Yoaniker morles2
•
0 likes•40 views
1) The differential equation dy/dx = xy + 3x - y - 3 / xy - 2x + 4y - 8 is separable. 2) The differential equation y' = 2y + x^2 + 5 is linear. 3) The differential equation (y^2 + yx)dx - x^2 dy = 0 is homogeneous.
Report
Share
Report
Share
Download to read offline
Recommended
Impicit differentiation
This document discusses techniques for finding derivatives of implicit functions. It provides examples of finding the derivative dy/dx for equations:
1) 2x + 3y = sinx
2) tan−1(x2 + y2) = a2
3) y = x sin(a + y)
4) y = √(x + √(x + √(x + − −-------))
The key steps are to differentiate both sides of the equation with respect to x and then isolate dy/dx.
Euler's and picard's
- The document discusses numerical methods for solving first order differential equations, namely Picard's method and Euler's method.
- Picard's method involves iteratively replacing y with the previous approximation in the differential equation to obtain better approximations that converge to the solution.
- Euler's method approximates the solution at the next point by the current value plus the rate of change times the change in x. This provides a first order approximation to the solution.
2.5 dividing integers ws day 2
The document contains examples and practice problems for evaluating expressions with integers. It includes:
1) Worked examples of evaluating expressions when given values for variables, such as finding 11 + 4(3) = 34 and 6(17)(3) = 5.
2) Practice problems for students to solve, such as evaluating expressions when k = -36, m = 6, and n = 3.
3) Exercises for students to try on their own, following the order of operations with integers.
S1230109
- The document discusses new special functions K_n(x) defined in terms of Legendre polynomials P_n(x).
- Recurrence relations and differential equations for the new functions K_n(x) are derived.
- Properties of Legendre polynomials such as the generating function and orthogonality are used to derive relationships between the K_n(x) functions.
Evaluating Algebraic Expression
You will learn how to evaluate algebraic expressions by substitution.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
differential equation Lecture#12
This lecture will improve your knowledge in differential equation
lecture is by Lecturer AZEEM INAAM of SMI university.
Newton Cotes Integration Method, Open Newton Cotes, Closed Newton Cotes Gauss...
the description about weddle's rule and newton cotes method and Gaussian quadrature method of numerical computing course.It contains introduction , Rules and Examples
Arithmetic sequence 10
This document defines arithmetic sequences and series. It provides examples of arithmetic sequences where each term is obtained by adding a constant to the previous term. Formulas are given for finding the nth term and the sum of the first n terms of an arithmetic sequence. Examples are worked through of finding missing terms, the nth term, and the sum of sequences. Arithmetic means are also defined and formulas are provided for finding the average of two numbers and the average of a data set.
Recommended
Impicit differentiation
This document discusses techniques for finding derivatives of implicit functions. It provides examples of finding the derivative dy/dx for equations:
1) 2x + 3y = sinx
2) tan−1(x2 + y2) = a2
3) y = x sin(a + y)
4) y = √(x + √(x + √(x + − −-------))
The key steps are to differentiate both sides of the equation with respect to x and then isolate dy/dx.
Euler's and picard's
- The document discusses numerical methods for solving first order differential equations, namely Picard's method and Euler's method.
- Picard's method involves iteratively replacing y with the previous approximation in the differential equation to obtain better approximations that converge to the solution.
- Euler's method approximates the solution at the next point by the current value plus the rate of change times the change in x. This provides a first order approximation to the solution.
2.5 dividing integers ws day 2
The document contains examples and practice problems for evaluating expressions with integers. It includes:
1) Worked examples of evaluating expressions when given values for variables, such as finding 11 + 4(3) = 34 and 6(17)(3) = 5.
2) Practice problems for students to solve, such as evaluating expressions when k = -36, m = 6, and n = 3.
3) Exercises for students to try on their own, following the order of operations with integers.
S1230109
- The document discusses new special functions K_n(x) defined in terms of Legendre polynomials P_n(x).
- Recurrence relations and differential equations for the new functions K_n(x) are derived.
- Properties of Legendre polynomials such as the generating function and orthogonality are used to derive relationships between the K_n(x) functions.
Evaluating Algebraic Expression
You will learn how to evaluate algebraic expressions by substitution.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
differential equation Lecture#12
This lecture will improve your knowledge in differential equation
lecture is by Lecturer AZEEM INAAM of SMI university.
Newton Cotes Integration Method, Open Newton Cotes, Closed Newton Cotes Gauss...
the description about weddle's rule and newton cotes method and Gaussian quadrature method of numerical computing course.It contains introduction , Rules and Examples
Arithmetic sequence 10
This document defines arithmetic sequences and series. It provides examples of arithmetic sequences where each term is obtained by adding a constant to the previous term. Formulas are given for finding the nth term and the sum of the first n terms of an arithmetic sequence. Examples are worked through of finding missing terms, the nth term, and the sum of sequences. Arithmetic means are also defined and formulas are provided for finding the average of two numbers and the average of a data set.
Numeros reales
The document defines key concepts related to sets and real numbers. It discusses definitions of sets, set operations including union, intersection, difference, and complement. It then defines real numbers and their properties, including that natural numbers, integers, rational and irrational numbers are subsets of real numbers. It also discusses inequalities and their properties, absolute value, and inequalities involving absolute value. Examples are provided to illustrate each concept.
ARITHMETIC SEQUENCE, MEAN AND SERIES WEEK 2 QUARTER 1
The presentation has first a drill on signed numbers. Then, it provides a definition examples and activities for the topics, " Finding the nth term of an Arithmetic Sequence, Arithmetic Mean and Arithmetic Series.".
Evaluating Algebraic Expressions - Math 7 Q2W4 LC1
This document provides instruction on evaluating algebraic expressions. It begins with an opening prayer related to mathematics. It then states the learning competency and objectives which are to evaluate expressions for given variable values and real-life expressions. Various math terms are defined such as constant, variable, term, and exponent. Examples of evaluating multi-step expressions are provided using the order of operations. The document also discusses substituting values for variables and performing operations. Real-life examples on costs are presented for students to evaluate. In closing, key ideas are summarized in notes on algebraic expressions, constants, variables, and the process of evaluating expressions.
Aplicación propiedades integral
1. The document discusses properties of definite integrals, including: the integral of kf(x) from a to b equals k times the integral of f(x) from a to b; the integral of f(x) + g(x) from a to b equals the integral of f(x) from a to b plus the integral of g(x) from a to b; and the integral of f(x) - g(x) from a to b equals the integral of f(x) from a to b minus the integral of g(x) from a to b.
2. It provides an example problem that applies these properties to evaluate the integral of (2x^3 - 3
Math 6 [Division of Integers] ppt Q2 W9
Class Observation in Math 6 on Division of Integers for Grade 6 @ Conalum Elementary School, Inopacan, Leyte
Simultaneous equations
Simultaneous equations in two variables. Finding solution to systems of linear equations by graphing. Solving systems of linear equations by elimination and substitution method.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Solving systems of equations by substitution
ejaymathact.wordpress.com
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Solving systems of Equations by Elimination
The document provides steps for solving systems of equations using the elimination method with addition and subtraction:
1) Put both equations in standard form.
2) Determine which variable to eliminate by finding terms with the same coefficients.
3) Add or subtract the equations to eliminate the chosen variable.
4) Substitute values back into one equation to find the other variable.
5) Check that the solution satisfies both original equations.
Ordinary Differential Equations: Variable separation method
First order and first degree differential equations, Variable separation method ,17 solved problems with detailed simplification
Sequence and series
The document discusses arithmetic sequences and series. An arithmetic sequence is a sequence where the difference between successive terms is constant. The nth term can be calculated using the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. The sum of an arithmetic sequence is called an arithmetic series, which can be calculated using the formula Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term.
Adding and Subtracting Polynomials - Math 7 Q2W4 LC1
This document discusses adding and subtracting polynomials. It defines key polynomial terms like monomial, binomial, and trinomial. It explains that when adding or subtracting polynomials, only like terms can be combined by adding or subtracting their coefficients while keeping the variable parts the same. Examples are provided to demonstrate adding and subtracting polynomials, including real-life word problems involving combining polynomial expressions to model total areas or profits. The overall goal is for students to learn how to perform operations on polynomials.
Derivatives of inverse trig functions
This document discusses derivatives of inverse trigonometric functions and provides examples of taking their derivatives. It contains the following key points:
1. The derivatives of the main inverse trigonometric functions are given as fractions involving the term 1/(1-x^2).
2. Two examples are worked through, differentiating compositions of inverse trig functions and using trigonometric substitutions.
3. The last example proves that if y = sin^(-1)(2x/(1+x^2)), then (1+x^2)dy/dx = 2 by making a u-substitution of x = tanθ.
Solving Quadratic Equations by Factoring
This document provides examples for solving quadratic equations by factoring. It explains how to solve equations of the form ax^2 + bx = 0 and ax^2 + bx + c = 0 by factoring and setting each factor equal to zero. Some example problems are worked out step-by-step, including solving 11x^2 - 13x = 8x - 3x^2 and 7x^2 + 18x = 10x^2 + 12x. The document also discusses using the fact that the roots of ax^2 + bx = 0 are x = 0 and x = -b/a to solve equations without factoring. It concludes by explaining how to use the zero product property to solve a quadratic
Evaluating an Algebraic Expression
This presentation is intended to help the education students by giving an idea on how they will use technology in education specially in teaching mathematics.
Surds revision card
1. Rationalizing surds means removing the radical sign from the denominator by multiplying the numerator and denominator by the conjugate.
2. The conjugate of a surd term keeps the radicand the same but changes the sign of any terms outside the radical.
3. Rationalizing terms of the form a - b involves multiplying the numerator and denominator by the conjugate a + b.
Presentación álgebra
This document contains information about a group project from the Universidad Politécnica Territorial del Estado Lara Andrés Eloy Blanco in Barquisimeto, Venezuela. The document lists the group members, Keishmer Amaro and Heycker Cuicas, and indicates they are studying hygiene and occupational safety in section 0102.
3l. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.12)
The document contains solutions to 3 algebra word problems involving systems of linear equations:
1) Solving the system 2x - y = 3 and 3x + y = 7 yields values of x = 2 and y = 1.
2) Solving the system x - y = 5 and 3x + 2y = 25 yields values of x = 7 and y = 2.
3) A word problem involving the ages of a man and his son 5 years ago and 5 years in the future is modeled with a system that is solved, yielding the man's age as 75 years and the son's age as 15 years.
Linear equations in two variables
Linear equations in two variables. Please download the powerpoint file to enable animation.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Absolute Value Notes
This document provides information about integers, absolute value, and opposites:
- Absolute value refers to the distance of a number from zero on the number line and is always positive. It is represented by vertical bars around a number.
- To evaluate expressions with absolute value, simplify values within the bars first before combining terms.
- The opposite of an absolute value expression is found by placing a negative sign before the absolute value bars.
Homogeneous Linear Differential Equations
The document defines a homogeneous linear differential equation as an equation of the form:
a0(dx/dy)n + a1(dx/dy)n-1 + ... + an-1(dx/dy) + any = X, where a0, a1, ..., an are constants and X is a function of x.
It provides the method of solving such equations by first reducing it to a linear equation with constant coefficients, then taking a trial solution of the form y = emz, and finally solving the resulting auxiliary equation.
It proves identities relating derivatives of y with respect to x and z, then uses these identities to solve two sample homogeneous linear differential equations of orders 2 and
Johelbys campos2
The document provides solutions to exercises involving determining whether differential equations are exact, separable, homogeneous, or linear. It analyzes four equations:
1) Equation 4) (1 + x^2 + y^2 + x^2y^2)dy = y^2dx is separable.
2) Equation 9) (x + 1)dy/dx + (x + 2)y = 2xe^-x is linear.
3) Equation 13) dy/dx = -(x^3 + y^3)/3xy^2 is exact.
4) Equation 30) (x + y)dx + xdy = 0 is homogeneous.
Lecture-1-Mech.pptx . .
1) The document discusses boundary value problems (BVPs) in ordinary differential equations. BVPs involve prescribing conditions (called boundary conditions) on the dependent variable and its derivatives at two or more values of the independent variable.
2) The finite difference method is introduced to solve BVPs numerically. It involves approximating derivatives as differences and setting up a system of equations to solve for the unknown values at grid points.
3) An example illustrates solving the BVP x y'' + y = 0 with boundary conditions y(1) = 1, y(2) = 2 using the finite difference method on a grid. The method yields a solution of the unknown function values at the grid points.
More Related Content
What's hot
Numeros reales
The document defines key concepts related to sets and real numbers. It discusses definitions of sets, set operations including union, intersection, difference, and complement. It then defines real numbers and their properties, including that natural numbers, integers, rational and irrational numbers are subsets of real numbers. It also discusses inequalities and their properties, absolute value, and inequalities involving absolute value. Examples are provided to illustrate each concept.
ARITHMETIC SEQUENCE, MEAN AND SERIES WEEK 2 QUARTER 1
The presentation has first a drill on signed numbers. Then, it provides a definition examples and activities for the topics, " Finding the nth term of an Arithmetic Sequence, Arithmetic Mean and Arithmetic Series.".
Evaluating Algebraic Expressions - Math 7 Q2W4 LC1
This document provides instruction on evaluating algebraic expressions. It begins with an opening prayer related to mathematics. It then states the learning competency and objectives which are to evaluate expressions for given variable values and real-life expressions. Various math terms are defined such as constant, variable, term, and exponent. Examples of evaluating multi-step expressions are provided using the order of operations. The document also discusses substituting values for variables and performing operations. Real-life examples on costs are presented for students to evaluate. In closing, key ideas are summarized in notes on algebraic expressions, constants, variables, and the process of evaluating expressions.
Aplicación propiedades integral
1. The document discusses properties of definite integrals, including: the integral of kf(x) from a to b equals k times the integral of f(x) from a to b; the integral of f(x) + g(x) from a to b equals the integral of f(x) from a to b plus the integral of g(x) from a to b; and the integral of f(x) - g(x) from a to b equals the integral of f(x) from a to b minus the integral of g(x) from a to b.
2. It provides an example problem that applies these properties to evaluate the integral of (2x^3 - 3
Math 6 [Division of Integers] ppt Q2 W9
Class Observation in Math 6 on Division of Integers for Grade 6 @ Conalum Elementary School, Inopacan, Leyte
Simultaneous equations
Simultaneous equations in two variables. Finding solution to systems of linear equations by graphing. Solving systems of linear equations by elimination and substitution method.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Solving systems of equations by substitution
ejaymathact.wordpress.com
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Solving systems of Equations by Elimination
The document provides steps for solving systems of equations using the elimination method with addition and subtraction:
1) Put both equations in standard form.
2) Determine which variable to eliminate by finding terms with the same coefficients.
3) Add or subtract the equations to eliminate the chosen variable.
4) Substitute values back into one equation to find the other variable.
5) Check that the solution satisfies both original equations.
Ordinary Differential Equations: Variable separation method
First order and first degree differential equations, Variable separation method ,17 solved problems with detailed simplification
Sequence and series
The document discusses arithmetic sequences and series. An arithmetic sequence is a sequence where the difference between successive terms is constant. The nth term can be calculated using the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. The sum of an arithmetic sequence is called an arithmetic series, which can be calculated using the formula Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term.
Adding and Subtracting Polynomials - Math 7 Q2W4 LC1
This document discusses adding and subtracting polynomials. It defines key polynomial terms like monomial, binomial, and trinomial. It explains that when adding or subtracting polynomials, only like terms can be combined by adding or subtracting their coefficients while keeping the variable parts the same. Examples are provided to demonstrate adding and subtracting polynomials, including real-life word problems involving combining polynomial expressions to model total areas or profits. The overall goal is for students to learn how to perform operations on polynomials.
Derivatives of inverse trig functions
This document discusses derivatives of inverse trigonometric functions and provides examples of taking their derivatives. It contains the following key points:
1. The derivatives of the main inverse trigonometric functions are given as fractions involving the term 1/(1-x^2).
2. Two examples are worked through, differentiating compositions of inverse trig functions and using trigonometric substitutions.
3. The last example proves that if y = sin^(-1)(2x/(1+x^2)), then (1+x^2)dy/dx = 2 by making a u-substitution of x = tanθ.
Solving Quadratic Equations by Factoring
This document provides examples for solving quadratic equations by factoring. It explains how to solve equations of the form ax^2 + bx = 0 and ax^2 + bx + c = 0 by factoring and setting each factor equal to zero. Some example problems are worked out step-by-step, including solving 11x^2 - 13x = 8x - 3x^2 and 7x^2 + 18x = 10x^2 + 12x. The document also discusses using the fact that the roots of ax^2 + bx = 0 are x = 0 and x = -b/a to solve equations without factoring. It concludes by explaining how to use the zero product property to solve a quadratic
Evaluating an Algebraic Expression
This presentation is intended to help the education students by giving an idea on how they will use technology in education specially in teaching mathematics.
Surds revision card
1. Rationalizing surds means removing the radical sign from the denominator by multiplying the numerator and denominator by the conjugate.
2. The conjugate of a surd term keeps the radicand the same but changes the sign of any terms outside the radical.
3. Rationalizing terms of the form a - b involves multiplying the numerator and denominator by the conjugate a + b.
Presentación álgebra
This document contains information about a group project from the Universidad Politécnica Territorial del Estado Lara Andrés Eloy Blanco in Barquisimeto, Venezuela. The document lists the group members, Keishmer Amaro and Heycker Cuicas, and indicates they are studying hygiene and occupational safety in section 0102.
3l. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.12)
The document contains solutions to 3 algebra word problems involving systems of linear equations:
1) Solving the system 2x - y = 3 and 3x + y = 7 yields values of x = 2 and y = 1.
2) Solving the system x - y = 5 and 3x + 2y = 25 yields values of x = 7 and y = 2.
3) A word problem involving the ages of a man and his son 5 years ago and 5 years in the future is modeled with a system that is solved, yielding the man's age as 75 years and the son's age as 15 years.
Linear equations in two variables
Linear equations in two variables. Please download the powerpoint file to enable animation.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Absolute Value Notes
This document provides information about integers, absolute value, and opposites:
- Absolute value refers to the distance of a number from zero on the number line and is always positive. It is represented by vertical bars around a number.
- To evaluate expressions with absolute value, simplify values within the bars first before combining terms.
- The opposite of an absolute value expression is found by placing a negative sign before the absolute value bars.
Homogeneous Linear Differential Equations
The document defines a homogeneous linear differential equation as an equation of the form:
a0(dx/dy)n + a1(dx/dy)n-1 + ... + an-1(dx/dy) + any = X, where a0, a1, ..., an are constants and X is a function of x.
It provides the method of solving such equations by first reducing it to a linear equation with constant coefficients, then taking a trial solution of the form y = emz, and finally solving the resulting auxiliary equation.
It proves identities relating derivatives of y with respect to x and z, then uses these identities to solve two sample homogeneous linear differential equations of orders 2 and
What's hot (20)
ARITHMETIC SEQUENCE, MEAN AND SERIES WEEK 2 QUARTER 1
ARITHMETIC SEQUENCE, MEAN AND SERIES WEEK 2 QUARTER 1
Evaluating Algebraic Expressions - Math 7 Q2W4 LC1
Evaluating Algebraic Expressions - Math 7 Q2W4 LC1
Ordinary Differential Equations: Variable separation method
Ordinary Differential Equations: Variable separation method
Adding and Subtracting Polynomials - Math 7 Q2W4 LC1
Adding and Subtracting Polynomials - Math 7 Q2W4 LC1
3l. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.12)
3l. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.12)
Similar to Yoaniker morles2
Johelbys campos2
The document provides solutions to exercises involving determining whether differential equations are exact, separable, homogeneous, or linear. It analyzes four equations:
1) Equation 4) (1 + x^2 + y^2 + x^2y^2)dy = y^2dx is separable.
2) Equation 9) (x + 1)dy/dx + (x + 2)y = 2xe^-x is linear.
3) Equation 13) dy/dx = -(x^3 + y^3)/3xy^2 is exact.
4) Equation 30) (x + y)dx + xdy = 0 is homogeneous.
Lecture-1-Mech.pptx . .
1) The document discusses boundary value problems (BVPs) in ordinary differential equations. BVPs involve prescribing conditions (called boundary conditions) on the dependent variable and its derivatives at two or more values of the independent variable.
2) The finite difference method is introduced to solve BVPs numerically. It involves approximating derivatives as differences and setting up a system of equations to solve for the unknown values at grid points.
3) An example illustrates solving the BVP x y'' + y = 0 with boundary conditions y(1) = 1, y(2) = 2 using the finite difference method on a grid. The method yields a solution of the unknown function values at the grid points.
DE-PS.pdf
This document provides solutions to problems involving different types of differential equations:
1) Separable differential equations involving solving dy/dx = xy^2 and dy/dx + xey = 0.
2) Homogeneous differential equations involving solving equations with homogeneous coefficients like 2(2x^2 + y^2)dx - xydy = 0.
3) Exact differential equations involving checking if equations like (x + y)dx + (x - y)dy are exact.
4) Linear differential equations involving solving equations like (5x + 3y)dx - xdy = 0.
5) An elementary application involving a tank being rinsed with fresh water flowing in at a rate.
Lesson 2: Final Exam Review (Part 1)
This document contains lecture materials from a Calculus III course covering several topics:
1) Equations of lines and planes in 3D space, finding the equation of a plane parallel or perpendicular to a given vector.
2) Finding the equation of the tangent plane to a surface at a given point and the normal line.
3) Finding relative extrema (maxima, minima, saddle points) of multivariate functions by analyzing their critical points.
4) Setting up iterated integrals to calculate the volume of solids with boundaries defined by surfaces and planes. Examples find the volume under a paraboloid and above a bounded region.
Functions of severable variables
Partial differentiation, total differentiation, Jacobian, Taylor's expansion, stationary points,maxima & minima (Extreme values),constraint maxima & minima ( Lagrangian multiplier), differentiation of implicit functions.
Maths-MS_Term2 (1).pdf
This document provides solutions to 10 math problems from a marking scheme for Class XII. The problems cover a range of calculus and vector topics. Key steps are shown in the solutions. For example, in problem 1, integrals involving logarithmic and trigonometric functions are solved using substitution techniques. In problem 3, vectors are used to prove an identity involving the sum of two unit vectors and the angle between them. Across the solutions, various mathematical concepts are applied concisely to arrive at the answers.
Plano numerico
1) The document discusses various geometric concepts in multi-variable calculus including the Cartesian plane R2, distance between points, midpoint of a line segment, circles, parabolas, ellipses, and hyperbolas.
2) It provides examples of solving problems related to these concepts, such as proving points are collinear, finding midpoints of diagonals of a quadrilateral, and graphing various equations.
3) The document concludes by listing two references used in teaching these multi-variable calculus topics.
B.tech ii unit-3 material multiple integration
1. The document discusses multiple integrals and double integrals. It defines double integrals and provides two methods for evaluating them: integrating first with respect to one variable and then the other, or vice versa.
2. Examples are given of evaluating double integrals using these methods over different regions of integration in the xy-plane, including integrals over a circle and a hyperbolic region.
3. The document also discusses calculating double integrals over a region when the limits of integration are not explicitly given, but the region is described geometrically.
Four Point Gauss Quadrature Runge – Kuta Method Of Order 8 For Ordinary Diffe...
Four Point Gauss Quadrature Runge – Kuta Method Of Order 8 For Ordinary Diffe...International journal of scientific and technical research in engineering (IJSTRE)
We present a strong convergence implicit Runge-Kutta method, with four stages, for solution of
initial value problem of ordinary differential equations. Collocation method is used to derive a continuous
scheme; and the continuous scheme evaluated at special points, the Gaussian points of fourth degree Legendre
polynomial, gives us four function evaluations and the Runge-Kutta method for the iteration of the solutions.
Convergent properties of the method are discussed. Experimental problems used to check the quality of the
scheme show that the method is highly efficient, A – stable, has simple structure, converges to exact solution
faster and better than some existing popular methods cited in this paper.Btech_II_ engineering mathematics_unit2
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
ANALISIS RIIL 1 3.2 ROBERT G BARTLE
1. The document contains exercises on limit theorems from an introduction to real analysis course. It includes 4 problems asking the student to determine if sequences converge or diverge based on given formulas, provide examples of sequences whose sum and product converge but the individual sequences diverge, and prove statements about convergent sequences.
2. The solutions show work for determining convergence or divergence of sequences defined by formulas in problem 1. Examples are given in problem 2 where the sum and product of divergent sequences converge. Theorems are applied in problems 3 and 4 to prove relationships between convergent sequences.
Ecuaciones lineales de orden superior
The document discusses solving linear differential equations of higher order with constant coefficients and initial value problems. It provides solutions to two homogeneous equations, two non-homogeneous equations, and determines if a given function satisfies an initial value problem and its uniqueness. The key steps are identifying the characteristic polynomial, finding its roots, using the general solution formula, and checking if initial conditions are met. Uniqueness is guaranteed when coefficient functions are continuous and the highest order coefficient is nonzero on the given interval.
Btech_II_ engineering mathematics_unit3
This document discusses multiple integrals and related concepts. It contains:
1. An introduction to double integrals, defining them as the limit of sums of products of elementary areas and function values over a region.
2. Methods for evaluating double integrals, including integrating with respect to one variable first while treating the other as a constant, and vice versa.
3. Examples of calculating double integrals over various regions, using techniques like changing the order of integration and changing variables.
4. Discussions of calculating integrals over a given region rather than explicitly stated limits, and calculating volumes using double integrals.
Functions ppt Dr Frost Maths Mixed questions
The document provides an overview of functions topics for GCSE/IGCSE mathematics, including understanding functions, inverse functions, composite functions, domain and range of functions, and piecewise functions. It contains examples of different types of functions and exercises for students to practice evaluating functions, finding inverse functions, and solving word problems involving functions. The document is intended to help students learn and teachers teach key concepts related to functions.
MATRICES AND CALCULUS.pptx
This document contains a summary of key topics in multivariable calculus including matrices, differential calculus, functions of several variables, and optimization. Some key points covered include:
- Cayley-Hamilton theorem and its applications
- Finding maxima, minima, and points of inflection for functions of one variable
- Continuity conditions for piecewise functions
- Euler's theorem on homogeneous functions
- Total derivatives and Jacobian matrices
- Taylor series expansions
- Using Lagrange multipliers to optimize functions with constraints
Tugas 5.3 kalkulus integral
1. The document provides information about exercises 51-88 on finding the definite integral to calculate the area between a curve and the x-axis over an interval [a,b].
2. Exercises 55-62 involve sketching graphs of functions and finding their average values over given intervals.
3. Exercises 63-70 involve using the integral definition as a limit of Riemann sums to evaluate definite integrals.
Semana 12 ecuaciones polinomiales i álgebra-uni ccesa007
The document is about algebra and solving equations. It discusses the history and importance of equations, defines key terms like solutions and sets of solutions. It also provides examples of solving different types of equations step-by-step, including linear equations, quadratic equations through factoring, completing the square, and the quadratic formula. The document emphasizes that solving equations involves finding the value(s) of the variable that satisfy the equality.
GraphTransformations.pptx
1. This document discusses graph transformations of functions, including translations, stretches, and reflections. It provides rules for how modifications inside and outside the function f(x) will affect the x-values and y-values of the graph.
2. Examples are given of applying transformation rules to specific points on a graph and determining the new coordinates. The document also demonstrates sketching a transformed graph using key points.
3. An exercise section provides multiple choice and short answer questions to test understanding of describing transformations and finding coordinates of transformed points.
B.tech ii unit-2 material beta gamma function
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals involving exponential and power functions.
2. Examples are provided to demonstrate properties and applications of the gamma function, including evaluating integrals involving the gamma function.
3. The beta function is defined in terms of an integral from 0 to 1, and its relationship to the gamma function is described.
Lesson 3: Problem Set 4
1. The document discusses vector calculus concepts including the dot product, cross product, gradient, divergence, and curl of vectors. It provides examples and explanations of how to calculate these quantities.
2. The dot product yields a scalar quantity and is used to calculate the angle between two vectors. The cross product yields a vector that is perpendicular to the plane of the two input vectors.
3. The gradient is the vector of partial derivatives of a scalar function and points in the direction of maximum increase. The divergence and curl are used to describe vector fields and involve taking partial derivatives.
Similar to Yoaniker morles2 (20)
Four Point Gauss Quadrature Runge – Kuta Method Of Order 8 For Ordinary Diffe...
Four Point Gauss Quadrature Runge – Kuta Method Of Order 8 For Ordinary Diffe...
Semana 12 ecuaciones polinomiales i álgebra-uni ccesa007
Semana 12 ecuaciones polinomiales i álgebra-uni ccesa007
Recently uploaded
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.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.
How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
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
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience Wahiba Chair Training & Consulting
Wahiba Chair's Talk at the 2024 Learning Ideas Conference. The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...Nguyen Thanh Tu Collection
https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Recently uploaded (20)
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Yoaniker morles2
- 1. PROGRAMA NACIONAL DE FORMACIÓN EN SISTEMA DE CALIDAD Y AMBIENTE. Matemática Aplicada. Ejercicios Unidad I. parte II Integrante: Yonaiker Morles C.I.: 25.814.152 Trayecto 3 Fase 2 Grupo-A Febrero de 2021
- 2. Ejercicios propuestos 1.2: Verifique si la ecuación diferencial es exacta, separable, homogénea o lineal. 𝟏) 𝒅𝒚 𝒅𝒙 = 𝒙𝒚 + 𝟑𝒙 − 𝒚 − 𝟑 𝒙𝒚 − 𝟐𝒙 + 𝟒𝒚 − 𝟖 Solución: Verificamos si la ecuación diferencial es variable separable si se cumple: 𝑓(𝑦)𝑑𝑦 = 𝑔(𝑥)𝑑𝑥 ; 𝐻(𝑥, 𝑦) 𝑔(𝑥) 𝑓(𝑥) Despejamos: (𝑥𝑦 − 2𝑥 + 4𝑦 − 8)𝑑𝑦 = (𝑥𝑦 + 3𝑥 − 𝑦 − 3)𝑑𝑥 𝑑𝑦 𝑥𝑦 + 3𝑥 − 𝑦 − 3 = 𝑑𝑥 𝑥𝑦 − 2𝑥 + 4𝑦 − 8 Por lo que la ecuación diferencial 𝑑𝑦 𝑑𝑥 = 𝑥𝑦+3𝑥−𝑦−3 𝑥𝑦−2𝑥+4𝑦−8 es separable. 𝟑) 𝒚´ = 𝟐𝒚 + 𝒙𝟐 + 𝟓 Solución: Veamos si la ecuación diferencial 𝑦´ = 2𝑦 + 𝑥2 + 5 se puede expresar en la forma estándar. 𝑑𝑦 𝑑𝑥 + 𝑝(𝑥)𝑦 = 𝑓(𝑥) Sabemos que 𝑦´ = 𝑑𝑦 𝑑𝑥 ; 𝑑𝑦 𝑑𝑥 = 2𝑦 + 𝑥2 + 5 Por lo que 𝑑𝑦 𝑑𝑥 + 𝑝(𝑥)𝑦 = 𝑓(𝑥) 𝑑𝑜𝑛𝑑𝑒 𝑝(𝑥) = 0 𝑦𝑓(𝑥) = 2𝑦 + 𝑥2 + 5 Asi la ecuación 𝑦´ = 2𝑦 + 𝑥2 + 5 es lineal.
- 3. 𝟖) (𝒚𝟐 + 𝒚𝒙)𝒅𝒙 − 𝒙𝟐 𝒅𝒚 = 𝟎 Solución: Sabemos que 𝑀(𝑥, 𝑦)𝑑𝑥 + 𝑁(𝑥, 𝑦)𝑑𝑦 = 0 Utilizando la def. 2: 𝑀(𝑡𝑥, 𝑡𝑦) = 𝑡𝑎1 𝑀(𝑥, 𝑦) 𝑦 𝑁(𝑡𝑥, 𝑡𝑦) = 𝑡𝑎2 𝑁(𝑥, 𝑦) 𝑎1 = 𝑎2 Verificamos que 𝑀(𝑥, 𝑦) = 𝑦2 + 𝑦𝑥 𝑦 𝑁(𝑥, 𝑦) = 𝑥2 Son homogéneas del mismo grado 𝑀(𝑡𝑥, 𝑡𝑦) = (𝑡𝑦)2 + (𝑡𝑦)(𝑡𝑥) ; 𝑁(𝑡𝑥, 𝑡𝑦) = (𝑡𝑥)2 = 𝑡2 𝑦2 + 𝑡2 𝑦𝑥 = 𝑡2 𝑥2 = 𝑡2 (𝑦2 + 𝑦𝑥) = 𝑡2 𝑁(𝑥, 𝑦) = 𝑡2 𝑀(𝑥, 𝑦) 𝑎1 = 2 𝑎2 = 2 Así tenemos que 𝑎1 = 𝑎2 , 𝑀(𝑥, 𝑦) 𝑦 𝑁(𝑥, 𝑦) son homogéneas del mismo grado. Por lo tanto (𝑦2 + 𝑦𝑥)𝑑𝑥 − 𝑥2 𝑑𝑦 = 0 es homogénea. 𝟏𝟏) (𝒚𝟑 − 𝒚𝟐 𝒔𝒆𝒏(𝒙) − 𝒙)𝒅𝒙 + (𝟑𝒙𝒚𝟐 + 𝟐𝒚𝒄𝒐𝒔(𝒙)) 𝒅𝒚 = 𝟎 Solución: En la ecuación diferencial (𝑦3 − 𝑦2 𝑠𝑒𝑛(𝑥) − 𝑥)𝑑𝑥 + (3𝑥𝑦2 + 2𝑦𝑐𝑜𝑠(𝑥))𝑑𝑦 = 0 𝑀(𝑥, 𝑦) = 𝑦3 − 𝑦2 𝑠𝑒𝑛(𝑥) − 𝑥 𝑌 𝑁(𝑥, 𝑦) = 3𝑥𝑦2 + 2𝑦𝑐𝑜𝑠(𝑥) Derivando 𝑀 con respecto a 𝑦 y a 𝑁 con respecto a 𝑥, se tiene que: 𝜕 𝜕𝑦 𝑀(𝑥, 𝑦) = 𝑦3 − 𝑦2 𝑠𝑒𝑛(𝑥) − 𝑥 = 3𝑦2 − 2𝑦𝑠𝑒𝑛(𝑥) 𝜕 𝜕𝑥 𝑁(𝑥, 𝑦) = 3𝑥𝑦2 + 2𝑦𝑐𝑜𝑠(𝑥) = 3𝑦2 − 2𝑦𝑠𝑒𝑛(𝑥) 𝑐𝑜𝑚𝑜 𝜕 𝜕𝑦 𝑀(𝑥, 𝑦) = 𝜕 𝜕𝑥 𝑁(𝑥, 𝑦) Por lo tanto (𝑦3 − 𝑦2 𝑠𝑒𝑛(𝑥) − 𝑥)𝑑𝑥 + (3𝑥𝑦2 + 2𝑦𝑐𝑜𝑠(𝑥))𝑑𝑦 = 0 es exacta.