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- Real Analysis Notes by Prof Syed Gul Shah
- tical functions, limits, and sequences, can often be a difficult topic for students. Prof. Syed Gul Sh... d fame for his extraordinary qualities as a human being. As a teacher, Prof. Syed Gul Shah's dedicati... on to excellence is unwavering. He goes above and beyond to ensure that his students thoroughly unders... tills in his students a deep appreciation for the beauty and elegance of mathematical analysis, inspir
- Advanced Analysis: Handwritten Notes
- Mathematics. See the contents of the notes given below to see the topics covered by these notes. ^ N... * Hyper-geometric Series * Gamma Function * Beta Function * Relation between Gama and Beta Function * Bessel Function * Differential Recurrence relation of Bessel Funct
- Notes of Algebra
- the study of vectors and linear transformations. Best notes to prepare the subject written by [[:peop... notes of groups theory for students of BS or MSc. Best to prepare a Group section of Algebra paper. </... initions with examples and results (theorems) may be useful to prepare interviews, [[:PPSC|PPSC]], FPS... initions with examples and results (theorems) may be useful to prepare interviews, [[:PPSC|PPSC]], FPS
- Metric Spaces (Notes)
- of previous notes. Many mistakes and errors have been removed. These notes are collected, composed an... xamples * Pseudometric and example * Distance between sets * Theorem: Let $(X,d)$ be a metric space. Then for any $x,y\in X$, $$\left| {\,d(x,\,A)\,... ball is a closed set. * Theorem: Let (//X,d//) be a metric space and $A\subset X$. If $x \in X$ is
- Mathematical Method by Sir Muhammad Awais Aun
- f an unknown function. Differential equations can be divided into two categories. The first chapter of... e of Laplace transformation * Unit function * Bessel Equation and Bessel Functions * Basic Identities and Recurrence formula * Parametric Bessel functions * Transforming the independent va
- Fluid Mechanics by Ali Raza
- studies how fluids (liquids, gases, and plasmas) behave and interact with forces and energy. Fluid me... , biology, and other fields. Fluid mechanics can be divided it into three parts; fluid statics, fluid... ty * Stream function * Flow along a curve * Bernoulli's equation </col> <col sm="6"> * Application of Bernoulli's equation * 2D Source * Complex veloc
- History of Mathematics by Muhammad Usman Hamid
- of human endeavor is marked by changes which can be considered as correction or extension. Thus, the ... ational, and finds the ways of other societies to be odd, laughable, or repulsive. But only among the ... e wrong in his views on falling bodies and had to be corrected by Galileo in the 1590s. Galen, the gre... atomical and physiological conclusions. He had to be corrected by Vesalius in 1543 and Harvey in 1628.
- Mathematical Statistics by Ms. Iqra Liaqat
- y==== In this section, the main heading are given below. <grid> <col sm="6"> * Probability * Mut... ility distributions * Uniform distribution * Bernoulli trials * Binomial experiment * Propert... ponential distribution * Gauss distribution * Beta function * Beta distribution (1st kind) * Beta distribution (2nd kind) * Normal distribution
- Functional Analysis by Prof Mumtaz Ahmad
- r algebra. It entails researching the connections between roles, things, incidents, actions, and outco... and stems from the calculus of variations. It can be used in many different areas, including approxima... A collection of points with a concept of distance between them make up a metric space. A metric or dis... <grid> <col sm="6"> * Metric Space * Distance between two sets * Sequence * Convergent Sequenc
- Functional Analysis by Mr. Tahir Hussain Jaffery
- gebra. It requires looking into the relationships between various roles, objects, incidents, actions, ... sis, and differential and integral equations, can benefit from its use. Handwritten notes of Function... oncepts linked to functional analysis. There have been many theorems proven, particularly in the fourt... mal sets in Hilbert spaces * Generalization of Bessel's inequality * Zorn's lemma * The Gram-
- Functional Analysis by M Usman Hamid and Zeeshan Ahmad
- itted mathematician, who is working very hard for better understanding of mathematics to it readers. ... ector spaces (mainly function space) and mappings between them. It deals with abstract spaces and diff... y==== In this section, the main heading are given below. **Metric Spaces:** A quick review, completen... paces:** linear spaces, normed spaces, difference between a metric and a normed space, Banach spaces,
- Special Functions by Dr. Muhey-U-Din
- unction * Some Properties of Gamma Function * Beta Function * Duplication Formula * Hypergeom... Generating function for Laguerre’s polynomial * Bessel’s Function * Solution of Bessel’s Differential Equation * Recurrence formula of Bessel Function * Rodrigues Formula * Special re
- Fluid Mechanics II by Dr Rao Muzamal Hussain
- quation of motion for in-viscus (real) fluid * Bernoulli Equation * Bernoulli Equation for steady flow * Navier-Stokes equation * Parallel flo... ille flow) * Couette-Poiseuille flow * Flow between two concentric rotating cylinders * Press
- General Topology by Azhar Hussain
- ation to another. Compact sets are those that can be completely covered by a small number of sets of any size. Connected sets are sets that cannot be split into two far-reaching portions. Using the i... by," "arbitrarily small," and "far apart" can all be clarified. ^ Name |Lecture Notes on General Top
- Handwritten Notes of Real Analysis by Asim Marwat
- numbers, sequences and series, and real functions behave. It focuses on real numbers and frequently ex... f calculus and its applications. Real analysis is becoming a crucial tool in a wide range of applicati... unded above set, least upper bound (lub), bounded below set, greatest lower bound (glb), Archimedean p