MathCity.org

Chapter 03 - Limits and Continuity

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:57 +0000

Chapter 03 - Limits and Continuity * Limit of the function, examples and definition * Theorem: Suppose (i) $(X,{d_x})$ and $(Y,{d_y})$ be two metric spaces (ii) $E\subset X$ (iii) $f:E\to Y$ i.e. f maps E into X (iv) p is the limit point of E. Then $\lim_{x\to p} f(x)=q$ iff $\lim_{n\to\infty}f(p_n)=q$ for every sequence {$p_n$} in E such that ${p_n}\ne p$$\lim_{n\to\infty}{p_n}=p$$\lim_{x\to c}f(x)$$c\in G$$\lim_{x\to c}f(x)=l$$\varepsilon$$\delta>0$$|f(t)-f(s)|<\varepsilon$$\left\{x:|x-c|…

Real Analysis: Short Questions and MCQs

anonymous@undisclosed.example.com (Anonymous) — Mon, 03 Apr 2023 04:06:26 +0000

Real Analysis: Short Questions and MCQs We are going to add short questions and MCQs for Real Analysis. The subject is similar to calculus but little bit more abstract. This is a compulsory subject in MSc and BS Mathematics in most of the universities of Pakistan. The author of this page is Dr. $\left\{\frac{1}{n+1} \right\}$$\left\{\frac{n+2}{n+1} \right\}$$\{x_n\}$$\{y_n\}$$\lim_{n\to\infty z_n}$$z_n=x_n-2y_n$$\{x_n\}$$\{y_n\}$$\lim_{n\to\infty z_n}$$x_n=2y_n-3z_n$$(1,2)$$\left(\frac{1}{2},\fr…

Fundamental of Complex Analysis: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:41 +0000

Fundamental of Complex Analysis: Viewer Solutions of some exercises from Fundamental of Complex Analysis written by Dr. M. Iqbal and published by Ilmi Kitab Khana, Lahore- PAKISTAN. These are handwritten notes by Prof.(Rtd) Muhammad Saleem. You can also download PDF of solutions from this page.

Chapter 04 - Differentiation

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:57 +0000

Chapter 04 - Differentiation * Derivative of a function * Theorem: Let f be defined on [a,b], if f is differentiable at a point $x\in [a,b]$, then f is continuous at x. (Differentiability implies continuity) * Theorem (derivative of sum, product and quotient of two functions)$x\in [a,b]$$f'(x)$$f'(x)=0$$\mathbb{R}^k$$\underline{f}$$x\in (a,b)$$\left|\underline{f}(b)-\underline{f}(a)\right|\le (b-a)\left|\underline{f'}(x)\right|$

Syllabus for PU

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:16 +0000

Syllabus for PU Syllabus and scheme of studies for Regular/Private students doing MSc Mathematics from University of the Punjab, Lahore. 2 years M.Sc Mathematics programme consists of two parts namely Part-I and Part II. The regulation, Syllabi and Courses of Reading for the M.Sc. (Mathematics) Part-I and Part-II (Regular Scheme) are given below.

Preparation Guide

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:44 +0000

Preparation Guide This guide is made by Mr. Anwar Khan, PhD. We are very thankful to him for sharing. This guide is helpful to prepare papers for MSc Mathematics (annual system) from University of Sargodha. Part 1 1. REAL ANAYSIS * Real Analysis (Notes by Syed Gul Shah) * Chapter # 08 sequences and series of Mathematical Method by SM Yousaf (solutions are available $z= f(x,y)$

Number Theory by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Tue, 11 May 2021 11:51:22 +0000

Number Theory by Ms. Iqra Liaqat [Number Theory by Ms. Iqra Liaqat] Notes of number theory provided Ms. Iqra Liaqat is a very good addition in the MSc notes section. We are actually quite grateful to her for giving these notes and likes her encouragement to distribute these notes on MathCity.org Name

Mathematical Method by Khalid Latif Mir (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Sat, 23 Dec 2023 16:48:39 +0000

Mathematical Method by Khalid Latif Mir (Solutions) [Mathematical Method by Khalid Latif Mir (Solutions)] We are very thankful to Prof. Fazal Abbas Sajid for sharing these solutions. Problems & Methods Mathematical Method by Khalid Latif Mir is a famous book taught in different universities of the Pakistan at BS and Master level. On this page, we have added the solutions of the exercises of the book. The solutions of Chapter 06: The Laplace Transform and its Applications is written by Marrium …

Targets

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:43 +0000

Targets Here we have listed the notes for MSc or BS Mathematics, which will be published on MathCity.org. We are working hard to find these notes. Whenever we found these notes we will put them on our website. Here are our targets. * Fluid Mechanics

Syllabus for UoS (Private only)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:15 +0000

Syllabus for UoS (Private only) Syllabus and scheme of studies for private students doing MSc Mathematics from University of Sargodha, Sargodha. The syllabus has been changed and few optional subjects has been dropped. Please be alert --- 2017/08/25 17:05