Function in Mathematics
•Download as PPTX, PDF•
10 likes•2,846 views
This is about Some features of function, Variation of Function, Explain of function, Interval , Domain, Use of Function
Report
Share
Report
Share
Recommended
Functions in mathematics
This document defines functions and related terminology such as domain, codomain, range, one-to-one functions, onto functions, and bijections. It provides examples of graphical representations of functions and discusses concepts like whether a function is one-to-one or onto based on its graph. The pigeonhole principle is also introduced as stating that if more items are put into fewer containers, at least one container must hold multiple items.
Different types of functions
This document defines and provides examples of different types of functions, including:
- Constant functions which always output the same number.
- Identity functions where the output is equal to the input.
- Polynomial functions defined by expressions involving powers of the variable.
- Absolute value functions which output the absolute value of the input.
- Square root functions which output the square root of the input.
- Rational functions where the output is a rational expression involving the input.
It also discusses the domain and range of these different function types.
Lesson 11: Limits and Continuity
The concept of limit is a lot harder for functions of several variables than for just one. We show the more dramatric ways that a limit can fail.
Functions and its Applications in Mathematics
A function is a relation between a set of inputs and set of outputs where each input is related to exactly one output. An example is given of a function that relates shapes to colors, where each shape maps to one unique color. A function can be written as a set of ordered pairs, where the input comes first and the output second. The domain is the set of inputs, the codomain is the set of possible outputs, and the range is the set of outputs the function actually produces. A function is one-to-one if no two distinct inputs map to the same output, and onto if every element in the codomain is mapped to by at least one input.
Functions
A function is a relation between a set of inputs (domain) and set of outputs (codomain) where each input is mapped to exactly one output. There are different types of functions such as one-to-one, onto, bijective, many-to-one, and inverse functions. Functions can be represented graphically or using function notation such as f(x). Common functions include polynomial, trigonometric, exponential, logarithmic, and composite functions which are the composition of two simpler functions.
Types of functions 05272011
The document discusses various types of functions including:
- Constant functions which assign the same real number to every element of the domain.
- Linear functions which have a degree of 1 and are defined by the equation f(x)=mx+b.
- Quadratic functions which are polynomial functions of degree 2.
- Cubic/power functions which are polynomial functions of degree 3.
It also briefly describes identity, absolute value, rational, and algebraic functions. The document concludes with instructions for a group activity on identifying different function types from graphs.
7 functions
This document defines functions and relations. It discusses identifying the domain and range of functions and relations, evaluating functions, and performing operations on functions such as addition, subtraction, multiplication, division, and composition. It also covers graphing functions, including piecewise functions, absolute value functions, greatest and least integer functions. Key examples are provided to illustrate how to identify domains and ranges, evaluate functions, perform operations on functions, and graph different types of functions.
Math - Operations on Functions, Kinds of Functions
Math 17 lesson
If downloaded, please credit A.B.Balbuena of the Institute of Mathematics, University of the Philippines-Diliman
Recommended
Functions in mathematics
This document defines functions and related terminology such as domain, codomain, range, one-to-one functions, onto functions, and bijections. It provides examples of graphical representations of functions and discusses concepts like whether a function is one-to-one or onto based on its graph. The pigeonhole principle is also introduced as stating that if more items are put into fewer containers, at least one container must hold multiple items.
Different types of functions
This document defines and provides examples of different types of functions, including:
- Constant functions which always output the same number.
- Identity functions where the output is equal to the input.
- Polynomial functions defined by expressions involving powers of the variable.
- Absolute value functions which output the absolute value of the input.
- Square root functions which output the square root of the input.
- Rational functions where the output is a rational expression involving the input.
It also discusses the domain and range of these different function types.
Lesson 11: Limits and Continuity
The concept of limit is a lot harder for functions of several variables than for just one. We show the more dramatric ways that a limit can fail.
Functions and its Applications in Mathematics
A function is a relation between a set of inputs and set of outputs where each input is related to exactly one output. An example is given of a function that relates shapes to colors, where each shape maps to one unique color. A function can be written as a set of ordered pairs, where the input comes first and the output second. The domain is the set of inputs, the codomain is the set of possible outputs, and the range is the set of outputs the function actually produces. A function is one-to-one if no two distinct inputs map to the same output, and onto if every element in the codomain is mapped to by at least one input.
Functions
A function is a relation between a set of inputs (domain) and set of outputs (codomain) where each input is mapped to exactly one output. There are different types of functions such as one-to-one, onto, bijective, many-to-one, and inverse functions. Functions can be represented graphically or using function notation such as f(x). Common functions include polynomial, trigonometric, exponential, logarithmic, and composite functions which are the composition of two simpler functions.
Types of functions 05272011
The document discusses various types of functions including:
- Constant functions which assign the same real number to every element of the domain.
- Linear functions which have a degree of 1 and are defined by the equation f(x)=mx+b.
- Quadratic functions which are polynomial functions of degree 2.
- Cubic/power functions which are polynomial functions of degree 3.
It also briefly describes identity, absolute value, rational, and algebraic functions. The document concludes with instructions for a group activity on identifying different function types from graphs.
7 functions
This document defines functions and relations. It discusses identifying the domain and range of functions and relations, evaluating functions, and performing operations on functions such as addition, subtraction, multiplication, division, and composition. It also covers graphing functions, including piecewise functions, absolute value functions, greatest and least integer functions. Key examples are provided to illustrate how to identify domains and ranges, evaluate functions, perform operations on functions, and graph different types of functions.
Math - Operations on Functions, Kinds of Functions
Math 17 lesson
If downloaded, please credit A.B.Balbuena of the Institute of Mathematics, University of the Philippines-Diliman
Differential in several variables
This document contains an introduction and table of contents for a chapter on differentiation of functions with several variables. It covers topics like limits and continuity, partial derivatives, chain rules, directional derivatives, gradients, tangent planes, and finding extrema. The chapter introduces concepts like functions of two or more variables, limits, continuity, partial derivatives and their properties, implicit differentiation using the chain rule, and finding directional derivatives and gradients. It provides definitions, theorems, examples and illustrations of key concepts in multivariable calculus.
mathematical functions
This document discusses functions and their properties. It defines a function as a relation where each input is paired with exactly one output. Functions can be represented numerically in tables, visually with graphs, algebraically with explicit formulas, or verbally. The domain is the set of inputs, the codomain is the set of all possible outputs, and the range is the set of actual outputs. Functions can be one-to-one (injective) if each input maps to a unique output, or onto (surjective) if each possible output is the image of some input.
Types of function
The document discusses different types of functions including:
1) Surjective functions where the range equals the co-domain.
2) Injective functions where distinct inputs have distinct outputs.
3) Bijective functions which are both injective and surjective.
It also discusses even and odd functions, inverses, composites, and examples of calculating different functions.
APPLICATION OF PARTIAL DIFFERENTIATION
The document discusses concepts related to partial differentiation and its applications. It covers topics like tangent planes, linear approximations, differentials, Taylor expansions, maxima and minima problems, and the Lagrange method. Specifically, it defines the tangent plane to a surface at a point using partial derivatives, describes how to find the linear approximation of functions, and explains how to find maximum and minimum values of functions using critical points and the second derivative test.
PPt on Functions
1. A function is a relation where each input is paired with exactly one output.
2. To determine if a relation is a function, use the vertical line test - if any vertical line intersects more than one point, it is not a function.
3. To find the value of a function, substitute the given value for x into the function equation and simplify.
Math presentation on domain and range
This document defines key concepts related to functions including domain, co-domain, and range. It provides examples of determining the domain and range of various functions. The domain of a function is the set of inputs, the co-domain is the set of all possible outputs, and the range is the set of actual outputs. Examples show how to use inequalities to find the domain by determining when a function gives real values and how to manipulate equations to find the range.
Relations and functions
The document discusses functions, relations, domains, ranges and using vertical line tests, mappings, tables and graphs to represent and analyze functions. It provides examples of determining if a relation is a function, finding domains and ranges, modeling function rules with tables and graphs using given domains, and solving other function problems.
Lesson 8 the definite integrals
The document defines definite integrals and discusses their properties. It states that a definite integral evaluates to a single number by integrating a function over a closed interval from a lower limit to an upper limit. It gives examples of using definite integrals to find areas bounded by curves. The mean value theorem for integrals is also introduced, which states that there is a rectangle between the inscribed and circumscribed rectangles with an area equal to the region under the curve. Exercises are provided on evaluating definite integrals and applying the mean value theorem.
Functions
This document provides an introduction to functions and their properties. It defines what a function is as a mapping from a domain set to a codomain set, and introduces related concepts like domain, codomain, range, and the notation for functions. It then gives examples of specifying functions explicitly and with formulas. The document discusses properties of functions like injectivity, surjectivity, and being increasing or decreasing. It provides examples of determining if a function has these properties. The document concludes by introducing the concept of the inverse function for bijective functions.
Linear differential equation with constant coefficient
The document discusses linear differential equations with constant coefficients. It defines the order, auxiliary equation, complementary function, particular integral and general solution. It provides examples of determining the complementary function and particular integral for different types of linear differential equations. It also discusses Legendre's linear equations, Cauchy-Euler equations, and solving simultaneous linear differential equations.
Composition Of Functions
Composing functions involves taking two functions, f(x) and g(x), and substituting the output of g(x) wherever x appears in f(x). For the functions f(x) = 3x^2 + 4 and g(x) = 6x - 8, the composition f(g(x)) is found by substituting g(x) = 6x - 8 for x in f(x), giving f(g(x)) = 3(6x - 8)^2 + 4, which simplifies to 108x^2 - 288x + 22.
Jacobians new
Changing variable is something we come across very often in Integration. There are many
reasons for changing variables but the main reason for changing variables is to convert the
integrand into something simpler and also to transform the region into another region which is
easy to work with. When we convert into a new set of variables it is not always easy to find the
limits. So, before we move into changing variables with multiple integrals we first need to see
how the region may change with a change of variables. In order to change variables in an
integration we will need the Jacobian of the transformation.
Limit of Function And Its Types
The document discusses different types of limits in calculus and analysis. A limit describes the behavior of a function near a particular input value. There are several types of limits including one-sided limits as x approaches a from the left or right, direct substitution limits where the value is simply substituted, and limits involving techniques like factoring, rationalization, as x approaches infinity, trigonometric functions, or the number e.
Inverse Functions
1) The document discusses finding the inverse of functions by interchanging the x and y variables and solving for y. It provides examples of finding the inverses of f(x)=3x-7 and g(x)=2x^3+1.
2) It also discusses verifying inverses by checking if the composition of a function and its inverse equals x. And finding inverses of functions with restricted domains, including an example of f(x)=sqrt(x+4).
3) Finally, it discusses the relationship between a function being one-to-one and having an inverse function, both algebraically and graphically.
Composite functions
Composite functions are formed by taking the output of one function and using it as the input of another function. This is shown notationally as f(g(x)), where the result of g(x) is used as the input for f. Changing the order of the functions changes the result, as the output of the inner function determines the input to the outer function. Examples show evaluating composite functions by substituting the output of the inner function into the outer function and simplifying.
Differentiation
The document discusses differentiation and its history. It was independently developed in the 17th century by Isaac Newton and Gottfried Leibniz. Differentiation allows the calculation of instantaneous rates of change and is used in many areas including mathematics, physics, engineering and more. Key concepts covered include calculating speed, estimating instantaneous rates of change, the rules for differentiation, and differentiation of expressions with multiple terms.
Relation and function
A function is a special type of relation where each input is mapped to exactly one output. For a relation to be a function, each x-value in the domain can only correspond to one y-value in the range. A relation specifies the connections between two variables but does not require each input to map to a single output, whereas a function uniquely associates each input with a unique output. It is important to distinguish the independent variable, which determines the possible inputs or domain, from the dependent variable, whose outputs or range depend on the values of the independent variable.
1551 limits and continuity
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Double Integrals
The double integral of a function f(x,y) over a bounded region R in the xy-plane is defined as the limit of Riemann sums that approximate the total value of f over R. This double integral is denoted by the integral of f(x,y) over R and its value is independent of the subdivision used in the Riemann sums. Properties and methods for evaluating double integrals are discussed, along with applications such as finding the area, volume, mass, and moments of inertia. Changes of variables in double integrals using the Jacobian are also covered.
Indefinite Integral
Here are the steps to solve this problem:
(a) Let t = time and y = height. Then the differential equation is:
dy/dt = -32 ft/sec^2
Integrate both sides:
∫dy = ∫-32 dt
y = -32t + C
Initial conditions: at t = 0, y = 0
0 = -32(0) + C
C = 0
Therefore, the equation is: y = -32t
When y = 0 (the maximum height), t = 0.625 sec
(b) Put t = 0.625 sec into the equation:
y = -32(0.625) = -20 ft
Graphing Functions and Their Transformations
This document discusses functions and their transformations. It introduces the basic linear function y=mx+b, and how changing the slope m or y-intercept b affects the graph. It then demonstrates how transformations like shifting the graph along the x- or y-axis, stretching or shrinking, and reflections change the function. Finally, it briefly covers quadratic, cubic, logarithmic, and exponential functions, and challenges the reader to match equation and graph.
Pc9 8 powersrootsc
De Moivre's theorem provides a formula for raising complex numbers to rational powers including negative exponents and fractions. The theorem states that (a + bi)^n = a^n(cos(nθ) + i*sin(nθ)) where a and b are real numbers, i is the imaginary unit, n is any rational number, and θ is the angle whose tangent is b/a. Classwork on powers and roots of complex numbers using De Moivre's theorem is due tomorrow for students who don't finish it in class today.
More Related Content
What's hot
Differential in several variables
This document contains an introduction and table of contents for a chapter on differentiation of functions with several variables. It covers topics like limits and continuity, partial derivatives, chain rules, directional derivatives, gradients, tangent planes, and finding extrema. The chapter introduces concepts like functions of two or more variables, limits, continuity, partial derivatives and their properties, implicit differentiation using the chain rule, and finding directional derivatives and gradients. It provides definitions, theorems, examples and illustrations of key concepts in multivariable calculus.
mathematical functions
This document discusses functions and their properties. It defines a function as a relation where each input is paired with exactly one output. Functions can be represented numerically in tables, visually with graphs, algebraically with explicit formulas, or verbally. The domain is the set of inputs, the codomain is the set of all possible outputs, and the range is the set of actual outputs. Functions can be one-to-one (injective) if each input maps to a unique output, or onto (surjective) if each possible output is the image of some input.
Types of function
The document discusses different types of functions including:
1) Surjective functions where the range equals the co-domain.
2) Injective functions where distinct inputs have distinct outputs.
3) Bijective functions which are both injective and surjective.
It also discusses even and odd functions, inverses, composites, and examples of calculating different functions.
APPLICATION OF PARTIAL DIFFERENTIATION
The document discusses concepts related to partial differentiation and its applications. It covers topics like tangent planes, linear approximations, differentials, Taylor expansions, maxima and minima problems, and the Lagrange method. Specifically, it defines the tangent plane to a surface at a point using partial derivatives, describes how to find the linear approximation of functions, and explains how to find maximum and minimum values of functions using critical points and the second derivative test.
PPt on Functions
1. A function is a relation where each input is paired with exactly one output.
2. To determine if a relation is a function, use the vertical line test - if any vertical line intersects more than one point, it is not a function.
3. To find the value of a function, substitute the given value for x into the function equation and simplify.
Math presentation on domain and range
This document defines key concepts related to functions including domain, co-domain, and range. It provides examples of determining the domain and range of various functions. The domain of a function is the set of inputs, the co-domain is the set of all possible outputs, and the range is the set of actual outputs. Examples show how to use inequalities to find the domain by determining when a function gives real values and how to manipulate equations to find the range.
Relations and functions
The document discusses functions, relations, domains, ranges and using vertical line tests, mappings, tables and graphs to represent and analyze functions. It provides examples of determining if a relation is a function, finding domains and ranges, modeling function rules with tables and graphs using given domains, and solving other function problems.
Lesson 8 the definite integrals
The document defines definite integrals and discusses their properties. It states that a definite integral evaluates to a single number by integrating a function over a closed interval from a lower limit to an upper limit. It gives examples of using definite integrals to find areas bounded by curves. The mean value theorem for integrals is also introduced, which states that there is a rectangle between the inscribed and circumscribed rectangles with an area equal to the region under the curve. Exercises are provided on evaluating definite integrals and applying the mean value theorem.
Functions
This document provides an introduction to functions and their properties. It defines what a function is as a mapping from a domain set to a codomain set, and introduces related concepts like domain, codomain, range, and the notation for functions. It then gives examples of specifying functions explicitly and with formulas. The document discusses properties of functions like injectivity, surjectivity, and being increasing or decreasing. It provides examples of determining if a function has these properties. The document concludes by introducing the concept of the inverse function for bijective functions.
Linear differential equation with constant coefficient
The document discusses linear differential equations with constant coefficients. It defines the order, auxiliary equation, complementary function, particular integral and general solution. It provides examples of determining the complementary function and particular integral for different types of linear differential equations. It also discusses Legendre's linear equations, Cauchy-Euler equations, and solving simultaneous linear differential equations.
Composition Of Functions
Composing functions involves taking two functions, f(x) and g(x), and substituting the output of g(x) wherever x appears in f(x). For the functions f(x) = 3x^2 + 4 and g(x) = 6x - 8, the composition f(g(x)) is found by substituting g(x) = 6x - 8 for x in f(x), giving f(g(x)) = 3(6x - 8)^2 + 4, which simplifies to 108x^2 - 288x + 22.
Jacobians new
Changing variable is something we come across very often in Integration. There are many
reasons for changing variables but the main reason for changing variables is to convert the
integrand into something simpler and also to transform the region into another region which is
easy to work with. When we convert into a new set of variables it is not always easy to find the
limits. So, before we move into changing variables with multiple integrals we first need to see
how the region may change with a change of variables. In order to change variables in an
integration we will need the Jacobian of the transformation.
Limit of Function And Its Types
The document discusses different types of limits in calculus and analysis. A limit describes the behavior of a function near a particular input value. There are several types of limits including one-sided limits as x approaches a from the left or right, direct substitution limits where the value is simply substituted, and limits involving techniques like factoring, rationalization, as x approaches infinity, trigonometric functions, or the number e.
Inverse Functions
1) The document discusses finding the inverse of functions by interchanging the x and y variables and solving for y. It provides examples of finding the inverses of f(x)=3x-7 and g(x)=2x^3+1.
2) It also discusses verifying inverses by checking if the composition of a function and its inverse equals x. And finding inverses of functions with restricted domains, including an example of f(x)=sqrt(x+4).
3) Finally, it discusses the relationship between a function being one-to-one and having an inverse function, both algebraically and graphically.
Composite functions
Composite functions are formed by taking the output of one function and using it as the input of another function. This is shown notationally as f(g(x)), where the result of g(x) is used as the input for f. Changing the order of the functions changes the result, as the output of the inner function determines the input to the outer function. Examples show evaluating composite functions by substituting the output of the inner function into the outer function and simplifying.
Differentiation
The document discusses differentiation and its history. It was independently developed in the 17th century by Isaac Newton and Gottfried Leibniz. Differentiation allows the calculation of instantaneous rates of change and is used in many areas including mathematics, physics, engineering and more. Key concepts covered include calculating speed, estimating instantaneous rates of change, the rules for differentiation, and differentiation of expressions with multiple terms.
Relation and function
A function is a special type of relation where each input is mapped to exactly one output. For a relation to be a function, each x-value in the domain can only correspond to one y-value in the range. A relation specifies the connections between two variables but does not require each input to map to a single output, whereas a function uniquely associates each input with a unique output. It is important to distinguish the independent variable, which determines the possible inputs or domain, from the dependent variable, whose outputs or range depend on the values of the independent variable.
1551 limits and continuity
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Double Integrals
The double integral of a function f(x,y) over a bounded region R in the xy-plane is defined as the limit of Riemann sums that approximate the total value of f over R. This double integral is denoted by the integral of f(x,y) over R and its value is independent of the subdivision used in the Riemann sums. Properties and methods for evaluating double integrals are discussed, along with applications such as finding the area, volume, mass, and moments of inertia. Changes of variables in double integrals using the Jacobian are also covered.
Indefinite Integral
Here are the steps to solve this problem:
(a) Let t = time and y = height. Then the differential equation is:
dy/dt = -32 ft/sec^2
Integrate both sides:
∫dy = ∫-32 dt
y = -32t + C
Initial conditions: at t = 0, y = 0
0 = -32(0) + C
C = 0
Therefore, the equation is: y = -32t
When y = 0 (the maximum height), t = 0.625 sec
(b) Put t = 0.625 sec into the equation:
y = -32(0.625) = -20 ft
What's hot (20)
Linear differential equation with constant coefficient
Linear differential equation with constant coefficient
Viewers also liked
Graphing Functions and Their Transformations
This document discusses functions and their transformations. It introduces the basic linear function y=mx+b, and how changing the slope m or y-intercept b affects the graph. It then demonstrates how transformations like shifting the graph along the x- or y-axis, stretching or shrinking, and reflections change the function. Finally, it briefly covers quadratic, cubic, logarithmic, and exponential functions, and challenges the reader to match equation and graph.
Pc9 8 powersrootsc
De Moivre's theorem provides a formula for raising complex numbers to rational powers including negative exponents and fractions. The theorem states that (a + bi)^n = a^n(cos(nθ) + i*sin(nθ)) where a and b are real numbers, i is the imaginary unit, n is any rational number, and θ is the angle whose tangent is b/a. Classwork on powers and roots of complex numbers using De Moivre's theorem is due tomorrow for students who don't finish it in class today.
Every day application of functions and relations
This document discusses various applications of functions and relations in mathematics. It provides four examples: 1) Money can be viewed as a function of time, allowing businesses to track spending over time. 2) Temperature depends on many factors but results in a single output, allowing it to be viewed as a function. 3) The locations of two people can be plotted as functions of time, with their lines crossing indicating when they meet. 4) Set theory has applications in analysis, boolean algebra, and topology. It provides the foundation for concepts like limit points and continuity of functions.
Complex number
This document contains information about Md. Arifuzzaman, a lecturer in the Department of Natural Sciences at the Faculty of Science and Information Technology, Daffodil International University. It includes his employee ID, designation, department, faculty, personal webpage, email, and phone number. The document also provides an overview of complex numbers, including their history, the number system, definitions of complex numbers, operations like addition and multiplication of complex numbers, and applications of complex numbers.
Complex Numbers And Appsfeb
1. A complex number can be represented as a sum of a real number and an imaginary number in the form a + bi, where a is the real part and b is the imaginary part.
2. Complex numbers can represent vectors and are useful for representing quantities that involve both magnitude and direction, such as forces.
3. Operations like addition, subtraction, multiplication, and division can be performed on complex numbers by separately applying the operations to the real and imaginary parts.
Data structure
A data type refers to the type of values that variables hold and includes a set of values and operations. There are primitive/built-in data types that are predefined by languages like int and float, and abstract data types that separate the representation of values from operations. Common data types include boolean, char, float, double, int and string. A data structure organizes data to reduce complexity and increase efficiency of algorithms. Common linear data structures include arrays, linked lists, stacks and queues, while trees and graphs are examples of non-linear data structures.
Data structure
Data structures are a way to organize data in a computer so it can be used efficiently. Common data structures include arrays, stacks, queues, linked lists, trees, and graphs. Arrays store elements in a linear order, stacks follow last-in first-out access with push and pop, queues are first-in first-out using enqueue and dequeue, and linked lists, trees and graphs have nodes connected by links or edges. These data structures enable efficient operations like inserting, deleting and searching for data.
Fairylights...Principles and Definition of Ohms Law
This document discusses Ohm's law and basic electrical circuit principles. It defines resistance, current, voltage, and other concepts. It explains that Ohm's law states that voltage is directly proportional to current. Kirchhoff's laws are also summarized, including that current is the same in series circuits and the total current into a parallel branch equals the total current out. Examples are provided of calculating resistance using Ohm's law and of the effects of adding components like cells or lamps to series and parallel circuits.
Equations Complex Numbers Quadratic Expressions Inequalities Absolute Value E...
Equations
Complex Numbers
Quadratic Expressions
Inequalities
Absolute Value Equations & Inequalities
Applications
Big Data As a service - Sethuonline.com | Sathyabama University Chennai
An Efficient Framework for Data As A Service in Hadoop EcoSystem.
R.Sethuraman M.E,(PhD).,
Assistant Professor,
Faculty of Computing,
Dept of Computer Science Engineering,
Sathyabama University
http://Sethuonline.com
Set data structure 2
The document discusses various data structures for representing sets and algorithms for performing set operations on those data structures. It describes representing sets as linked lists, trees, hash tables, and bit vectors. For linked lists, it provides algorithms for union, intersection, difference, equality testing, and other set operations. It also discusses how bit vectors can be used to efficiently represent the presence or absence of elements in a set and perform operations using bitwise logic.
Linked lists in Data Structure
A linked list is a data structure made up of nodes that are connected to each other via pointers. Each node contains a data field as well as a pointer to the next node. Linked lists allow dynamic sizes and efficient insertion/deletion of nodes. Common linked list operations include appending nodes to the end, inserting nodes in a sorted order, traversing the list to display nodes, and deleting nodes. The code sample shows a template for a linked list class with functions to implement these operations by traversing the list and manipulating the node pointers accordingly.
Introduction to data structure
This document provides an introduction to data structures. It defines data structures as a way of organizing data so that it can be used efficiently. The document then discusses basic terminology, why data structures are important, how they are studied, and how they are classified as simple or compound, and linear or non-linear. It proceeds to describe common data structures like arrays, stacks, queues, linked lists, trees, and graphs, and how they support basic operations. The document concludes by discussing how to select an appropriate data structure based on the problem constraints and required operations.
Data Structure (Stack)
Stack is a data structure that only allows elements to be added and removed from one end, called the top. It has components like a top pointer variable, elements that hold data, and a maximum size. Stacks can be implemented as arrays or linked lists. The main operations on a stack are push, which adds an element to the top, and pop, which removes an element from the top. These operations work similarly in array and linked list implementations, by incrementing or decrementing the top pointer and adding or removing the top element.
Calculus Lecture 1
In this lecture 1 we are going to cover :
Equations
Complex Numbers
Quadratic Expressions
Inequalities
Absolute Value Equations & Inequalities
Applications
Complex Numbers
Complex numbers have various applications in mechanical engineering, including air foil design, control theory, quantum mechanics, and relativity. In air foil design, the Joukowsky transform uses complex analysis to model air flow around a foil by distorting it from potential flow around a cylinder. Control theory involves using complex numbers to represent rotations and model systems like cruise control. Quantum mechanics formulations make use of complex wave functions and Hilbert spaces. Relativity formulas sometimes use imaginary time to simplify metrics in spacetime.
Effective Semantic Web Service Composition Framework Based on QoS
Effective Semantic Web Service Composition Framework Based on QoS
by
R.Sethuraman
Research Scholar
Sathyabama University
Set data structure
Sets are collections of unique elements that do not allow repetition. Elements must satisfy membership rules to be included in a set. Common set operations include union, intersection, difference and subset testing. Sets can be mutable, allowing addition and removal of elements, or immutable. Hash functions are used to map elements to locations in hash tables, enabling fast set operations on large collections. Spelling checkers use hash tables to implement sets and check dictionary words against input words.
Viewers also liked (20)
Fairylights...Principles and Definition of Ohms Law
Fairylights...Principles and Definition of Ohms Law
Equations Complex Numbers Quadratic Expressions Inequalities Absolute Value E...
Equations Complex Numbers Quadratic Expressions Inequalities Absolute Value E...
Big Data As a service - Sethuonline.com | Sathyabama University Chennai
Big Data As a service - Sethuonline.com | Sathyabama University Chennai
Effective Semantic Web Service Composition Framework Based on QoS
Effective Semantic Web Service Composition Framework Based on QoS
Similar to Function in Mathematics
3. Functions II.pdf
Properties of Functions
Odd and Even Functions
Periodic Functions
Monotonic Functions
Bounded Functions
Maxima and Minima of Functions
Inverse Function
Sequence and Series
4.1 inverse functions
The document discusses inverse functions. An inverse function reverses the input and output of a function. For a function f(x) to have an inverse function f-1(y), it must be one-to-one, meaning that different inputs produce different outputs. The inverse of a function f(x) is found by solving the original function equation for x in terms of y. Examples show finding the inverse of specific functions like f(x) = x - 5 by solving for x. A function is one-to-one if for any two different inputs u and v, their outputs f(u) and f(v) are also different.
2. Functions I.pdf
Types of Functions
Constant, Step, and Piecewise functions
Power functions
Polynomial Functions
Rational Functions
Algebraic Functions
Transcendental Functions
.
The document discusses functions and their characteristics including domain, range, and inverse functions. It provides examples of evaluating, adding, multiplying, and dividing functions. It also covers compound functions, using graphs to determine domain and range, and recognizing functions using the vertical line test. Logarithms are also briefly introduced.
Calculus 1 Lecture Notes (Functions and Their Graphs)
Calculus 1 Lecture Notes
Functions and Their Graphs
Convex Analysis and Duality (based on "Functional Analysis and Optimization" ...
In this presentation, we explain the monograph ”Functional Analysis and Optimization” by Kazufumi Ito
https://kito.wordpress.ncsu.edu/files/2018/04/funa3.pdf
Our goal in this presentation is to
-Understand the basic notions of functional analysis
lower-semicontinuous, subdifferential, conjugate functional
- Understand the formulation of duality problem
primal (P), perturbed (Py), and dual (P∗) problem
-Understand the primal-dual relationships
inf(P)≤sup(P∗), inf(P) = sup(P∗), inf supL≤sup inf L
Lesson 23: Antiderivatives (slides)
We can define the area of a curved region by a process similar to that by which we determined the slope of a curve: approximation by what we know and a limit.
Lesson 23: Antiderivatives (slides)
At times it is useful to consider a function whose derivative is a given function. We look at the general idea of reversing the differentiation process and its applications to rectilinear motion.
Limits and Continuity - Intuitive Approach part 1
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
U1 Cn2 Functions
Functions relate dependent and independent variables, where the dependent variable is determined by the independent variable. Functions can be expressed as equations, tables, or graphs. Even functions are symmetric about the y-axis and odd functions are symmetric about the origin. The domain of a function is the set of valid inputs and the range is the set of outputs. A function can be restricted to only certain domain values or composed of multiple functions.
Definitionand properties of measurable function.pptx
definition of measurable function
some theorem
properties
Sadiq Hussain
The document discusses the inverse tangent function, tan-1(x). It begins by reviewing one-to-one functions and their inverses. Examples are provided to illustrate one-to-one functions. The lesson aim is to teach students the inverse tangent function. The domain of tan-1(x) is all real numbers, and the range is (-π/2, π/2). The graph of tan-1(x) is the reflection of the tangent function graph over the line y=x. Students are asked to find the values of various inverse tangent functions. Homework problems are assigned involving evaluating inverse tangent functions without a calculator.
GENERAL MATHEMATICS - Week 3.pptx
One-to-one functions have the property that each element of the range corresponds to exactly one element of the domain. An inverse function is obtained by switching the x and y variables of the original function. For a function to have an inverse, it must be one-to-one. The document provides examples of finding the inverse of various functions by changing f(x) to y, interchanging x and y, and solving for y in terms of x.
1.6 inverse function (optional)
The document discusses inverse functions. It begins by defining a function f(x) that takes an input x and produces an output y. It then introduces the concept of finding the inverse of this function - the reverse procedure that takes the output y and finds the corresponding input(s) x. This reverse procedure may or may not be a function. For it to be a function, f(x) must be one-to-one, meaning that different inputs x produce different outputs y. The document provides examples and diagrams to illustrate one-to-one functions and their inverses. It concludes that if f(x) is one-to-one, then its inverse function f-1(y) is well-defined
5.1 Defining and visualizing functions. Dynamic slides.
Selected items from the Introduction to set theory and to methodology and philosophy of mathematics and computer programming.
29 inverse functions x
The document discusses inverse functions. An inverse function reverses the input and output of a function. For a function f(x) to have an inverse function f^-1(y), it must be one-to-one, meaning that different inputs map to different outputs. The inverse of f(x) is obtained by solving the original function equation for x in terms of y. Examples show how to determine if a function has an inverse and how to calculate the inverse function. For non one-to-one functions like f(x)=x^2, the inverse procedure is not a well-defined function.
Chapter on Functions and Graphs.ppt
A relation is a set of ordered pairs. A function is a relation where each domain value has only one range value. To determine if a relation is a function, use the vertical line test or check if each x-value only has one y-value. An equation defines a function if each x only corresponds to one y when solving the equation for y. Piecewise functions are defined by two or more equations over different parts of the domain. The slope of a line is rise over run and can be found by calculating change in y over change in x between any two points. You can write the equation of a line from its point-slope form or by finding the slope between two points and plugging into point-slope form
7.4 inverse functions
1. An inverse relation maps the outputs of a function back to the inputs by switching the domain and range.
2. To find the inverse of a function, switch x and y and solve for y.
3. Two functions are inverse functions if applying one function after the other returns the original input.
5.1 Defining and visualizing functions. A handout.
This document introduces concepts related to functions including:
- Defining functions in terms of unique mappings between inputs and outputs
- Distinguishing between total, partial, and non-functions
- Specifying domains and ranges
- Using vertical line tests to identify functions from graphs
- Examples of functions defined by formulas or mappings
Calc 5.3
This document discusses inverse functions and their derivatives. It defines inverse functions as switching the x- and y-values of a function to "undo" the original function. A function has an inverse only if it passes the horizontal line test. The derivative of an inverse function at a point equals the reciprocal of the derivative of the original function at the corresponding point.
Similar to Function in Mathematics (20)
Calculus 1 Lecture Notes (Functions and Their Graphs)
Calculus 1 Lecture Notes (Functions and Their Graphs)
Convex Analysis and Duality (based on "Functional Analysis and Optimization" ...
Convex Analysis and Duality (based on "Functional Analysis and Optimization" ...
Definitionand properties of measurable function.pptx
Definitionand properties of measurable function.pptx
5.1 Defining and visualizing functions. Dynamic slides.
5.1 Defining and visualizing functions. Dynamic slides.
5.1 Defining and visualizing functions. A handout.
5.1 Defining and visualizing functions. A handout.
Recently uploaded
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
CACJapan - GROUP Presentation 1- Wk 4.pdf
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdTop five deadliest dog breeds in America
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
Recently uploaded (20)
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Function in Mathematics
- 2. Presentation On: Function Submitted To: MD. ARIFUZZAMAN (AZ) Lecturer in Mathematic, Department of Natural Sciences Submitted By: MD. MAHABUB JAHAN ID: 142-15-4054
- 3. Slide overview Function Some features of function Variation of Function Explain of function Interval Domain: Use of Function
- 4. Function Let, X and Y are two on empty set. A formula/rule establishing relation between the numbers of X and Y. It assigns each value of X to each value of Y then f is called a Function.
- 5. Some features of function Even and odd function: If f(-x)=f(x), so f(x) is call even function. If f(x)=f(x), so f(x) is called odd function. One-one function: f(x1)=f(x2), if x1=x2 f(x1)=f(x2), if x1≠ x2
- 6. Onto function: A function f:x→ 𝑌 a set to be onto function if for every y∈Y there is a value x∈ 𝑋such that f(x)=y Onto Function Not onto Function
- 7. Variation of Function 1. Algebraic function Algebraic function are two kinds of *Polynomial function Ex: y=x2+5x-9 *Rational function Ex: R(x) = 𝑝(𝑥) 𝑞(𝑥) , 𝑞 𝑥 ≠ 0 2. Trigonometric function Example: y=sin 𝑥
- 8. 3. Exponential function Example: y=𝑒 𝑥 4. Logarithmic function Example: y=logx
- 9. Explain of function y=f(x) y is a function of x. Where y is a dependent variable and x is an independent variable.
- 10. Interval ( )→ 𝑂𝑝𝑒𝑛 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 Ex: 1< 𝑥 < 5 (1, 5) [ ]→ 𝐶𝑙𝑜𝑠𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 Ex: 1≤ 𝑥 ≤ 5 [1, 5]
- 11. Domain: • There are two kinds of Domain. 1. Natural Domain Y=f(x), Df=ℝ 2. Restricted Domain y=x, Df= 0, ∞
- 12. Use of Function: • We use function in Programming Language to create program or software just like C/C++. • We can solve many difficult mathematics by using Function. • Many Industry, Bank and other organization use function for many reason.