Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 05:16:23 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/notes/advanced-analysis-handwritten-notes Advanced Analysis: Handwritten Notes [Advanced Analysis: Handwritten Notes] These notes are provided by Mr. Anwar Khan. We are really very thankful to Mr. Anwar Khan for providing these notes and appreciates his effort to publish these notes on MathCity.org It covers the complete syllabus of Advanced Analysis paper of MSc Mathematics. See the contents of the notes given below to see the topics covered by these notes. anonymous@undisclosed.example.com (Anonymous) Fri, 14 Apr 2023 17:55:33 +0000 https://www.mathcity.org/notes/advanced-analysis-iqra-liaqat Advance Analysis by Ms. Iqra Liaqat [Advance Analysis by Ms. Iqra Liaqat] These notes are send by Ms. Iqra Liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org Name Advance Analysis Sender Ms. Iqra Liaqat Author $\sigma$ anonymous@undisclosed.example.com (Anonymous) Fri, 21 Mar 2025 15:08:17 +0000 https://www.mathcity.org/notes/affine-and-euclidean-geometry-shahzad-idress Affine and Euclidean Geometry by Shahzad Idress [Affine and Euclidean Geometry by Shahzad Idress] These notes are sent by shahzad-idress. We acknowledged his efforts to published these notes on MathCity.org. These are short notes containing topics related to Affine and Euclidean Geometry. The main sections includes $R^n$ anonymous@undisclosed.example.com (Anonymous) Mon, 24 Jul 2023 10:30:52 +0000 https://www.mathcity.org/notes/algebra-ii-by-syed-sheraz-asghar Algebra II by Syed Sheraz Asghar [Algebra II by Syed Sheraz Asghar] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org * Name: Algebra II * Provider: Mr. Muzammil Tanveer anonymous@undisclosed.example.com (Anonymous) Sun, 10 Dec 2023 14:02:42 +0000 https://www.mathcity.org/notes/classical-mechanics-muhammad-usman-hamid Classical Mechanics by Muhammad Usman Hamid [Classical Mechanics by Muhammad Usman Hamid] Objectives of the course: To provide solid understanding of classical mechanics and enable the students to use this understanding while studying courses on quantum mechanics, statistical mechanics, electromagnetism, fluid dynamics, space-flight dynamics, astrodynamics and continuum mechanics. anonymous@undisclosed.example.com (Anonymous) Mon, 29 Jul 2024 18:38:28 +0000 https://www.mathcity.org/notes/complex-analysis-dr-amir-mahmood Complex Analysis (Easy Notes of Complex Analysis) [Complex Analysis (Easy Notes of Complex Analysis) ] The study of complex numbers, together with their manipulation, derivatives, and other characteristics, is known as complex integration. Contour integration is a technique for analysing specific integrals along pathways in the complex plane in the field of complex analysis mathematics. The complex analytic technique known as the calculus of residues and contour integration are closely linked. anonymous@undisclosed.example.com (Anonymous) Sun, 06 Aug 2023 11:17:51 +0000 https://www.mathcity.org/notes/complex-analysis-iqra-liaqat Complex Analysis (Notes) by Ms. Iqra Liaqat [Notes of Complex Analysis by Ms. Iqra Liaqat] These notes are send by Ms. Iqra Liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org Complex analysis is the study of functions of complex numbers. It is useful in a variety of mathematical fields, such as algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics fields like… anonymous@undisclosed.example.com (Anonymous) Sun, 06 Aug 2023 09:33:02 +0000 https://www.mathcity.org/notes/complex-analysis-m-usman-hamid Complex Analysis by M Usman Hamid [Complex Analysis by M Usman Hamid] We are really very thankful to Muhammad Usman Hamid for providing these notes and appreciates his effort to publish these notes on MathCity.org It covers the one part of the syllabus of Complex Analysis paper of MSc Mathematics. See the contents of the notes given below to see the topics covered by these notes.$$ x^2+4=0, x^2+x+1=0 \text{ and } x^2-2x+3=0 $$$i=\sqrt{-1}$$i^2=-1$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Feb 2025 08:11:42 +0000 https://www.mathcity.org/notes/complex-analysis-quick-review Complex Analysis (Quick Review) [Complex Analysis: Quick Review] These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his efforts to publish these notes on MathCity.org. Important definitions and important results are the part of these notes, these might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.$z_1, z_2 \in S$$S$$v(x,y)$$u(x,y)$$f(z)=u(x,y)+iv(x,y)$$f$$D$$C$$D$… anonymous@undisclosed.example.com (Anonymous) Wed, 26 Jun 2024 18:33:42 +0000 https://www.mathcity.org/notes/computing-tools-for-mathematics-asif-arshad Computing Tools for Mathematics by Asif Arshad [omputing Tools for Mathematics by Asif Arshad] Computing tools for mathematics are algorithms that use computers to solve mathematical issues. They are employed in a number of scientific, technical, industrial, and technological domains where computer is crucial and central. They may assist in creating precise and effective numerical techniques, for instance, to solve physical or biological models. anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 20:30:34 +0000 https://www.mathcity.org/notes/differential-geometry-kaushef_salamat Differential Geometry (Notes) by Ms. Kaushef Salamat [Differential Geometry by Ms. Kaushef Salamat] Differential Geometry is an important field in the mathematical sciences. Usually, this is a compulsory or core subject for BS mathematics students. These notes are send by Ms. Kaushef Salamat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org anonymous@undisclosed.example.com (Anonymous) Sat, 23 Aug 2025 11:29:10 +0000 https://www.mathcity.org/notes/differential-geometry-m-usman-hamid Differential Geometry by M Usman Hamid [Differential Geometry by M Usman Hamid] These notes are initially provided by Mr. Anwar Khan. Later send by many persons. We are really very thankful to all for providing these notes and appreciates their effort to publish these notes on MathCity.org anonymous@undisclosed.example.com (Anonymous) Sat, 23 Aug 2025 11:29:44 +0000 https://www.mathcity.org/notes/differential-geometry-syed-hassan-waqas Differential Geometry by Syed Hassan Waqas [Differential Geometry by Syed Hassan Waqas] In the field of mathematics known as differential geometry, smooth manifolds—also known as smooth shapes and spaces—and their geometry are studied. Investigating the geometric characteristics of curves and surfaces involves the use of the tools of differential and integral calculus, linear algebra, and multilinear algebra. Differential calculus and mathematical analysis are related to differential geometry.… anonymous@undisclosed.example.com (Anonymous) Sat, 23 Aug 2025 11:28:41 +0000 https://www.mathcity.org/notes/elementary-linear-algebra-m-usman-hamid Elementary Linear Algebra by Muhammad Usman Hamid [Elementary Linear Algebra by Muhammad Usman Hamid] Linear Algebra is the study of vectors and linear transformations. The main objective of this course is to help students learn in rigorous manner, the tools and methods essential for studying the solution spaces of problems in mathematics, engineering, the natural sciences and social sciences and develop mathematical skills needed to apply these to the problems arising within their field of st… anonymous@undisclosed.example.com (Anonymous) Sun, 10 Dec 2023 14:05:12 +0000 https://www.mathcity.org/notes/fluid-dynamics-i-m-usman-hamid Fluid Dynamics I by Muhammad Usman Hamid [Fluid Dynamics I by Muhammad Usman Hamid] Explore comprehensive notes on Fluid Dynamics by Muhammad Usman Hamid. Covers fundamental concepts (viscosity, stress fields, continuum), fluid statics, and differential analysis. Special thanks to Mr. Anwar Khan for contributing these resources to MathCity.org. anonymous@undisclosed.example.com (Anonymous) Sun, 03 May 2026 08:26:32 +0000 https://www.mathcity.org/notes/fluid-mechanics-ali-raza Fluid Mechanics by Ali Raza [Fluid Mechanics by Ali Raza] Fluid mechanics is the branch of physics that studies how fluids (liquids, gases, and plasmas) behave and interact with forces and energy. Fluid mechanics has many applications in engineering, geophysics, biology, and other fields. anonymous@undisclosed.example.com (Anonymous) Sat, 27 Jul 2024 16:23:08 +0000 https://www.mathcity.org/notes/fluid-mechanics-i-muzammil-tanveer Fluid Mechanics I by Dr Rao Muzamal Hussain [Fluid Mechanics I by Muzammil Tanveer] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These notes are based on lectures delivered by Mr. Muzammil Hussain at GC University Faisalabad. anonymous@undisclosed.example.com (Anonymous) Mon, 24 Jul 2023 12:45:33 +0000 https://www.mathcity.org/notes/fluid-mechanics-ii-muzammil-tanveer Fluid Mechanics II by Dr Rao Muzamal Hussain [Fluid Mechanics I by Muzammil Tanveer] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These notes are based on lectures delivered by Mr. Muzammil Hussain at GC University Faisalabad. anonymous@undisclosed.example.com (Anonymous) Tue, 29 Aug 2023 06:36:09 +0000 https://www.mathcity.org/notes/fluid-mechanics-m-usman-hamid Fluid Mechanics by Muhammad Usman Hamid [Fluid Mechanics by Muhammad Usman Hamid] We casually look around most things seem to be solids but when one thinks of the oceans, the atmosphere and on out into space it becomes rather obvious that a large portion of the earth surface and of the entire universe is in a fluid state. Therefore, it becomes essential for sciences and engineers to know something about fluid mechanics. anonymous@undisclosed.example.com (Anonymous) Sun, 16 Mar 2025 12:46:08 +0000 https://www.mathcity.org/notes/functional-analysis-by-prof-mumtaz-ahmad Functional Analysis by Prof Mumtaz Ahmad [Functional Analysis by Prof Mumtaz Ahmad] Functional analysis is a subfield of mathematics that deals with vector space theory and linear algebra. It entails researching the connections between roles, things, incidents, actions, and outcomes. The word $l^\infty$$l^\infty$ anonymous@undisclosed.example.com (Anonymous) Wed, 18 Sep 2024 18:11:56 +0000 https://www.mathcity.org/notes/functional-analysis-m-usman-hamid-and-zeeshan-ahmad Functional Analysis by M Usman Hamid and Zeeshan Ahmad [Functional Analysis by M Usman Hamid and Zeeshan Ahmad] These notes are send by Muhammad Usman Hamid and written by Muhammad Usman Hamid and Zeeshan Ahmad. We are really very thankful to him for providing these notes and appreciate his effort to publish these notes on MathCity.org. Usman is dedicated and committed mathematician, who is working very hard for better understanding of mathematics to it readers. anonymous@undisclosed.example.com (Anonymous) Wed, 18 Sep 2024 18:09:17 +0000 https://www.mathcity.org/notes/fuzzy-sets-theory-umar-saeed-bunarai Fuzzy Sets Theory by Umar Saeed Bunarai [Fuzzy Sets Theory by Umar Saeed Bunarai] In the field of mathematics known as fuzzy set theory, sets having varying degrees of membership are studied. This implies that an element can be a member of a set only partially or not at all. In several disciplines, including logic, control, data analysis, and decision-making, fuzzy set theory is used to model uncertainty, vagueness, and imprecision. anonymous@undisclosed.example.com (Anonymous) Tue, 08 Aug 2023 11:56:34 +0000 https://www.mathcity.org/notes/group-theory-important-definitions-and-results Group Theory: Important Definitions and Results [Group Theory: Important Definitions and Results] These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These notes contains important definitions with examples and related theorem, which might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.$G$$a\in G$$\exists$$e\in G$$a\… anonymous@undisclosed.example.com (Anonymous) Wed, 10 Aug 2022 15:31:46 +0000 https://www.mathcity.org/notes/groups-theory-m-iftikhar Group Theory by Mr. Muhammad Iftikhar [Group Theory by Mr. Muhammad Iftikhar] These notes are send by Mr. Muhammad Iftikhar. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Name Lecture Notes on Group Theory Author Mr. Muhammad Iftikhar anonymous@undisclosed.example.com (Anonymous) Tue, 09 Aug 2022 18:28:27 +0000 https://www.mathcity.org/notes/handwritten-notes-real-analysis-asim-marwat Handwritten Notes of Real Analysis by Asim Marwat [Handwritten Notes of Real Analysis by Asim Marwat] Real analysis is a branch of mathematics that analyses how real numbers, sequences and series, and real functions behave. It focuses on real numbers and frequently extends the real line by including positive and negative infinity. Real analysis investigates a number of the properties of real-valued sequences and functions, including convergence, limits, continuity, smoothness, differentiabilit… anonymous@undisclosed.example.com (Anonymous) Sat, 15 Apr 2023 17:26:13 +0000 https://www.mathcity.org/notes/linear-algebra-important-definitions-and-results Linear Algebra: Important Definitions and Results [Linear Algebra: Important Definitions and Results] These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his efforts to publish these notes on MathCity.org. These notes contains important definitions with examples and related theorem, which might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.$V$$n$$n$$V$$W$$V$$A$$A$$A… anonymous@undisclosed.example.com (Anonymous) Wed, 10 Aug 2022 16:49:49 +0000 https://www.mathcity.org/notes/mathematical-method-muzammil-tanveer Mathematical Method by Sir Muhammad Awais Aun [Mathematical Method by Muzammil Tanveer] Mathematical methods are the approaches employed by mathematicians to address issues in mathematics and science. Algebra, functions, relations and associated graphs, calculus, and statistics are examples of mathematical techniques. Through their usage in resolving practical issues, they are applied to modelling. anonymous@undisclosed.example.com (Anonymous) Mon, 17 Apr 2023 09:02:35 +0000 https://www.mathcity.org/notes/mathematical-method-usman-hamid Mathematical Method by Muhammad Usman Hamid [Mathematical Method by Muhammad Usman Hamid] These notes are send by Muhammad Usman Hamid. We acknowledged his efforts to published these notes on MathCity.org. The main objective of this course is to provide the students with a range of mathematical methods that are essential to the solution of advanced problems encountered in the fields of applied physics and engineering. In addition this course is intended to prepare the students with mathematic… anonymous@undisclosed.example.com (Anonymous) Mon, 17 Apr 2023 08:43:53 +0000 https://www.mathcity.org/notes/mathematical-statistics-i-muzammil-tanveer Mathematical Statistics I by Muzammil Tanveer [Mathematical Statistics I] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org Name Mathematical Statistics anonymous@undisclosed.example.com (Anonymous) Thu, 20 Apr 2023 16:11:58 +0000 https://www.mathcity.org/notes/mathematical-statistics-ii-muzammil-tanveer Mathematical Statistics II by Sir Haidar Ali [Mathematical Statistics II] A subfield of mathematics called mathematical statistics is concerned with using mathematical techniques to solve statistical problems. It involves using mathematical analysis and probability theory to the study of statistical issues like estimate, hypothesis testing, and confidence intervals. Financial, engineering, and scientific fields all benefit from the use of mathematical statistics, which is a significant area of… anonymous@undisclosed.example.com (Anonymous) Thu, 20 Apr 2023 12:16:43 +0000 https://www.mathcity.org/notes/mathematical-statistics-iqra-liaqat Mathematical Statistics by Ms. Iqra Liaqat [Mathematical Statistics by Ms. Iqra Liaqat] These notes are send by Ms. Iqra Liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org Name Mathematical Statistics Provided by anonymous@undisclosed.example.com (Anonymous) Thu, 20 Apr 2023 12:30:11 +0000 https://www.mathcity.org/notes/measure-theory-notes-asim-marwat Measure Theory Handwritten Notes by Asim Marwat [Measure Theory Notes by Asim Marwat] These notes are made and shared by Mr. Asim Marwat. He has our sincere gratitude for supplying these notes, and we value his effort in having them published on MathCity.org. Measure Theory is an important subject in BS Mathematics. These notes contain topic from base level, like equivalence set, to advance level, like convergent in measure.$L_p$$L_p$$L^\infty$$L_p$ anonymous@undisclosed.example.com (Anonymous) Fri, 10 Feb 2023 17:43:56 +0000 https://www.mathcity.org/notes/mechanics-by-dr-amir-mahmood Mechanics (Easy Notes of Mechanics) [Easy Notes of Mechanics] These notes are provided and prepared by Dr. Amir Mahmood. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org If there is error or mistake in the notes, then please directly contact to Dr. Amir Mahmood for correction. He can be accessed via his email address at anonymous@undisclosed.example.com (Anonymous) Tue, 08 Aug 2023 11:46:58 +0000 https://www.mathcity.org/notes/mechanics-by-sir-nouman-siddique Mechanics by Sir Nouman Siddique These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org * Name: Mechanics * Provider: Mr. Muzammil Tanveer anonymous@undisclosed.example.com (Anonymous) Wed, 26 Jun 2024 18:35:58 +0000 https://www.mathcity.org/notes/mechanics-i-statics-dr-babar-ahmad Mechanics I (Statics) by Dr Babar Ahmad [Mechanics I (Statics) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book. anonymous@undisclosed.example.com (Anonymous) Mon, 24 Jul 2023 12:49:29 +0000 https://www.mathcity.org/notes/mechanics-ii-analytic-dynamics-i-dr-babar-ahmad Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad [Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book. anonymous@undisclosed.example.com (Anonymous) Sat, 24 May 2025 18:13:54 +0000 https://www.mathcity.org/notes/mechanics-iii-analytic-dynamics-ii-dr-babar-ahmad Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad [Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book. anonymous@undisclosed.example.com (Anonymous) Sat, 10 May 2025 17:33:01 +0000 https://www.mathcity.org/notes/method-of-mathematical-physics-m-usman-hamid Method of Mathematical Physics by Mr. Muhammad Usman Hamid [Method of Mathematical Physics by Mr. Muhammad Usman Hamid] Method of Mathematical Physics is an area of mathematics concerned with the application of mathematical methods to physics problems. Mathematical techniques for statistical mechanics, quantum mechanics, and classical mechanics are all included in this large field. anonymous@undisclosed.example.com (Anonymous) Thu, 20 Apr 2023 11:54:01 +0000 https://www.mathcity.org/notes/multiple-choice-questions-bsc-bs-ppsc-akhtar-abbas Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas [Multiple Choice Questions (BSc/BS/PPSC)] These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his efforts to publish these notes on MathCity.org. Multiple Choice Questions (MCQs) are given in these notes, which might be helpful in BSc, BS or Punjab Public Service Commission (PPSC) exams.$a$$b$$n$$na > b$$(p − 1)! \equiv −1(mod p)$$p$$p$$p$ anonymous@undisclosed.example.com (Anonymous) Sun, 24 May 2026 17:45:10 +0000 https://www.mathcity.org/notes/multivariable-calculus-sheikh-muhammad-saleem-shahzad Multivariable Calculus by Sheikh Muhammad Saleem Shahzad [Multivariable Calculus by Sheikh Muhammad Saleem Shahzad] * Have you ever wondered how we can understand the speed of a moving object at any instant of time? * Did you know that Calculus can help us predict future trends by analyzing patterns in data? anonymous@undisclosed.example.com (Anonymous) Sun, 17 Dec 2023 17:13:50 +0000 https://www.mathcity.org/notes/note-for-numerical-methods-m-usman-hamid Notes for Numerical Methods by M Usman Hamid [Notes for Numerical Methods by M Usman Hamid] These notes are initially provided by Mr. Anwar Khan. Later the updated version is send by Muhammad Tahir. We are really very thankful to Mr. Anwar Khan and Muhammad Tahir for providing these notes and appreciates their effort to publish these notes on MathCity.org$\left(\frac{1}{3}\right)$$\left(\frac{3}{8}\right)$ anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 17:59:07 +0000 https://www.mathcity.org/notes/number-theory-umer-shuaib Number Theory by Dr Muhammad Umer Shuaib [Number Theory Notes] A subfield of mathematics called number theory studies the characteristics of positive integers. Higher arithmetic is another name for it. The study of the relationships between various types of numbers, including prime numbers, rational numbers, and algebraic integers, is done using number theory, one of the oldest fields of mathematics.$\phi$ anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 18:11:04 +0000 https://www.mathcity.org/notes/numerical-analysis-by-m-usman-hamid Numerical Analysis by M Usman Hamid These notes are initially provided by Mr. Anwar Khan. Later the updated version is send by Muhammad Tahir. We are really very thankful to Mr. Anwar Khan and Muhammad Tahir for providing these notes and appreciates their effort to publish these notes on MathCity.org anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 17:01:51 +0000 https://www.mathcity.org/notes/numerical-analysis-ii Numerical Analysis II [Numerical Analysis by Muzammil Tanveer] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Name Numerical Analysis II Compiled by Muzammil Tanveer anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 17:56:32 +0000 https://www.mathcity.org/notes/operation-research-haidar-ali Operation Research by Sir Haidar Ali [Notes of Operation Research by Sir Haidar Ali] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These are based on lectures delivered by Sir Haidar Ali at GC University Faisalabad. anonymous@undisclosed.example.com (Anonymous) Fri, 21 Mar 2025 17:42:28 +0000 https://www.mathcity.org/notes/partial-differential-equations-m-usman-hamid Partial Differential Equations (PDE) by M Usman Hamid The course provides a foundation to solve PDE’s with special emphasis on wave, heat and Laplace equations, formulation and some theory of these equations are also intended. We are really very thankful to Prof. Muhammad Usman Hamid for providing these notes and appreciates his effort to publish these notes on MathCity.org anonymous@undisclosed.example.com (Anonymous) Sun, 09 Mar 2025 09:27:42 +0000 https://www.mathcity.org/notes/partial-differential-equations-muzammil-tanveer Partial Differential Equations (PDE) by Muzammil Tanveer [Partial Differential Equations] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org Name: Partial Differential Equations or PDEs anonymous@undisclosed.example.com (Anonymous) Sun, 09 Mar 2025 09:29:35 +0000 https://www.mathcity.org/notes/qr1-exploring-quantitative-skills-m-usman-hamid Quantitative Reasoning-I (QR1: Exploring Quantitative Skills) [Quantitative Reasoning-I (Exploring Quantitative Skills) by M Usman Hamid] This handout offers a comprehensive introduction to numeracy and quantitative reasoning, laying a solid foundation for analytical thinking. It explores fundamental concepts, from basic arithmetic and unit analysis to more advanced topics like probability and statistics. A unique highlight is its exploration of the contributions of mathematicians and statis… anonymous@undisclosed.example.com (Anonymous) Mon, 15 Dec 2025 16:47:25 +0000 https://www.mathcity.org/notes/qr2-tools-for-quantitative-reasoning-m-usman-hamid Quantitative Reasoning II (QR2: Tools for Reasoning Skills) [Quantitative Reasoning II (Tools for Reasoning Skills)] This handout provides a comprehensive exploration of fundamental mathematical and logical concepts, making it an essential read for students and professionals alike. It begins with an introduction to enumeration and its practical applications, followed by an in-depth discussion on quantitative reasoning, number systems, and arithmetic operations. The book highlights the contribut… anonymous@undisclosed.example.com (Anonymous) Fri, 01 Aug 2025 18:31:56 +0000 https://www.mathcity.org/notes/ring_notes Ring (Notes) by Prof. M. Dabeer Mughal [Ring (Notes) by Prof. M. Dabeer Mughal] A handwritten notes on Ring (Algebra) by Prof. M. Dabeer Mughal (Federal Directorate of Education, Islamabad, Pakistan). It is best to prepare a “Rings and Vector Spaces” section of your algebra paper or Algebra II for BS or MS Mathematics.$\phi$ anonymous@undisclosed.example.com (Anonymous) Sat, 01 Apr 2023 06:56:21 +0000 https://www.mathcity.org/notes/rings-and-modules-iqra-liaqat Rings & Modules by Ms. Iqra Liaqat Ring is a mathematical structure with two operations. With one operation it is abelian group and with other operation it is semi-group with distributive law holds with first operation w.r.t the other operation. This concept is of pure in nature in mathematics. These advanced level notes are typically taken as an elective in a mathematics undergraduate degree. anonymous@undisclosed.example.com (Anonymous) Sat, 01 Apr 2023 14:30:33 +0000 https://www.mathcity.org/notes/special-functions-muzammil-tanveer Special Functions by Dr. Muhey-U-Din These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Thease notes are based on the lectures by Dr. Muhey-U-Din. anonymous@undisclosed.example.com (Anonymous) Sun, 23 Jul 2023 16:48:30 +0000 https://www.mathcity.org/notes/special-theory-of-relativity-usman-hameed-and-zeeshan-ahmad Special Theory of Relativity by M Usman Hamid and M Zeeshan Ahmad [Special Theory of Relativity by M Usman Hamid and M Zeeshan Ahmad] Special theory of relativity developed by Einstein in 1905, after the failure of Newton‘s laws, when he was dealing with the relative motion in space. The theory of relativity deals with relations which exist between physical quantities (such as mass of a particle, length of a rod, electric field at a point etc.) as they appear to different observers in relative … anonymous@undisclosed.example.com (Anonymous) Tue, 23 Aug 2022 12:32:09 +0000 https://www.mathcity.org/notes/theory-of-optimization-muzammil-tanveer Theory of Optimization by Ma'am Iqra Razzaq [Special Theory of Optimization by Ma'am Iqra Razzaq] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These notes are based on the lectures by Ma'am Iqra Razzaq. anonymous@undisclosed.example.com (Anonymous) Sun, 23 Jul 2023 16:28:59 +0000 https://www.mathcity.org/notes/topology-and-functional-analysis-solved-pu Topology and Functional Analysis Solved Paper by Noman Khalid These solved papers are written and provided by Mr. noman-khalid. We are very thankful to him for providing these notes to publish on MathCity.org. Topology and Functional Analysis is considered as one the tough subject in BS/MSc Mathematics in different universities. Here solved paper for the said subject is given for the University of the Punjab (PU), Lahore. anonymous@undisclosed.example.com (Anonymous) Sun, 11 Feb 2024 12:38:09 +0000 https://www.mathcity.org/notes/vector-spaces-review-by-rashad-wattu Vector Space (Review) by Rashad Wattu Mathematical vector space is a crucial and fundamental idea. It depends on the concept of field. These notes were primarily written to help maths students understand vector space, which is a concept that they all need to be familiar with. anonymous@undisclosed.example.com (Anonymous) Sat, 01 Apr 2023 14:51:01 +0000