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UNIVERSITY OF ABUJA FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL/ELECTRONIC ENGINEERING FIRST SEMESTER EXAMINATIONS FOR 2023/2024 ACADEMIC SESSION INSTRUCTIONS: FEG311-ENGINEERING MATHEMATICS III TIME: 3 HOURS CREDIT UNITS: 3 ANSWER FIVE QUESTIONS-ALL IN SECTION A, ONE IN SECTION B and ONE IN SECTION C QUESTION 1. (14 marks) a) The three equations SECTION A 2x+3y=11 2x-4y=-24 y=mx+3 Have a common point of intersection. Find the value of m. (Apply matrix algebra to your solution) (5 marks) b) Determine the eigenvectors of the matrix below: 1 -1 -1 2 -1 (9 marks) 0 -1 1 QUESTION 2. (14 marks) a) Prove that L(3) = from first principles (5 marks) b) Determine the inverse Laplace transform of the following 11-34 L (4 marks) st+21-3 7s+5c+13 II. (5 marks) (x+2)(x+1) QUESTION 3. (14 marks) Show that the Fourier series for the periodic function of period 2 defined by: 0 when-<0<0 0<0< f(0)-(sin when is given by cos 29 cos 48 f(0)= 3 cos 60 (3)(5) (5)(7) SECTION B QUESTION 4. (14 marks) a) Find the motion of the mass-spring system corresponding to the given equation and Initial condition y" + 25y=24sin x y(0) 1: y'(0) = 1 (7 marks) b) Verify that y, is a solution to the given equation. Solve the initial value problem y"-y=2e y(0) -1: y'(0) =0; y=xe* (7 marks) 1|Page

UNIVERSITY OF ABUJA FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL/ELECTRONIC ENGINEERING FIRST SEMESTER EXAMINATIONS FOR 2023/2024 ACADEMIC SESSION INSTRUCTIONS: FEG311-ENGINEERING MATHEMATICS III TIME: 3 HOURS CREDIT UNITS: 3 ANSWER FIVE QUESTIONS-ALL IN SECTION A, ONE IN SECTION B and ONE IN SECTION C QUESTION 1. (14 marks) a) The three equations SECTION A 2x+3y=11 2x-4y=-24 y=mx+3 Have a common point of intersection. Find the value of m. (Apply matrix algebra to your solution) (5 marks) b) Determine the eigenvectors of the matrix below: 1 -1 -1 2 -1 (9 marks) 0 -1 1 QUESTION 2. (14 marks) a) Prove that L(3) = from first principles (5 marks) b) Determine the inverse Laplace transform of the following 11-34 L (4 marks) st+21-3 7s+5c+13 II. (5 marks) (x+2)(x+1) QUESTION 3. (14 marks) Show that the Fourier series for the periodic function of period 2 defined by: 0 when-<0<0 0<0< f(0)-(sin when is given by cos 29 cos 48 f(0)= 3 cos 60 (3)(5) (5)(7) SECTION B QUESTION 4. (14 marks) a) Find the motion of the mass-spring system corresponding to the given equation and Initial condition y" + 25y=24sin x y(0) 1: y'(0) = 1 (7 marks) b) Verify that y, is a solution to the given equation. Solve the initial value problem y"-y=2e y(0) -1: y'(0) =0; y=xe* (7 marks) 1|Page

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.3DP
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UNIVERSITY OF ABUJA FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL/ELECTRONIC ENGINEERING FIRST SEMESTER EXAMINATIONS FOR 2023/2024 ACADEMIC SESSION INSTRUCTIONS: FEG311-ENGINEERING MATHEMATICS III TIME: 3 HOURS CREDIT UNITS: 3 ANSWER FIVE QUESTIONS-ALL IN SECTION A, ONE IN SECTION B and ONE IN SECTION C QUESTION 1. (14 marks) a) The three equations SECTION A 2x+3y=11 2x-4y=-24 y=mx+3 Have a common point of intersection. Find the value of m. (Apply matrix algebra to your solution) (5 marks) b) Determine the eigenvectors of the matrix below: 1 -1 -1 2 -1 (9 marks) 0 -1 1 QUESTION 2. (14 marks) a) Prove that L(3) = from first principles (5 marks) b) Determine the inverse Laplace transform of the following 11-34 L (4 marks) st+21-3 7s+5c+13 II. (5 marks) (x+2)(x+1) QUESTION 3. (14 marks) Show that the Fourier series for the periodic function of period 2 defined by: 0 when-<0<0 0<0< f(0)-(sin when is given by cos 29 cos 48 f(0)= 3 cos 60 (3)(5) (5)(7) SECTION B QUESTION 4. (14 marks) a) Find the motion of the mass-spring system corresponding to the given equation and Initial condition y" + 25y=24sin x y(0) 1: y'(0) = 1 (7 marks) b) Verify that y, is a solution to the given equation. Solve the initial value problem y"-y=2e y(0) -1: y'(0) =0; y=xe* (7 marks) 1|Page
Transcribed Image Text:UNIVERSITY OF ABUJA FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL/ELECTRONIC ENGINEERING FIRST SEMESTER EXAMINATIONS FOR 2023/2024 ACADEMIC SESSION INSTRUCTIONS: FEG311-ENGINEERING MATHEMATICS III TIME: 3 HOURS CREDIT UNITS: 3 ANSWER FIVE QUESTIONS-ALL IN SECTION A, ONE IN SECTION B and ONE IN SECTION C QUESTION 1. (14 marks) a) The three equations SECTION A 2x+3y=11 2x-4y=-24 y=mx+3 Have a common point of intersection. Find the value of m. (Apply matrix algebra to your solution) (5 marks) b) Determine the eigenvectors of the matrix below: 1 -1 -1 2 -1 (9 marks) 0 -1 1 QUESTION 2. (14 marks) a) Prove that L(3) = from first principles (5 marks) b) Determine the inverse Laplace transform of the following 11-34 L (4 marks) st+21-3 7s+5c+13 II. (5 marks) (x+2)(x+1) QUESTION 3. (14 marks) Show that the Fourier series for the periodic function of period 2 defined by: 0 when-<0<0 0<0< f(0)-(sin when is given by cos 29 cos 48 f(0)= 3 cos 60 (3)(5) (5)(7) SECTION B QUESTION 4. (14 marks) a) Find the motion of the mass-spring system corresponding to the given equation and Initial condition y" + 25y=24sin x y(0) 1: y'(0) = 1 (7 marks) b) Verify that y, is a solution to the given equation. Solve the initial value problem y"-y=2e y(0) -1: y'(0) =0; y=xe* (7 marks) 1|Page
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