Engineering Mathematics-III Dr. P.K. Shirvastava

Engineering Mathematics-III Dr. P.K. Shirvastava
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Engineering Mathematics-III Dr. P.K. Shirvastava

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Publisher: Vayu Education
ISBN: 9789383137121
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Contents
1. Partial Differentiation and Partial Differential Equation...................... 1-37 2. Partial Differential Equations............................................................. 38-85 3. Fourier Series....................................................................................86-113 4. Laplace Transformation....................................................................114-152 5. Numerical Techniques. ..................................................................... 153-184 6. Numerical Methods for Solution .
of
Partial Differential Equation. 185-221
Chapter-1
1.1 Functions of Two or More Variables A symbol z which has a definite value for every pair of values of x and y is called a function of two independent variables x and y and is written as z f x, y or x, y 1.2 Limits The function f x, y is said to tend to limit l as x a and y b if and only if the limit l is independent of the path followed by the point x, y as x a and y b and we write lim f x , y l
x y
a b
Or, in circular neighbourhood we define the limit as The function f x, y defined in a region R, is said to tend to the limit l as x a and y b if and only if corresponding to a positive number , another positive number such that
f x , y
l
e for 0 x a 2 y b
for every point x, y in R .