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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... \frac{1}{2}s$. * Theorem: Let //a// and //b// be fixed real numbers if $\{s_n\}$ and $\{t_n\}$ con... o \infty}{r_n}=x$. * Let a sequence $\{s_n\}$ be a bounded sequence. (i) If $\{s_n\}$ is monotonic... or all $n>m>n_0$. * Theorem: Let $\sum {a_n}$ be an infinite series of non-negative terms and let
- 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.
- Metric Spaces (Notes)
- * Distance between sets * Theorem: Let $(X,d)$ be a metric space. Then for any $x,y\in X$, $$\left|... ball is a closed set. * Theorem: Let (//X,d//) be a metric space and $A\subset X$. If $x \in X$ is... et * Separable Space * Theorem: Let (//X,d//) be a metric space, $A \subset X$ is dense if and onl... chy. * Subsequence * Theorem: (i) Let $(x_n)$ be a Cauchy sequence in (//X,d//), then $(x_n)$ conv
- 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
- Notes of Algebra
- 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
- Complex Analysis (Quick Review)
- results are the part of these notes, these might be helpful to prepare interviews or any other writte... = * If any pair of points $z_1, z_2 \in S$ can be connected by a polygonal line that consists of a
- Theory of Optimization by Ma'am Iqra Razzaq
- n impact on the objective function must typically be defined along with an objective function that has to be maximized or minimized. ^ Name |Theory of Optim
- Notes of Analysis
- he complex analysis by [[:people:akhtar]]. It may be useful to prepare interviews, PPSC, FPSC or any o
- Complex Analysis (Easy Notes of Complex Analysis)
- ontact to Dr. Amir Mahmood for correction. He can be accessed via his email address at <amir4smsgc@gma
- Fluid Mechanics by Ali Raza
- , biology, and other fields. Fluid mechanics can be divided it into three parts; fluid statics, fluid
- Functional Analysis by Prof Mumtaz Ahmad
- and stems from the calculus of variations. It can be used in many different areas, including approxima
- Fuzzy Sets Theory by Umar Saeed Bunarai
- hip are studied. This implies that an element can be a member of a set only partially or not at all. I
- Group Theory: Important Definitions and Results
- ns with examples and related theorem, which might be helpful to prepare interviews or any other writte
- Linear Algebra: Important Definitions and Results
- ns with examples and related theorem, which might be helpful to prepare interviews or any other writte
- Mathematical Method by Sir Muhammad Awais Aun
- f an unknown function. Differential equations can be divided into two categories. The first chapter of