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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
- MTH321: Real Analysis I (Spring 2023) @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, Rollesā€™s Theorem, extreme value theorem, and the
- FSc Part 1 (KPK Boards) @fsc
- al representation. * use vector to prove simple theorems of descriptive geometry. * recognize rectangul... 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
- 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... Euclidean Tools, The Method of Loci * Classical Theorems in Affine Geometry * Sensed Magnitudes, Pos... gments, Range of Points and Complete Range, Basic Theorems. * Menelaus, Ceva and Desargues Theorems: The ratio š¯‘Øš¯‘·/š¯‘·š¯‘©, Angles Associated with Parallel Lines, Thal
- 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
- 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
- Mathematics 10 (Science Group) @matric
- rd, 4th, mean and continued proportion. * apply theorems of invertendo, alternendo, componendo, dividendo... dents will learn: * how to prove the following theorems alongwith corollaries and apply them to solve ap... are congruent. ==== Solutions ==== The following theorems was send by [[people:Bahadar-Ali-Khan]]. We are ... l to him for sending these notes. * Important Theorems | {{ :matric:10th_science:10th-science-ch-9-theo
- 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 * Kelvinā€™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-Lefflersā€™ 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 * Chaslesā€™ Theorem * Angular Equation motion * Screw Motion * ... "6"> * Wallis Formulaā€™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-Lagrangeā€™s Theorem * Permutations * Cycles * Transpositions