© Annie Patton Newton-Raphson Method Next Slide. © Annie Patton Aim of lesson To learn how the Newton- Raphson method can be used for finding non integer.

Slides:

Advertisements

Similar presentations

Numerical Methods: Finding Roots Department of Mathematics University of Leicester.

Advertisements

© Annie Patton Differentiation by First Principles Next Slide.

© Annie Patton 2007 Paper 1 No 7 Next Slide. © Annie Patton Leaving Certificate 2007 Higher Level Paper 1 no 7(a) Start clicking when you want to see.

Nonlinear Equations Your nonlinearity confuses me “The problem of not knowing what we missed is that we believe we haven't missed anything” – Stephen Chew.

Lecture #18 EEE 574 Dr. Dan Tylavsky Nonlinear Problem Solvers.

A few words about convergence We have been looking at e a as our measure of convergence A more technical means of differentiating the speed of convergence.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 9 Roots of Equations Open Methods.

ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 8 Roots of Equations Open Methods.

Paper 1 Algebra Leaving Certificate Helpdesk 20 th September 2012.

Finding a Quadratic Equation from Complex Roots. Write an equation from the Roots Find the equation of a quadratic function that has the following numbers.

Higher Quadratic Past Paper Questions

2-4 completing the square

Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = – x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy

© Annie Patton Differentiation of Inverse Trigonometric Function Next Slide.

© Annie Patton Parametric Functions Next Slide. © Annie Patton Aim of Lesson To establish what is a set of Parametric Functions and how to differentiate.

© Annie Patton Implicit Functions Next Slide. © Annie Patton Aim of Lesson Next Slide To establish, what is an Implicit Function and how to differentiate.

Asymptotes Next slide © Annie Patton.

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

5.5 – The Quadratic formula Objectives: Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate.

Warm Up. Solving Quadratic Equations by the Quadratic Formula.

Lesson 8-5:Classes of Functions Algebra II CP Mrs. Mongold.

Review: 6.5f Mini-Quiz 1. Solve: Verify by factoring. 2. Solve by Graphing: y = x 2 – 4x. Verify by factoring.

DO NOW 1) What is the graph of this inequality -2y >= - 10 – 5x 2) M = 6 n = -3 4 ( m – 2) + 3n + 5 Answers: 1) thru (0, 5) and shade right area 2) 12.

LINEARIZATION AND NEWTON’S METHOD Section 4.5. Linearization Algebraically, the principle of local linearity means that the equation of the tangent.

5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.

Lucan Community College Leaving Certificate Mathematics

© Annie Patton Differentiation of Products Next Slide.

Chapter 6 – Polynomials and Polynomial Functions 6.6 –Polynomials of Greater Degree.

Review: 6.5e Mini-Quiz 1. Solve: 16x 2 – 24x = – 4x Solve: (x – 3)(x – 2) = 30.

Quality Core Rational Roots Find Those Roots Factor Completely Name That Function! $500 $400 $300 $200 $100.

6.4 Completing the Square The Square Root Property.

4.8 Newton’s Method Mon Nov 9 Do Now Find the equation of a tangent line to f(x) = x^5 – x – 1 at x = 1.

Newton’s Method Problem: need to solve an equation of the form f(x)=0. Graphically, the solutions correspond to the points of intersection of the.

Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D

Graphing Functions Mr.Kaslavage Grade 11 trig Mathematics.

SAT Problem of the Day. 5.5 The Quadratic Formula 5.5 The Quadratic Formula Objectives: Use the quadratic formula to find real roots of quadratic equations.

 The equation with one variable. At P(atm) equals 0.5 atm, What is T ? ? ?

9-2 Solving Quadratic Equations by Graphing

Algebra 1 Warm up #3 Solve by factoring:.

Trigonometric Functions

LECTURE 4 OF SOLUTIONS OF NON-LINEAR EQUATIONS OBJECTIVES

Exponential Function Next slide © Annie Patton.

4.5: Linear Approximations, Differentials and Newton’s Method

9-2 Solving Quadratic Equations by Graphing

LECTURE 3 OF SOLUTIONS OF NON -LINEAR EQUATIONS.

Solving Quadratic Equations by Completing the Square

9.1 Solving quadratic equations using square roots

Finding polynomial roots

2005 Paper 1 No 7 © Annie Patton Next Slide.

The graph of a function f(x) is given below

Unit 2. Day 11..

Lesson 5.4 Vertex Form.

Zeros to Quadratic Functions

Graphs 10 y 5 x © Annie Patton Next Slide.

Trigonometric Functions

Warm-up: Find the equation of a quadratic function in standard form that has a root of 2 + 3i and passes through the point (2, -27). Answer: f(x) = -3x2.

Class Greeting.

Parent Functions.

Second Derivatives © Annie Patton Next slide.

Parent Functions.

General Rule © Annie Patton Next Slide.

WARM – UP 1. Find all of the real roots of the function:

3.8 Newton’s Method How do you find a root of the following function without a graphing calculator? This is what Newton did.

Quotient Next Slide © Annie Patton.

Miscellaneous Differential Problems

Class Greeting.

Review: 10.2b Mini-Quiz The revenue R (in dollars) from selling x units of an infant stroller is modeled by

Solving Quadratic Equations by Finding Square Roots

4. If y varies inversely as x and y=3 when x=4, find y when x=15.

Presentation transcript:

© Annie Patton Newton-Raphson Method Next Slide

© Annie Patton Aim of lesson To learn how the Newton- Raphson method can be used for finding non integer roots of a cubic equation. Next Slide

© Annie Patton Newton-Raphson Method Next Slide Newton-Raphson states that if x 1 is an approximation to a root of a cubic equation then x 2 is a more accurate result.

© Annie Patton Next Slide Leaving Certificate 2006 Higher Level Paper 1 no 7(a) Start clicking when you want to see the answer.

© Annie Patton (x 1, f(x 1 )) (x 1,0) (x 2,0) Proof of Newton-Raphson Method Next Slide

© Annie Patton Steps to using the Newton- Raphson Method The more times Step 4 is repeated the more accurate the answer. Next Slide

© Annie Patton Leaving Certificate 2007 Higher Level Paper 1 no 7(a) Start clicking when you want to see the answer. Next Slide

© Annie Patton Start clicking when you want to see the answer. Next Slide

© Annie Patton Leaving Certificate 2005 Higher Level Paper 1 no 7(c)(i)(ii) Start clicking when you want to see the answer. Quadratic Next Slide

© Annie Patton Leaving Certificate 2005 Higher Level Paper 1 no 7(c)(iii) Start clicking when you want to see the answer. Next Slide

© Annie Patton Leaving Certificate 2003 Higher Level Paper 1 no 6(b) Start clicking when you want to see the answer. Next Slide

© Annie Patton Leaving Certificate1998 Higher Level Paper 1 part no 7( c) Start clicking when you want to see the answer. Next Slide

© Annie Patton Next Slide Start clicking when you want to see the answer.

© Annie Patton Newton-Raphson states that if x 1 is an approximation to a root of a cubic equation then x 2 is a more accurate result. Next Slide

© Annie Patton Homework Leaving Certificate Higher Paper 1 No 7(a) Next Slide

© Annie Patton Steps to using the Newton- Raphson Method The more times Step 4 is repeated the more accurate the answer.