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- Definitions: FSc Part 2 (Mathematics): PTB @fsc-part2-ptb
- ===== Unit 01 (Functions and Limits) ===== * **Function:** A function is a rule or correspondence, relating to two sets in such a way that each element in the firs... e and only one element in the second set. Or \\ A function from //X// to //Y// is a rule that assigns to eac... // in //Y//. \\ e.g. $A=x^2$, that is, //A// is a function of //x//. * **Domain:** In a function $f:X\to
- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- objects is called - Relation - Sets - Function - None of these - The objects in a set are ... \sim p \wedge \sim q$ - Every relation is - Function - Cartesian product - May or may not be function - None of these - For two non-empty sets $A$... - Binary operation - Binary relation - Function - None of these - The set of the first elem
- Khuram Ali Khan
- ip Pečarić, Popoviciu type inequalities via Green function and generalized Montgomery identity, Mathematical... .com/18-118/Popoviciu-type-inequalities-via-Green-function-and-generalized-Montgomery-identity|Link]]) - L... ip Pečarić, Popoviciu type inequalities via Green function and Taylor polynomial, Turk. J. Math, (2016) 40(2... Integral form of Popoviciu inequality for convex function, Proceedings of the Pakistan Academy of Sciences,
- Unit 01: Functions and Limits @fsc:fsc_part_2_solutions
- & summary ==== * Introduction * Concept of Function * Definition (Function-Domain-Range) * Notation and Values of a Function * Graphs of Algebraic functions * Graph of Fu... Piece-Wise * Types of Functions * Algebraic Function * Trigonometric Functions * Inverse Trigo
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- w q)\wedge (p \vee q)$ is the contingency. * **Function:** Let $A$ and $B$ be two non-empty set sets. If\... $F$ have same 1st elements. Then $F$ is called a function from $A$ to $B$ and is written as $F:A \to B$ denoted by $y=f(x)$. * **Bijective function:** (1-1 and onto) A function f which is both one to one and onto is called bijective function. * **Inje
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- of \( p \) and \( q \) and false for others. ====Function==== A function is a relation between two non-empty sets \( A \) and \( B \), where each element of set \( A... ( A = \{1, 2, 3\} \) and \( B = \{a, b, c\} \). A function \( f: A \rightarrow B \) could be defined as \( f(1) = a, f(2) = b, f(3) = c \). ====Bijective Function==== A bijective function is a function that is bo
- Special Functions by Dr. Muhey-U-Din @notes
- |853 kB | ====Contents & Summary==== * Gamma Function * Some Properties of Gamma Function * Beta Function * Duplication Formula * Hypergeometric Function * Historical Background of Hypergeometric Function
- MTH322: Real Analysis II (Fall 2021) @atiq
- differentiation, the exponential and logarithmic function, the trigonometric functions. **Series of functi... - Define pointwise convergence of sequence of function. - Define uniform convergence of sequence of function. - Define pointwise convergence of series of function. - Define uniform convergence of series of functi
- Advanced Analysis: Handwritten Notes @notes
- retation of Equivalent Set * Duality * Choice Function * Characteristic Function * Cardinal Numbers * Arithmetic Cardinal Number * Transfinite Cardinal Nu... ial Equation * Hyper-geometric Series * Gamma Function * Beta Function * Relation between Gama and Beta Function * Bessel Function * Differential Recurre
- MTH424: Convex Analysis (Fall 2020) @atiq
- ets, convex functions, Differential of the convex function. Developing ability to study the Hadamard-Hermite... ==Lecture 01=== * Definitions: Interval, convex function, strictly convex function, concave function, strictly concave function * Example of convex & concave functions * By definition, p
- Measure Theory Notes by Anwar Khan @notes
- annot be seen. In measure theory, a measure is a function that assigns a non-negative integer to subsets of a given set. Additionally, the function must meet a number of requirements, such as being... \sigma-$set * Set of extended real numbers; Set function; Properties of set function * Measure * Finite measure; $\sigma-$finite measure * Monotone convergen
- Are the functions are same? @dyk
- ==== Answer ===== <WRAP center round red 70%> A //function// is a relation between a set of inputs and a set... Set of inputs is usually know as //domain of the function//. When we are saying set of input values, it mea... ch cannot taken as input. <wrap em>So to define a function, we must first have set of input values.</wrap> ... natively, we say a relation $f:A \to B$ is called function if - Domain of $f = A$. - There is a unique e
- FSc Part 2 (KPK Boards) @fsc
- ons through graphs. * draw the graph of modulus function and identify its domain and range. * recognize the composition of a function and then to find out the composition of two functions. * describe the inverse of a function and then to find out the inverse of composition o... compound functions. * introduce the limit of a function with respect to real number intervals on the real
- PPSC Paper 2021 (Lecturer in Mathematics) @ppsc
- [x],\) greatest integer \(\leq x;\) be integrable function on \([0,4]\), then \(\displaystyle \int_{0}^{4}[x... mic equations - Algebraic equations - For a function \(f\), if \(f_{xx}=f_{xy}=f_{yy}=0\), the point \... - \(X^\perp + Y\) - Normed subspace - The function \(f(x)=x^{(-1)}\) is not: \\ - Uniform contin... }\) is a continuously differentiable vector point function and \(V\) is the volume bounded by a closed surfa
- Mathematical Method by Sir Muhammad Awais Aun @notes
- Many physical occurrences are characterised by a function whose value at one place relies on its value at another. Derivatives of the function, such as the first derivative, which indicates th... are included in the equation that determines this function. A differential equation is the name given to suc... or involves one or more derivatives of an unknown function. Differential equations can be divided into two c