**AREAS OF CONCENTRATION EMT 201 FINAL 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 86C to an Engineering student. After 2 minutes, the tea has cooled to 72C. If the canteen temperature is 24C, how many minutes that the student must wait to cool the tea to 51CUse 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

DR. VICTOR E. ODARVE, BSME, MEP-ME, MAED, EDD

Lecturer, Madonna, University, Nigeria, Africa

Mayana, Jagna, Bohol, Philippines, Asia

## Leo Atsikidi Elisha

/ February 24, 2014this is the first time i am commenting on this site, so i want to use this medium to say thank you for making it easy for me to understand Engineering maths. I Pray God continues to strengthen you. God bless u Sir

## vicodar

/ March 1, 2014Thanks for the comments. Let us make use the advance technology so as not left behind with other countries in education.