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- Chapter 03: General Theorem, Intermediate Forms
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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
- 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//
- 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... sing and decreasing functions. Intermediate value theorem and its immediate consequence (only statements) ... Convergence and divergence of sequences. Cauchy’s theorem. Nth-term test, comparison test, ratio test, root
- Groups (Handwritten Notes) @notes
- , isomorphism, endomorphism, examples and related theorem * Kernel, definition and related theorems * C... on and examples * Index of subgroup, Lagrange's theorem * Double coset, related theorem * Normalizer, definition and related theorems * Centralizer, centre of group, related theorem * Conjugate or transform of a group, definition
- 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 * Cauch
- MTH604: Fixed Point Theory and Applications (Spring 2020) @atiq
- focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equ... Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also educated. ==... tions===== - State and prove intermediate value theorem. - State and prove the fixed point theorem. - Define attracting, repelling and neutral fixed point the
- Functional Analysis by Mr. Tahir Hussain Jaffery @notes
- Finite category (or meager) * Baire's category theorem * The principal of uniform boundedness or Banach-Steinhaus theorem * Subadditive, positive homogeneous * Subli... orm * Extensions, restriction * Hahn-Banach theorem (real version) * Hahn-Banach theorem (complex version) * Hahn-Banach theorem for non-linear spaces
- MTH604: Fixed Point Theory and Applications (Fall 2022) @atiq
- focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equ... Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also educated. ==... ample questions===== - State intermediate value theorem. - State and prove the fixed point theorem. - Define attracting, repelling and neutral fixed points.
- Handwritten Notes of Real Analysis by Asim Marwat @notes
- lower bound (glb), Archimedean property, density theorem, Bolzano Weierstrass theorem. * Chapter 02: Limit of the Function * Sequence, bounded sequence, Sandwhich theorem, monotone sequence, monotonic convergent theorem, nested intervals, sub-sequence, Cauchy sequence, compari
- Chapter 04 - Differentiation @msc:real_analysis_notes_by_syed_gul_shah
- tiation ====== * Derivative of a function * Theorem: Let //f// be defined on [//a//,//b//], if //f// ... //x//. (Differentiability implies continuity) * Theorem (derivative of sum, product and quotient of two functions) * Theorem (Chain Rule) * Examples * Local Maximum * Theorem: Let //f// be defined on [//a//,//b//], if //f// h
- MTH321: Real Analysis I (Fall 2021) @atiq
- accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the Mean Value theorem and emphasize the proofs’ development. Define Riemann integral and Riemann sum
- MTH322: Real Analysis II (Fall 2021) @atiq
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests... (x)dx}$ is convergent. - State and prove Abel's theorem for infinite integral. - If $f(x)$ is bounded,
- Chapter 03: PDF Viewer @bsc:notes_of_calculus_with_analytic_geometry:ch03_general_theorem_intermediate_forms
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university