold.




?






?






?

Maximum Marks: 15

Due Date: Oct 22, 2009

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Evaluate the proposition

For the truth values

P = F, q = T, r = F

(Don’t use truth table)

Formulate the arguments symbolically and test its validity using truth table. Also mention critical row.

If 7 = 6, then you ate banana.

You ate banana.

Where k : 7 = 6
m : You ate banana.

Construct circuit for Boolean expression

PÚ(~PÙQ)