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- MTH322: Real Analysis II (Fall 2021)
- differentiation, the exponential and logarithmic function, the trigonometric functions. **Series of functi... - Define pointwise convergence of sequence of function. - Define uniform convergence of sequence of function. - Define pointwise convergence of series of function. - Define uniform convergence of series of functi
- MTH424: Convex Analysis (Fall 2020)
- ets, convex functions, Differential of the convex function. Developing ability to study the Hadamard-Hermite... ==Lecture 01=== * Definitions: Interval, convex function, strictly convex function, concave function, strictly concave function * Example of convex & concave functions * By definition, p
- MTH322: Real Analysis II (Spring 2023)
- differentiation, the exponential and logarithmic function, the trigonometric functions. **Series of functi... b]$. If $f_n \to f$ uniformly on $[a,b]$ and each function $f_n$ is continuous on $[a,b]$, then \begin{equat... ll } x\in\mathbb{R}.$$ - Consider a sequence of function $\{E_n(x)\}$ define by $$E_n(x)=1+\frac{x}{1!}+\f... he interval $[-A,A]$, where $A>0$. - Consider a function $E:\mathbb{R} \to \mathbb{R}$ defined by $E'(x)=E
- MTH321: Real Analysis I (Spring 2023)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis 1
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis I (Fall 2015)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis I (Fall 2018)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis I (Fall 2019)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis I (Fall 2021)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis I (Fall 2022)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis 1
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis 1 (Spring 2015)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH321: Real Analysis I (Spring 2020)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH604: Fixed Point Theory and Applications (Spring 2021)
- of $x_0$ under $F$, where $F$ is some real valued function. - Draw the orbit of $2$ under $\exp(x)$, $x\in \mathbb{R}$. - Let $F:E\to \mathbb{R}$ be a function. Then prove that $p$ is fixed point of $F$ iff $p... g and neutral fixed point theorem. - Consider a function $f(x)=x^2-1$. Find its fixed points and also find... point. - Define orbit of the point $x_0$ under function $f$. - Consider $C(x)=\cos (x)$. Draw the cobwe
- MTH604: Fixed Point Theory and Applications
- d point with example. * Find fixed point of the function $f(x)=x^2-3x+4$. * Define Lipschitzian. * Def... ermediate value theorem. * Give an example of a function which don't satisfy intermediate value theorem. ... nt. * Find the nature of the fixed point of the function $F(x)=\cos x$ in the interval $[0,\frac{\pi}{2}]$. * Find fixed point of the function $F(x)=x-x^2$ and determine its nature. * State