Tensor Algebra

Defines what a tensor is and shows its attributes. Please note the submission dates of the homework assignments. No lateness in submission allowed.

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We will need to arrange one extra class in the next two weeks in order to complete the section. A class test is for the week of April 4.

Questions & Answers for First Test

The first test will be based on the questions answered here. They will likely come in the form of objective questions covering the same scope.

You are expected to practice these and let me know if there are things you still do  not understand by posting specific questions below.

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Please endeavour to discuss with others and make an effort before posting a question. After a good effort, all questions are welcomed.

Welcome Address to the Set of 2020

It is my duty and joy to welcome you, the class of 2020, to the University of Lagos. It is not an easy thing to get into this University – especially to be one of the new students at our Engineering faculty. There are several reasons to be proud. The competition to be here is as stiff as it is to enter any other university in the world! Of course, there are several of you who may envy your colleagues that have been able to “escape” from Nigeria with our difficult infrastructural challenges and get to places where things are easier. I will still want you to congratulate yourselves on your achievement and tell you some reasons why you still can eke out a bright future for yourself.

Akinsete, Awojobi, Adekola, etc. were some of the big names that arrested my ears 42 years ago when I was in your situation. At that time, this same building was the most wonderful large building I had ever seen in my life! Those people were the embodiment of knowledge and they dished it out to us as we marveled! I still remember Professor Awojobi, then just 36 years old, teaching us Engineering Graphics. Students from other faculties would sometimes like to come and peep just to hear him talk!

A lot of waters have passed under the bridge since my time as an undergraduate. Our roles as lecturer and professors have changed tremendously. It is important for you to be fully aware of this and adjust well to make the best of your time here. You are at the university of Lagos in two senses: Spatially and temporally. The spatial aspect is more immediate because the environment is the most important thing to our senses. There are the buildings, the lecturers, the classes, and of course your classmates. You may be surprised to hear me say that the most important people here are NOT your lecturers! Who then are more important? Your classmates, roommates, colleagues from other faculties and many others that are your companions as you try to make sense out of your place in your nation and the difference you can make! Of course, your lecturers are important! But, unlike in my days, we are no longer the storehouses of knowledge! The Internet has deposed us! You can check now if what we are teaching you is up to standard! In fact, you can, by virtue of modern communications facilities, reach the same kind of information available to every other student in the world!

Why are then then paying us to be here, you may ask? We are your coaches. We are more experienced than you are and can guide you. As we do so, you will be fully engaged in ideas sharing with your mates. That is one of the great reasons why you are lucky to be at the University of Lagos. Our Engineering is difficult to enter. Your papers must all be at one sitting and they must include Further Maths! Not easy! But that has selected for you, some of the most competitive group of students you will ever meet! You may have been a local champion in your old school where mommy and daddy got you spoon-fed and provided a lot of help to keep you ahead. At Unilag, you will have to struggle harder, longer and more intently as your neighbor was also a prodigy like you! Together, you will navigate the worlds of engineering and other interests that may contribute to making you the kind of person that can make a difference to your family, your nation.

In the temporal aspect therefore, you can see that you are passing through the most impressionable part of your lives.

I want you to be ambitious. One of the biggest problems of the African mind is the absence of serious ambition. Once a Naija man can be a little better than his neighbor, he appears satisfied! If there is no electricity, and you get a small noise maker that helps you to watch Manchester United, you are already in heaven! You seem to forget that the same electricity is available to young people in Singapore 24 hours a day! And that there is absolutely no reason why Enyimba, the people’s Elephant, cannot be more popular than Manchester United! What do they have? Football grass fields, one ball, 22 men and hundreds of thousands of passionate fans! With some clever marketing, this nets them more money than Nigeria’s oil in its most comfortable price regimes, can get Nigeria. More depressing is that the City State of Singapore, smaller in population and size than Lagos, can actually consume over 60% of Nigeria’s oil! That is the meaning of industrialization! It is lack of ambition that will cause a Minister of Aviation to steal two jeeps! Two jeeps! Even for all their rapacity, our thieves are not sufficiently ambitious! Why, for example, cannot the Minister of Aviation ensure than Nigeria can buy 100 of the latest wide body jets such as A380 of B777 and then steal two of them at the cost of nearly 1 billion dollars each! But once he/she can drive two jeeps in a convoy and use sirens to chase others from the road, even if they cannot comfortably get to where they are going, they are already satisfied!

Remember that Bill Gates, Steve Jobs, MarkProtea meeting Zuckerberg, etc., were impressionable young people when they created the future out of their big ambitions! Be more ambitious about building the future. If, for example, you are an Aristo and have access to more money than you need, do not think that joining a cult is the thing to do! Be more ambitious! Cause your money to provide 50 Raspberry Pis for your classmates and begin to competitively build projects that can control equipment and you can later market and make even more money! Internet is replete with projects that you can order parts to do that can mop up all the time you have. If you don’t have a lot of money, you have to think even harder! The futures belongs to the hardest thinkers!

Another problem with we Africans is the level of noise we can tolerate. In fact, my time in Canada as a postgraduate student convinced me that we are all deaf here! Those people only talk in whispers while we keep shouting. It appears that students here cannot have an intellectual feast. Only loud feasts are allowed. Of course, boys will be boys! I grant you the need to unwind once in a while. Yet, the state of permanent noisemaking to the detriment of your health, rest and tranquility; it is something to be avoided because will not help you to think!

And, think, we must. The nation is broke! Oil prices are low. In fact, some of your parents and sponsors may struggle this year! Yet, you are lucky to live in these interesting times. It is in these times that Nigeria will finally get rid of its dependency on crude oil. Crude oil, crude cassava, crude mango, crude exports and crude anything has not, cannot, will not make any nation great. What contributes to the development of any people is the addition of value. That is the primary calling of an engineer. The surveyors are part of the people that will engineer the future that is why in Unilag, it is part of Engineering. Every problem you meet, discuss with your mates, not how best to complain about it, but whether an idea that can make its solution contribute to our progress cannot be brought out! Then you are thinking like an engineer!

I welcome you to the Faculty of Engineering, University of Lagos. I am proud to be the dean of our faculty as you enter our university. It is my desire that the hopes and aspirations that made your parents invest in your education will be met and surpassed. It is my prayer that Nigeria will become a better place because of the education and human development that will be yours here.