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- Real Analysis Notes by Prof Syed Gul Shah
- mplexities of mathematical functions, limits, and sequences, can often be a difficult topic for students. Pr... * Chapter 01: Real Number system * Chapter 02: Sequence and Series * Sequence, Subsequence, Increasing Sequence, Decreasing Sequence, Monotonic Sequence, Strictly Increasing or Decreasi
- Metric Spaces (Notes)
- erever //G// is open in //Y//. * Convergence of Sequence * Theorem: If $(x_n)$ is converges then limit ... $(x_n)$ is unique. * Theorem: (i) A convergent sequence is bounded. (ii) ii) If ${x_n}\to x$ and ${y_n}\to y$ then $d(x_n,y_n)\to d(x,y)$. * Cauchy Sequence * Theorem: A convergent sequence in a metric space (//X,d//) is Cauchy. * Subsequence * Theorem: (i)
- Real Analysis Handwritten Notes by Kaushef Salamat
- over * Separable Sets * Disconnected * Sequences * Monotone Sequences * Euler Number * Subsequences * Urysohn Property * Monotone Subsequence Theorem * The Bolzano-weirstrass Theorem * Cau
- Handwritten Notes of Real Analysis by Asim Marwat
- ch of mathematics that analyses how real numbers, sequences and series, and real functions behave. It focuse... tigates a number of the properties of real-valued sequences and functions, including convergence, limits, co... orem. * Chapter 02: Limit of the Function * Sequence, bounded sequence, Sandwhich theorem, monotone sequence, monotonic convergent theorem, nested intervals, su
- Functional Analysis by Prof Mumtaz Ahmad
- * Metric Space * Distance between two sets * Sequence * Convergent Sequence * Cauchy Sequence * Complete Space * Dense Subset * Somewhere & Nowhere Dense Subset * Nested Sequence * Normed Space * $l^\infty$-Space * $l^\inf
- Measure Theory Notes by Anwar Khan
- algebra; Largest $\sigma-$algebra * Increasin & sequence of sets * Decreasing sequence of sets * Define $\lim\limits_{k\to \infty} \sup A_k$ and $\lim\limits_{k... * Limit inferior and limit superior of real value sequence * Sequence of $\mathcal{A}-$measurable functions & its limits & their properties * Larger & smaller o
- Topology: Handwritten Notes
- etric space and complete metric space * Cauchy sequence * Bounded sequence * Nested interval property or Cantor's intersection theorem * Continuous functi... logies) * Product topology * Convergence of sequence in topological spaces </col> <col sm="6"> * Re
- Measure Theory Handwritten Notes by Asim Marwat
- e * Measurable Function * Limit Superior of a Sequence * Limit Inferior of a Sequence * Limit Superior, Limit Inferior * Characteristic Function, Simple Fun
- Partial Differential Equations (PDE) by M Usman Hamid
- * MATHEMATICAL MODELS * Heat Equations and consequences, Wave Equations and consequences. * CLASSIFICATION OF SECOND-ORDER LINEAR EQUATIONS * Second-Order
- Functional Analysis by Mr. Tahir Hussain Jaffery
- * Inner product on complex linear space * Consequences of the definition of inner product spaces * E
- History of Mathematics by Muhammad Usman Hamid
- he rise of a Genghis Khan, for example, or the consequences of the short-lived Mongol Empire. Other changes
- Multivariable Calculus by M Usman Hamid and M Zeeshan Ahmad
- l equations, Laplace and Fourier Transformations, Sequence, Series and Complex Integration. Through a combin
- Quantitative Reasoning-I (Exploring Quantitative Skills)
- * Simple and compound interest * Numbers * Sequence and series * Statistics * Descriptive stati
- Quantitative Reasoning II (Tools for Reasoning Skills)
- nd Inequalities * Linear equation and its consequences * Analytical approach to solve simultaneous
- Ring (Notes) by Prof. M. Dabeer Mughal
- ing, ring with unity (identity), examples * Consequences from the definition * Unit element of ring