By C. F. Chan Man, D. De Kee, P. N. Kaloni

ISBN-10: 9812382917

ISBN-13: 9789812382917

ISBN-10: 9812564837

ISBN-13: 9789812564832

This can be a mathematical textual content compatible for college kids of engineering and technological know-how who're on the 3rd 12 months undergraduate point or past. it's a publication of acceptable arithmetic. It avoids the method of directory basically the concepts, via a couple of examples, with no explaining why the ideas paintings. therefore, it offers not just the information 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 by way of their proofs. The authors' objective is to assist scholars increase an figuring out of arithmetic and its functions. they've got kept away from utilizing clichés like "it is clear" and "it may be shown", that could be actual in simple terms to a mature mathematician. frequently, the authors were beneficiant in writing down the entire steps in fixing the instance problems.

The booklet includes ten chapters. every one bankruptcy includes numerous solved difficulties clarifying the brought recommendations. the various examples are taken from the hot literature and serve to demonstrate the purposes in quite a few fields of engineering and technological know-how. on the finish of every bankruptcy, there are task issues of degrees of hassle. an inventory of references is supplied on the finish of the book.

This ebook is the fabricated from a detailed collaboration among mathematicians and an engineer. The engineer has been useful in pinpointing the issues which engineering scholars come upon in books written through mathematicians.

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**Sample text**

Examples of first-order differential equations are separable equations, exact differential equations, linear differential equations, homogeneous linear equations, etc. For each of these types, there exists a known, standardized, procedure to arrive at a solution. 10, we summarize the approach, leading to the solution of several of the types of ordinary differential equations encountered in practice. 19, we look at the modeling problem. 10-2) N(x, y) Equations of this type occur in problems dealing with orthogonal trajectories, growth, decay, and chemical reactions.

6-10) we essentially have two equations involving three variables. We choose the only independent variable to be x. 6-1 la, b) form a system of two algebraic equations involving two unknowns ^- and ^—. 6-12c) o &u v y ' 3y 9u Thus for ^— and ^— to exist, the Jacobian J must not vanish. 7-4) becomes xH+y|+udl=nf(x'y'u) (L7-5) 22 ADVANCED MATHEMATICS -\ * Note that we substitute (= x) etc. 7-4) before setting a = 1, otherwise we would be trying to differentiate by a constant. 7-5) is known as Euler's theorem.

7-4) before setting a = 1, otherwise we would be trying to differentiate by a constant. 7-5) is known as Euler's theorem. 7-5) is x ^ + y ^ +u^- f (x, y, u) = n ( n - 1) ... 7-6) Taylor's Theorem Taylor's theorem for functions of one variable can be extended to functions of several variables. For simplicity we give the formula for two independent variables. f(x0+h,y0+k) = f(x0,y0) + {h^ + k | } + l j h 2 g + 2 h k ^ + k 2 g j + .. + _L (h» ^L + (n\ h n-l k __lL_ + + (n) hn-r kr _ 3 ^ _ + ... 7-7) The remainder term Rn is given by R = n __L- h n+1 ^—I + hn k 1-JL + (n+1)!

### Advanced Mathematics for Engineering and Science by C. F. Chan Man, D. De Kee, P. N. Kaloni

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