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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
- FSc Part 1 (KPK Boards) @fsc
- know its application. * recognize the addition theorem (or law) of probability and its deduction. * recognize the multiplication theorem (or law) of probability and its deduction. * Use theorem of addition and multiplication of probability to ... == Chapter 7: Mathematical Induction and Binomial Theorem ===== === Objectives === After reading this unit
- Functional Analysis by M Usman Hamid and Zeeshan Ahmad @notes
- mensional spaces, F. Riesz Lemma, the Hahn-Banach theorem, the HB theorem for complex spaces, The HB theorem for normed spaces, the open mapping theorem, the closed graph theorem, uniform boundedness principle and i
- MTH321: Real Analysis I (Spring 2023) @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
- Question 1 Exercise 7.2 @math-11-kpk:sol:unit07
- =====Question 1(i)===== Expand by using Binomial theorem: $(x^2-\dfrac{1}{y})^4$ ====Solution==== Using binomial theorem \begin{align}(x^2-\dfrac{1}{y})^4&=(x^2)^4+{ }^4 ... =====Question 1(ii)===== Expand by using Binomial theorem: $(1+x y)^7$ ====Solution==== Using binonial theorem \begin{align} & (1+x y)^7=1+{ }^7 C_1(1)^6(x y)+{ }^7
- MTH321: Real Analysis I (Fall 2022) @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
- Affine and Euclidean Geometry by Shahzad Idress @notes
- f Cosine and Sines: The Law of Cosine, Pythagoras Theorem, Parallelogram Law, The Law of Sines, * Eucl... 𝑩, Angles Associated with Parallel Lines, Thales’ Theorem, Menelaus Point, Menelaus’ Theorem, Cevian Line, Ceva’s Theorem, Copolar Triangles, Coaxial Triangles, Desargues’ Theorem. * Platonic Polyh
- Fluid Mechanics II by Dr Rao Muzamal Hussain @notes
- Flow along a curve * Circulation * Kelvins Theorem (For rotation or circulation) or State and prove Kelvins theorem for circulation * Uniqueness Theorem * Single Infinite Row of Vortices * Double Infinite Row of V... Irrotational Motion * Kelvin’s Minimum Energy Theorem * Laplace Equation * Normal stress * Tan
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- \sqrt{x+2}+\sqrt{x-3}=7$ * **Remainder Theorem:** If a polynomial $f(x)$ of degree $n \geq 1$ is... as a polynomial function of $x$. * **Factor Theorem:** The polynomial $(x-a)$ is a factor of the poly... = Chapter 08: Mathematical induction and binomial theorem ===== * **Binomial Theorem:** An algebraic expression consisting of two terms is called binomial expre
- Complex Analysis (Easy Notes of Complex Analysis) @notes
- ontour integration * Mittag-Lefflers’ Expansion Theorem ==== Download or View online ==== <callout type... -v.pdf}} </modal> * Mittag-Lefflers Expansion Theorem and Exercises | **{{ :notes:complex-analysis-mittag-lefflers-expansion-theorem-exercises.pdf |Download PDF}}** %%|%% <btn type="... :notes:complex-analysis-mittag-lefflers-expansion-theorem-exercises.pdf}} </modal> </callout> ====There a
- Mechanics by Sir Nouman Siddique @notes
- ational Motion * Rotational Motion * Chasles’ Theorem * Angular Equation motion * Screw Motion * ... "6"> * Wallis Formula’s * Perpendicular axis theorem * K.E in general motion * Momental Ellipsoid * Equimomental System * Principle axis * Theorem (Existence of Principle axis theorem) * Working rule of finding Principle M.I and Principle Axis * Sph
- MTH322: Real Analysis II (Spring 2023) @atiq
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests
- Differential Geometry (Notes) by Ms. Kaushef Salamat @notes
- of centre of spherical curvature * Fundamental theorem for space curves * Intrinsic equation of a curv... mal section of a surface at a point * Meunier's theorem * Normal curvature and radius of normal curvatu... ial equation for principal directions * Euler's theorem * Surface of revolution * Normal surface *
- Topology: Handwritten Notes @notes
- Nested interval property or Cantor's intersection theorem * Continuous function * Topological spaces ... int * Open cover; Lindelof space * Lindelof theorem * Relative topology, subspace * Separation ... palonius identity * Hilbert space; Pythagorian theorem * Minimizing vector * Direct sum * Ortho
- Chapter 02: Groups @bsc:notes_of_mathematical_method
- nition (idempotent) * Properties of Group * Theorem (The Cancellation Law) * Theorem (Solution of Linear Equations ) * Subgroups * Definition ( subgr... efinition ( cyclic group ) * Cosets-Lagrange’s Theorem * Permutations * Cycles * Transpositions