By Shiferaw Berhanu (Editor), et al
The papers during this quantity hide many vital themes of present curiosity in partial differential equations and several other complicated variables. a global staff of recognized mathematicians has contributed unique learn articles on different subject matters equivalent to the geometry of advanced manifolds, the suggest curvature equation, formal strategies of singular partial differential equations, and intricate vector fields. the cloth during this quantity turns out to be useful for graduate scholars and researchers drawn to partial differential equations and several other complicated variables. Readership Graduate scholars and examine mathematicians attracted to partial differential equations and features in numerous complicated variables
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Additional resources for Recent Progress on Some Problems in Several Complex Variables and Partial Differential Equations
Example: The function f(x) = (x + 1)/x is neither even nor odd : f(– x) = ((_ x) + 1)/(_ x) = 1 _ 1/x = (x _ 1)/x which is not equal to f(x) and is not equal to – f(x) either. CHAPTER 2 – limits LIMITS AND CONTINUITY: A very important concept in Calculus is that of the limit of a function: if f(x) is a function of x, what happens to the value of the function y as x approaches some number? For example, if f(x) = x2 + 3, what is the value of y = f(x) as x approaches 5? 9001 As x approaches 5, the value of y = f(x) approaches 52 + 3 = 28.
Interchanging x and y, we obtain x = y2. Solving for y, we obtain two solutions: positive and negative square roots of x. That is, y = + Öx or y = – Öx, for all x ³ 0. Since for every x there are two different y, this is not a function. Therefore, there is no inverse function for h(x) = x2. Exercises: Find the inverse function f –1(x) if it exists for the following functions: 1. f(x) = 3x 2. f(x) = 4x + 1 3. f(x) = 5 + 2x 4. f(x) = 4(x + 1) 5. f(x) = (1/2)(6x – 3) 6. f(x) = (3x + 5) ¸ 7 7. f(x) = (1/2)(x – 2) + 2 8.
6. Trigonometric functions: sin x, cos x, tan x, cot x, sec x, csc x. SYMMETRY, EVEN AND ODD FUNCTIONS: A function f(x) is called an even function if exchanging – x for x does not change the function. That is, f(– x) = f(x) for all x in the domain of the function. A function f(x) is called an odd function if exchanging – x for x changes the sign of the function. That is, f(– x) = – f(x) for all x in the domain of the function. Examples: If f(x) = x2, then f(– x) = (– x)2 which is the same as f(x) = x2.
Recent Progress on Some Problems in Several Complex Variables and Partial Differential Equations by Shiferaw Berhanu (Editor), et al