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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
- Definitions: Mathematics 12: PTB by Muzzammil Subhan @fsc-part2-ptb
- is given below =====Sample===== * **Polynomial Function:** A function of the form $P(x)=a_0 x^0+a_1 x^1+a_2 x^2+\ldots . .+a_{n-1} x^{n-1}+a_n x^n$ is called polynomial function where $n \in W$ and $a_0, a_1, a_2, \ldots, a_n \in R$. * **Linear Function:** A function of the form $f(x)=a x+b$ where $a,
- Khuram Ali Khan
- ip Pečarić, Popoviciu type inequalities via Green function and generalized Montgomery identity, Mathematical... .com/18-118/Popoviciu-type-inequalities-via-Green-function-and-generalized-Montgomery-identity|Link]]) - L... ip Pečarić, Popoviciu type inequalities via Green function and Taylor polynomial, Turk. J. Math, (2016) 40(2... Integral form of Popoviciu inequality for convex function, Proceedings of the Pakistan Academy of Sciences,
- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- objects is called - Relation - Sets - Function - None of these - The objects in a set are ... \sim p \wedge \sim q$ - 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
- 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
- Definitions: Mathematics 11: PTB by Muzzammil Subhan @fsc-part1-ptb
- given below =====Sample===== * **Exponential Function:** A function in which variable appear as power of a constant is called exponential Function. e.g. $y=2^x$, $y=e^x$ * **Logarithmic Function:** The functions $f(x)=\log_a x$ and $f(x)=\log_e x$ are
- 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