By C. F. Chan Man, D. De Kee, P. N. Kaloni
It is a mathematical textual content compatible for college students of engineering and technological know-how who're on the 3rd yr undergraduate point or past. it's a e-book of appropriate arithmetic. It avoids the strategy of directory simply the recommendations, through a couple of examples, with out explaining why the strategies paintings. hence, it presents not just the knowledge but in addition the know-why. both, the textual content has no longer been written as a ebook of natural arithmetic with a listing of theorems via their proofs. The authors' objective is to aid scholars boost an knowing of arithmetic and its functions. they've got shunned utilizing clichés like "it is clear" and "it should be shown", that may be precise basically to a mature mathematician. ordinarily, the authors were beneficiant in writing down the entire steps in fixing the instance problems.
The booklet contains ten chapters. each one bankruptcy includes numerous solved difficulties clarifying the brought strategies. many of the examples are taken from the new literature and serve to demonstrate the purposes in a number of fields of engineering and technology. on the finish of every bankruptcy, there are task issues of degrees of trouble. an inventory of references is equipped on the finish of the book.
This publication is the made from a detailed collaboration among mathematicians and an engineer. The engineer has been worthy in pinpointing the issues which engineering scholars stumble upon in books written by way of mathematicians.
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Extra info for Advanced Mathematics for Engineering and Science
The average velocity in the tubular reactor is (v z ). The concentration of A is given at the inlet (z = 0) of the reactor by c A and at the outlet (z = L) by c ^ . 16-44) JJ^ We now propose a solution of the form cA = e a z . 16-49) SOLUTIONS BY LAPLACE TRANSFORM Linear differential equations can sometimes be reduced to algebraic equations, which are easier to solve. A way of achieving this is by performing a so called Laplace transform. The Laplace transform L[f(t)] of a function f(t) is defined as L[f(t)] = F(s) = I f(t)e- st dt Jo where the integral is assumed to converge.
The differential df may be regarded as a function of 4 independent variables x, y, dx and dy. Higher differentials d2f, d3f, ... , dnf can also be defined. 5-16d) It can be shown by induction that dnf = ^ (dx)n + f " ) - ^ L _ (dx)11"1 dy + ... + ( n ) -^*- (dx)n-r (dy) r+ ... + ^L ax n I ! 5-18), the right side can be expanded formally as a binomial expansion. 5-22a, b, c, d) again express the chain rule. 5-1. 5-23) We change to polar coordinates (r, 9). 5-24a,b) n , , , 3f , 3f Calculate ^— and — .
The reaction is characterized by the rate expression — ^ = - k c A . The average velocity in the tubular reactor is (v z ). The concentration of A is given at the inlet (z = 0) of the reactor by c A and at the outlet (z = L) by c ^ . 16-44) JJ^ We now propose a solution of the form cA = e a z . 16-49) SOLUTIONS BY LAPLACE TRANSFORM Linear differential equations can sometimes be reduced to algebraic equations, which are easier to solve. A way of achieving this is by performing a so called Laplace transform.
Advanced Mathematics for Engineering and Science by C. F. Chan Man, D. De Kee, P. N. Kaloni