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- Metric Spaces (Notes) @notes
- ometric and example * Distance between sets * Theorem: Let $(X,d)$ be a metric space. Then for any $x,y... \,y).$$ * Diameter of a set * Bounded Set * Theorem: The union of two bounded set is bounded. * Ope... closed ball, sphere and examples * Open Set * Theorem: An open ball in metric space //X// is open. * Limit point of a set * Closed Set * Theorem: A subset //A// of a metric space is closed if an
- Real Analysis Notes by Prof Syed Gul Shah @notes
- Sequence * Convergence of the Sequence * Theorem: A convergent sequence of real number has one and... sequence is unique.) * Cauchy Sequence * Theorem: A Cauchy sequence of real numbers is bounded. * Divergent Sequence * Theorem: If $s_n<u_n<t_n$ for all $n\ge n_0$ and if both ... the sequence $\{u_n\}$ also converges to s. * Theorem: If the sequence $\{s_n\}$ converges to //s// the
- Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
- nded Sequence * Convergence of the Sequence * Theorem: A convergent sequence of real number has one and... the sequence is unique.) * Cauchy Sequence * Theorem: A Cauchy sequence of real numbers is bounded. * Divergent Sequence * Theorem: If $s_n<u_n<t_n$ for all $n\ge n_0$ and if both ... n the sequence $\{u_n\}$ also converges to s. * Theorem: If the sequence $\{s_n\}$ converges to //s// the
- Groups (Handwritten Notes) @notes
- , isomorphism, endomorphism, examples and related theorem * Kernel, definition and related theorems * Cyclic group, related theorems * Complex in a group, product of complexes and related theorems * Coset, definition and examples * Index of
- A-Course of Mathematics (Paper A & B) @bsc:paper_pattern:sargodha_university
- lated rates. Higher order derivatives. Leibnitz’s theorem. Limits and continuity of functions of two variab... l meaning for functions of two variables. Euler’s theorem. Increments and differentials. Chain Rule. Extrem... e test and by Lagrange multiplier method. General theorems and indeterminate forms. L’ Hospital rule and it... sing and decreasing functions. Intermediate value theorem and its immediate consequence (only statements)
- MTH604: Fixed Point Theory and Applications (Spring 2020) @atiq
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- Chapter 03 - Limits and Continuity @msc:real_analysis_notes_by_syed_gul_shah
- imit of the function, examples and definition * Theorem: Suppose (i) $(X,{d_x})$ and $(Y,{d_y})$ be two m... \to\infty}{p_n}=p$. * Examples and exercies * Theorem: If $\lim_{x\to c}f(x)$ exists then it is unique. * Theorem: Suppose that a real valued function //f// is def... /t// are in $\left\{x:|x-c|<\delta \right\}$. * Theorem (Sandwiching Theorem): Suppose that //f//, //g//
- MTH604: Fixed Point Theory and Applications (Fall 2022) @atiq
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- Vector Spaces (Handwritten notes) @notes
- d examples * Subspaces, definition and related theorems * Linear sum, definition and related theorems * Homomorphism, kernel, linear combination * Linear span, related theorem * Finite dimensional vector space, linear dependent and independent, related theorem * Basis of a vector space and related theore
- MTH604: Fixed Point Theory and Applications @atiq
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- MTH604: Fixed Point Theory and Applications (Spring 2021) @atiq
- to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generali... ons and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued map
- MTH321: Real Analysis I (Fall 2021) @atiq
- sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emph... d uniform continuity of a function, prove various theorems about continuous functions and emphasize the pro... efine the derivative of a function, prove various theorems about the derivatives of functions and emphasize... accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the
- Real Analysis Handwritten Notes by Kaushef Salamat @notes
- * Urysohn Property * Monotone Subsequence Theorem * The Bolzano-weirstrass Theorem * Cauchy Sequence * Contractive Sequence * Properly Diverg... Sequence * Properly Divergent * Comparison Theorem </col> <col sm="6"> * Limit Inferior and... Superior * Cluster Point * Cauchy's Second theorem on Limit * Sets of Real Numbers * Heine-Bor
- Chapter 03: General Theorem, Intermediate Forms @bsc:notes_of_calculus_with_analytic_geometry
- ====== Chapter 03: General Theorem, Intermediate Forms ====== {{ :bsc:notes_of_calculus_with_analytic_geom... === What is in the this chapter?===== * Rolle's theorem * Geometrical interpretation of Rolle's theorem * The mean value theorems * Another form of mean value theorem * Increasing and decreasing functions
- MTH321: Real Analysis I (Spring 2020) @atiq
- sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emph... d uniform continuity of a function, prove various theorems about continuous functions and emphasize the pro... efine the derivative of a function, prove various theorems about the derivatives of functions and emphasize... accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university
- Chapter 03: PDF Viewer @bsc:notes_of_calculus_with_analytic_geometry:ch03_general_theorem_intermediate_forms
- Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch08