FINAL EXAM - EMT 201 - Engineering Math 1

AREAS OF CONCENTRATION                EMT 201         FINAL EXAM       
 ENGINEERING MATHEMATICS 1        FIRST SEMESTER 2013/2014                        

Due to the wide coverage of our course EMT 201 I advise to concentrate on the following exercises. Similar exercises will be coming out in the final exam.

1. A tank contains 234 liters of water. A bitter lemon solution containing 5 kg/liter of sugar enters the tank at the rate of 6 liters/min and runs out at 4 liters/min. The tank has a paddle that keeps stirring to keep the mixture uniform. Find the amount of sugar in the tank after 30 minutes. Solve by ODE method.

2. A student deposited N100000.00 at an annual rate of 8% compounded continuously, how long will it take the amount to double in value? Solve by a) ODE              b) Laplace

3. Solve                the first order linear DE                          a) y’ – 6y =12.                 b) y’ + 5xy = 10x.

4. How much will be left after 500 years for a radioactive elements carbon 14 which has a half life of 5750 years if the initial amount is 50 grams? Solve by ODE and Laplace transform methods.

5. Solve the equation y” +y’ –6y = e ^4x by a) undetermined coefficient method b) variation of parameters

  

6. A university canteen serves a cup of tea at 86   to an Engineering student. After 2 minutes, the tea has cooled to 72 . If the canteen temperature is 24 , how many minutes that the student must wait to cool the tea to 51  Use Newton’s law of cooling. Solve by ODE method.

7.  Solve the initial value DE          y’ – 3y=0,   y (0) =1,   find the value of     y (0.4) using        a) ODE 

b) Laplace    c) Power series         D) Euler’s numerical method with N=4.

8. Find the equation of motion of a  4 kg mass suspended to a coiled spring with k = 100 N/m, initially displaced a distance of 1 meter from equilibrium position, and released with zero velocity and subjected to no damping or external forces. Find                a) Equation of motion by ODE and Laplace methods        b) amplitude      c) angular frequency      d) natural frequency           e) Period             f) graph of the curve

Mathematics Text?Workbook

EMT 201 Students

DR. VICTOR E. ODARVE BSME, MEP-ME

MAED, EDD, PHILIPPINES,SOUTHEAST ASIA

OLD PICTURES STIR MEMORIES

BY Vic Odarve

As he opened the door, an old and gray haired Mang Peter said, “Come, Victor, come inside”. Excited, I slowly walked inside the old house which seemed the same features as fifty years ago when I was playing with Henry, his youngest son. Suddenly the framed picture hanging on the wall caught my attention. Looking nearer to the picture, I recognized my Dad and said,” Ah this is my father when he was young. The rests are his school mates.” “Yes, that was fifty years ago”, said Mang Peter.

Boy Scout of the Philippines

“Come, Victor, come. I am going to show you some old pictures that I have kept for some time”, he said as he opened the old cabinet and got the dusty old albums.  I was surprised to see number of photographs of their family members and some old folks that I used to see in the days of my youth. One of the pictures drew my attention. It was a picture where I was a platoon leader of a scout group ready for jamboree competition to a nearby village Lonoy. We were in complete uniform with a cap on the heads in a scout drill formation. Even in black-and-white, it was easy to tell that we were then kids schooling at Mayana Primary Schools. Scouting has been a part of my life for longer than I can remember. My parents have always told me that I always love scouting life during my primary education. And this old picture confirms!

College days

Upon scanning the pictures, old memories gradually flash back and forth on my minds from the events of the distant past. The traces of memories that appear to disintegrate over time seem real and fresh. Looking back to my childhood days, these memories are beyond forgetting!

“Where is Henry, Mang Peter?” I broke the silence as I noticed two children were playing few meters away from the backyard. Henry was my childhood playmate before our family transferred to the other province.” He is gone already Victor and the two youngsters playing are his two kids. His wife is now in Hongkong”, he said. Some tears in my eyes when he informed that my friend was no longer there. He returned to where he belonged. From dust to dust!

 Chocolate Hills Tour

Old pictures stir our memories and recall the days of our youth. Now, the place is one of my favorite getaway destinations. Going back to the old trail, I can feel like walking through mist and clouds along the mountain ranges, meet all the fairies and magical creatures, and watch the birds doing orchestra along the canopies. Remembering my good old childhood days, it is sort of feeling that cannot be captured on camera and more than the old pictures hanging on the wall. 

There really is no place like home. Old pictures remind me the place and events where I come from; the land of my birth, and with all its diversity, the good and the bad, I would like to go there first over anywhere else in the world.

For us the living, the old photographs keep us remember and stir our memories. It is beyond forgetting!

WHY DO SOME UNIVERSITIES TEACH BETTER?

                                                          BY VIC ODARVE

Some universities teach better than others; hence producing better quality of graduates. People believe that the performance of these universities largely depends on their management style; may a private or federal government funded. Whatever the reasons, these universities that teach better have common denominators on their graduates. They produce a higher level of student achievements. Their graduates are potential to become future great statesmen, world leaders, scientists, etc. Because of their good training and problem thinking skills, graduates are also enjoying widespread job opportunities. There are even multinational companies who give priority for their immediate employment over others. These graduates are extremely well prepared for high skilled-level jobs globally.

CEBU CITY, PHILIPPINES

These institutions establish a name by themselves and students feel proud on them. But what really make these schools teach better? Are there any secrets? It could be. But most educators and parents agree that these universities have shared common denominators, as follows;

1. Highly qualified lecturers/teachers.

This is the main factor that contributes to the student’s academic success or educational quality. Mathematically speaking, knowledge to be imparted from the lecturers is directly proportional to what lecturers are having. With highly qualified lecturers there is a predetermined body of knowledge that the teacher should pass on to the student. These

BOHOL, PHILIPPINES

universities believe that qualifications and competency of the lecturers bear some direct correlation to their work as lecturers.

 

Retention of these lecturers/teachers maintains the good performance of the institution.  Good lecturers foster student mastery of more rigorous and challenging academic contents. They can create a positive learning environment in the classroom. These lecturers allow students to feel comfortable, safe and engaged – something that all students deserve. The academic success of any school depends on the instruction provided by the hands of able, high quality and committed teachers.

2. Strong management support to teachers/lecturers

/students.

These universities do have a strong support to the lecturers as well as students by having seminars, upgrading activities, incentives, and other forms of relevant enrichments.

Some do have programs on students such as allowing them to spend time at a clinic, establishments, or school to observe the work of a professional in the field. In most cases the students may participate in the work in addition to field trips and on the job training.

3. Sufficient and modern laboratory facilities

These universities do have better and updated laboratory equipments and apparatus to meet the advancement of science and technology. Hands- on- training develops student skills and first -hand knowledge application from the classroom lectures.

Students can conduct experiments that replicate or illustrate a scientific principle introduced in the course. Laboratory experiments are important in courses such as Physics, acoustics, thermodynamics, and mechanics. Laboratory sections usually augment lectures or discussions in the classrooms. Speech laboratories allow students to listen to audiotapes or use other interactive forms of instruction. These laboratories can provide necessary training for students’ creativity, insight, and analytical skills

4. Offer competitive salaries.

These universities offer attractive salaries to the lecturers. Good salaries tend to attract more competent teachers. The managements believe that, with good salaries, lecturers would stay long at the university, meet the cost of living, bring contentment in the teaching profession, and drive motivation in the day to day activities in the classroom.

The management does not focus too much on monetary profit.

5. Good working environment.

Good performing schools support their lecturers as well as to the students by providing good working environment. School management provided basic amenities to teachers and students within the university campus.

Universities policy guidelines provide protection for lecturers and students on problems such as violence and crime, and alcohol, drug, and sexual abuse. These schools have also introduced policies aimed at eliminating the widespread problem of hard liquor drinking, and smoking inside the school premises.

Universities with the above features teach the students better; hence producing world class graduates. In contrast, low performing schools do not give much attention to the above schools’ environments.

LEARNING TO LIE AT INTERNATIONALAIRPORT

LEARNING TO LIE AT INTERNATIONAL AIRPORT

By Vic Odarve

Sometimes a little lying at airport works! Jonathan observes that religious personalities like evangelists, pastors, priests, nuns, sisters and brothers of Christian congregations are less likely interrogated during inspections at the airport.

International Airport

After the snake like cordoned queuing in the immigration checkpoint inside the international airport, Jonathan was told to replace his blue card with a yellow card in a nearby clinic. So he did! With only few people inside the clinic office, Jonathan immediately handed his blue card to one of the officer and said” Good day Sir, can I change this one to a yellow card”. “Your passport, visa, and valid ID please!” the officer replied. He complied. After 5 minutes, the officer asked” You are a foreigner, what are you doing here in Nigeria?” “Am a missionary here working with Faith Ministry in Port Harcourt,

Passengers waiting area

Rivers State” Jonathan said with a smile. “So you are a priest” the officer said. Thinking for a while, he said, “Ah…..ah…yes Sir”. The officer looked please and seemed very courteous. Then silence for a few minutes! The officer fixed his signature and handed back the documents. Then Jonathan said,” Thank you very much, God bless you all”. Then the officer and his fellow workers said in chorus” Thank you, Father, Amen”.

Then Jonathan went to the domestic airport for another flight. This time he was met by a Rev. Sister. After queuing for almost an hour in a baggage and weighing stations, Jonathan was again called up by

African travelers

one of the officer to finally check and confirm his baggage before transporting to a waiting cart nearby.” Come here, show me your baggage and let me inspect what’s inside!", the officer said. Sensing that the baggage would be opened again for inspection, he pointed to Reverend Sister as the owner. The sister was few meters away. She was in religious attire! “Okay”, the officer said. No inspection was done. The baggage was actually his. He was again lying! Lying worked!

Actually Jonathan is not a priest. He really owns the baggage. He is a mere employee in one of the great school in Nigeria. Outright lying works! A little deception is needed! While lying can leave us indelible torture in our conscience but the same goes for being too honest and open. Why? Telling the truth may entail too much delay in interrogation or may end with solicitation. Remember the airport greeting “Do you have something for me?”

Lying is hurting us. God hates lying. Bible says in Colossians 3:9-10, NIV. "Do not lie to each other, since you have taken off your old self with its practices and have put on the new self, which is being renewed in knowledge in the image of its Creator." Colossians 3:9-10, NIV

. "The Lord detests lying lips, but He delights in men who are truthful." Proverbs 12:22, NIV

Though lying is not considered to be the right thing to do, sometimes it produces favorable result as what Jonathan did.

Lying also happened in the biblical history. Facing a horrible evil, Hebrew midwives lie to the Egyptian Pharaoh and save the lives of many newborn baby. Read the passages in Exodus 1:15-22 NIV, as follows;

15 Then the king of Egypt gave orders to the Hebrew midwives - one of whom was called Shiprah and the other Puah -

16 that when they attended Hebrew women who were on the birthstool and saw that it was a boy, they were to kill it, but if it was a girl they were to let it live.

17 But the midwives feared God and did not do as the king of Egypt commanded but let the children live.

18 The king called the midwives and said, "Why have you acted like that and let the children live?"

19 The midwives replied, "Because the Hebrew women are not like the Egyptian women. They are vigorous and give birth even before a midwife arrives."

20 God blessed the midwives, and the people increased and became even more numerous.

21 Because the midwives revered God, he made them mothers of families.

22 Pharaoh then gave this order to all the people: "Every infant boy born to the Hebrews must be thrown into the Nile, but every girl may live."

That’s it how my friend Jonathan has learned to lie at the airport! And lying at airport works!