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- MTH604: Fixed Point Theory and Applications (Spring 2020)
- ove Banach contraction principle. - Let $(X,d)$ be a complete metric space and $T:X\to X$ be a mapping such that for some integer $m$, $T^m=\underbrace ... - State extreme value theorem. - Let $(X,d)$ be a compact metric space and $T:X\to X$ be a contractive mapping. Then prove that $T$ has unique fixed
- MTH604: Fixed Point Theory and Applications (Fall 2022)
- ve Banach contraction principle. - Let $(X,d)$ be a metric space and $F:X\to X$ be a contration, then prove that $\{ F^n(x)\}$ is Cauchy sequence. - Let $(X,d)$ be a metric space and $F:X\to X$ be a contration, then prove that $\{d(F^m(x),F^n(x) \leq \frac{L^n}{1-L
- MTH321: Real Analysis I (Spring 2023)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... }_{n}} \right\}$ and $\left\{ {{t}_{n}} \right\}$ be two convergent sequences such that $\underset{n\t... inuous, but the converse is not true. - Let $f$ be defined on $\left[ a,b \right]$ and it is differe... if ${f}'(x)$ exist, then ${f}'(x)=0$. - Let $f$ be continuous on $[a,b]$and differentiable on $(a,b
- MTH322: Real Analysis II (Spring 2023)
- eq 1 \hbox{ and } x\in [a,b].$$ - Let $\{f_n\}$ be a sequence of functions, such that $\lim\limits_{... _n \quad \hbox{for all}\,\, n.$ - Let $\{f_n\}$ be a sequence of functions defined on $[a,b]$. If $f... /HTML> ====Resources for midterm ==== There will be two questions having three parts each. First part of each question will be any definitions, second part will be from questio
- MCQs or Short Questions @atiq:sp15-mth321
- need to find the answer them self. This page will be updated occasionally and new MCQs or short question will be posted here. - A number which is neither even ... al numbers is countable? - A set $A$ is said to be countable if there exists a function $f:A\to \mat... None of these - A sequence $\{s_n\}$ is said to be bounded if * (A) there exists number $\lambd
- MTH251: Set Topology
- ===== At the end of this course the students will be able to understand the theory of metric spaces an... en in correct mathematical English. Students will be able to devise, organize and present brief soluti... their overall mathematical development. They will be improving such skills as mathematical writing and... the relative topology of $A=\{c,d\}$. * Let $A$ be a subset of topological space $X$. Then prove tha
- MTH321: Real Analysis I (Fall 2021)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v... m. * 2.23- Suppose that $\{x_n\}$ and $\{y_n\}$ be two convergent sequences such that $\lim\limits_{
- MTH321: Real Analysis I (Spring 2020)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v... m. * 2.23- Suppose that $\{x_n\}$ and $\{y_n\}$ be two convergent sequences such that $\lim\limits_{
- MTH322: Real Analysis II (Fall 2021)
- on an interval containing $0$. - Let $\{f_n\}$ be a sequence of functions, such that $\lim\limits_{... {2n}}{n^{p+1}(1+x^{2n})}, p>0.$ - Let $\{f_n\}$ be a sequence of functions defined on an interval $I... f$ is also continuous at $x_0$. - Let $\{f_n\}$ be a sequence of functions defined on an interval $I... $f$ is also continuous on $I$. - Let $\{f_n\}$ be a sequence of functions defined on $[a,b]$. If $f
- MTH480: Introductory Quantum Mechanics
- s explored to illustrate how physical objects can be viewed both as a particle and a wave. ===== Cou... notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v... } ===== Online Videos ===== * https://youtu.be/2Xqoa5FB8So?si=cb3HD4GwPWLh1pzx * https://youtu
- MATH-510: Topology
- 70%> Some questions are given below. These should be considered as sample and thousands of such questions can be created or constructed but if you understand the ... pology and confinite topology on $X$? - Let $X$ be a non-empty finite set. Then what is the differen... crete and cofinite toplogy on $X$. - Let $\tau$ be a cofinite toplogy on $\mathbb{N}$. Then write an
- MTH103: Exploring Quantitative Skills
- lya's strategy, and sets. The basic concepts will be develop with applications form the real world suc... th equations, rates, ratios, and percentages will be discussed. Students will also explore linear mode... notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v
- MTH604: Fixed Point Theory and Applications
- * Examples related to above notions. * Let $d$ be usual metric on $\mathbb{R}$. Then find open ball... e Banach's contraction principle. * Let $(X,d)$ be a compact metric space with $F:X\to X$ satisfying... has a unique fixed point in $X$. * Let $(X,d)$ be a complete metric space and let $B(x_0, r) = \{x ... xed point in $B(x_0,r)$. * Let $\overline{B_r}$ be the closed ball of radius $r>0$, centred at zero,
- MTH321: Real Analysis I (Fall 2018)
- TML> At the end of this course the students will be able to understand the basic set theoretic statem... notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v
- MTH321: Real Analysis I (Fall 2019)
- ck}} At the end of this course the students will be able to understand the basic set theoretic statem... notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone. It can be downloaded from [[:Software]] section or a user v