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Chapter 03 - Limits and Continuity @msc:real_analysis_notes_by_syed_gul_shah
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- Limits and Continuity ====== * Limit of the function, examples and definition * Theorem: Suppose (i)... s unique. * Theorem: Suppose that a real valued function //f// is defined on an open interval //G// except... Theorem): Suppose that //f//, //g// and //h// are functions defined on an open interval //G// except possibl... Theorem: Let $f_1,f_2,f_3,...,f_k$ be real valued functions on a metric space //X// and $\underline{f}$ be a
Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
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set $A$ is said to be countable if there exists a function $f:A\to \mathbb{N}$ such that * (A) $f$ is bi... is convergent.</collapse> </panel> ==== Limit of functions ==== <panel> 1. A number $L$ is called limit of the function $f$ when $x$ approaches to $c$ if for all $\varep... lapsed="true">(B): It is a definition of limit of functions. </collapse> </panel><panel> 2. If $\lim_{x \to
Fundamental of Complex Analysis: Viewer @msc:notes:fundamental_of_complex_analysis
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/Solution-Ch02-Analytic-or-Regular-or-Holomorphic-Functions|Solutions of Chapter 02: Analytic or Regular or Holomorphic Functions]] * [[mdoku>msc:notes:fundamental_of_complex_... -analysis/Solution-Ch03-Elementary-Transcendental-Functions|Solutions of Chapter 03: Elementary Transcendental Functions]] * [[mdoku>msc:notes:fundamental_of_complex_a
Chapter 04 - Differentiation @msc:real_analysis_notes_by_syed_gul_shah
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04 - Differentiation ====== * Derivative of a function * Theorem: Let //f// be defined on [//a//,//b//... m (derivative of sum, product and quotient of two functions) * Theorem (Chain Rule) * Examples * Local... tion * Riemann differentiation of vector valued function * Theorem: Let //f// be a continuous mapping of
Syllabus for PU @msc:syllabus
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on shall be: * a) Analysis (Real, Complex and Functional) * b) Algebra and Topology * c) Mechani... - Paper IV: Mechanics - Paper V: Topology and Functional Analysis //Note: All the papers of M.Sc. Part-... and Splines * Paper IV-VI option (xii) Advanced Functional Analysis * Paper IV-VI option (xiii) Solid Me
Preparation Guide @msc:syllabus:uos
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y those exercises related to maxima and minima of function $z= f(x,y)$ ) of Calculus and analytic Geometry ... s by Sankara Rao. ==== 5. Topology ( topology and functional analysis )==== Books: * Schaums Outline of General Topology. * Elements of Topology and Functional Analysis by Dr. Abdul Majeed * [[:msc:notes:t
Number Theory by Ms. Iqra Liaqat @msc:notes
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perty * Multiple * Divisibility * The floor function and ceiling function * The division algorithm * Div and mod operators * Basic representation theorem
Mathematical Method by Khalid Latif Mir (Solutions) @msc:notes
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transforms preliminaries * Piecewise continuous functions * Definition and notation * Necessary and su
Targets @msc:notes
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Mechanics** * **Numerical Analysis** * **<del>Functional Analysis</del>** Notes added --- // 2017/02/26
Syllabus for UoS (Private only) @msc:syllabus
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er IV: Mechanics | 100 | | 5 |Paper V: Topology & Functional Analysis | 100 | | **Total Marks**|| **500**