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- MTH322: Real Analysis II (Fall 2021)
- e is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock camp... onvergence or divergence. - Suppose that $f\in \mathcal{R}[a,b]$ for every $b\ge a$. Assume that $f(x)... x} \le M$ for every $b\ge a$. - Assume $f\in \mathcal{R}[a,b]$ for every $b\ge a$. If $0\le f(x)\le ... {a}^{\infty }{g\,dx}$. - Suppose that $f,g\in \mathcal{R}[a,b]$ for every $b\ge a$, where $f(x)\ge 0
- MTH322: Real Analysis II (Spring 2023)
- se is offered to BS, Semester VI at Department of Mathematics, COMSATS University Islamabad, Attock camp... estions from Chapter 01** - Suppose that $f\in \mathcal{R}[a,b]$ for every $b\ge a$. Assume that $f(x)... $\int_{a}^{\infty }{f(x)dx}$. - Suppose $f\in \mathcal{R}[a,b]$ for every $b\ge a$ and for every $\va... a}^{\infty }{f\,dx}$ is convergent. - If $f\in \mathcal{R}[a,b]$ for every $b\ge a$ and if $\int\limit
- MTH321: Real Analysis I (Spring 2023)
- ent sequences such that $\underset{n\to \infty }{\mathop{\lim }}\,{{s}_{n}}=\underset{n\to \infty }{\mathop{\lim }}\,{{t}_{n}}=s$. If ${{s}_{n}}<{{u}_{n}}<{{... onal numbers such that $\underset{n\to \infty }{\mathop{\lim }}\,\,{{r}_{n}}=x$. **Questions from Chapt... }}$ is convergent then $\underset{n\to \infty }{\mathop{\lim }}\,{{a}_{n}}=0$ but converse is not true.
- MATH-608: History of Mathematics
- ~~NOTOC~~ ====== MATH-608: History of Mathematics ====== <HTML> <img src="https://dl.dropbox.com/u/64787761/Timeline_of_the_History_of_Mathematics.png" alt="Time line" title="Time line" cla... aplace. <WRAP center round tip 60%> * [[:atiq:math-608:what is mathematics]] * [[https://www.media
- MATH-300: Basic Mathematics for Chemist
- ====== MATH-300: Basic Mathematics for Chemist ====== <WRAP center round box 70%> //Without mathematics the sciences cannot be understood, nor mad... /en.wikipedia.org/wiki/Number * A number is a mathematical object used to count, label, and measure.
- What is Mathematics? @atiq:math-608
- ====== What is Mathematics? ====== {{ :atiq:math-608:what-is-mathematics.jpg?nolink|}} Different people would gave different answers of the above title... too many students of calculus would also say that mathematic is about rules and formulas and impossible
- MATH-510: Topology
- ~~NOTOC~~ ====== MATH-510: Topology ====== <HTML> <img src="../images/Mug_and_Torus_morph.gif" alt="A co... ><br> </HTML> Topology is an important branch of mathematics that studies all the "qualitative" or "dis... Davis, Topology, McGraw-Hill Science/Engineering/Math, 2004. - Seymour Lipschutz, Schaums Outline of... n every set? - Give an example of open set in $\mathbb{R}$ with usual topology, which is not an open i
- MTH424: Convex Analysis (Fall 2020)
- students to be self independent and enhance their mathematical ability by giving them home work and proj... By definition, prove that $f(x)=x$ is convex on $\mathbb{R}$. * By definition, prove that $f(x)=x^2$ is convex on $\mathbb{R}$. ===Lecture 02=== * Prove that every c... ed interval is bounded above. * If $f:[a,b]\to \mathbb{R}$ is convex, then $f$ is bounded above by $\m
- CHEM-501: Basic Mathematics for Chemist
- ====== CHEM-501: Basic Mathematics for Chemist ====== ===== Course contents ===== Introdtuction; Review... /en.wikipedia.org/wiki/Number * A number is a mathematical object used to count, label, and measure. In mathematics, the definition of number has been extende... * http://en.wikipedia.org/wiki/Factorial * In mathematics, the factorial of a non-negative integer n
- MTH251: Set Topology
- Set Topology}} Topology is an important branch of mathematics that studies all the "qualitative" or "dis... r solutions as rigorous proofs written in correct mathematical English. Students will be able to devise,... ply them, but also to continue with their overall mathematical development. They will be improving such skills as mathematical writing and the presentation of rigorous
- MTH604: Fixed Point Theory and Applications (Spring 2021)
- - 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 $p$ is ... of $F(x)-x$. - Prove that $x^2+1$, where $x\in \mathbb{R}$ does not have fixed point. - Show graphically that $\cos x$ has fixed point for $x\in \mathbb{R}$. - Show graphically that $e^x$, $x\in \ma
- MTH322: Real Analysis II (Fall 2018)
- e is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock camp... ine]] NEW ===Online resources=== * https://www.mathsisfun.com/numbers/infinity.html * http://www.sosmath.com/calculus/improper/absconv/absconv.html * http://world.mathigon.org/Sequences * http://www.math.wisc.edu/~p
- MTH322: Real Analysis II (Fall 2019)
- e is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock camp... wer.php}} ===Online resources=== * https://www.mathsisfun.com/numbers/infinity.html * http://www.sosmath.com/calculus/improper/absconv/absconv.html * http://world.mathigon.org/Sequences * http://www.math.wisc.edu/~p
- MTH322: Real Analysis II (Fall 2020)
- e is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock camp... > </HTML> ===Online resources=== * https://www.mathsisfun.com/numbers/infinity.html * http://www.sosmath.com/calculus/improper/absconv/absconv.html * http://world.mathigon.org/Sequences * http://www.math.wisc.edu/~p
- MTH322: Real Analysis II (Spring 2019)
- e is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock camp... wer.php}} ===Online resources=== * https://www.mathsisfun.com/numbers/infinity.html * http://www.sosmath.com/calculus/improper/absconv/absconv.html * http://world.mathigon.org/Sequences * http://www.math.wisc.edu/~p