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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 $E'(x)=E
- MTH321: Real Analysis I (Spring 2023)
- s statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. ... e the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function, prove various theorems about the derivatives of
- MTH424: Convex Analysis (Spring 2025)
- ac{f(x)-f(a)}{x-a}$, where $x>a$ is an increasing function. - If $f_1$ and $f_2$ are convex on $I$, then $... convex and $g$ is increasing, then the composite function $g\circ\ f$ is convex on $I$. - Let $f_i:I\righ... of convex functions converging to a finite limit function $f$ on $I$, then $f$ is convex on $I$. - If $f:... creasing and convex on $I$. - Define log-convex function and prove that if $f$ and $g$ are two log-convex
- 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