Boundary value problems workshop

Slides:



Advertisements
Similar presentations
Prof. Muhammad Saeed ( Ordinary Differential Equations )
Advertisements

TNPL JoongJin-Cho Runge-kutta’s method of order 4.
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM Read , 26-2, 27-1 CISE301_Topic8L8&9 KFUPM.
P460 - harmonic oscialltor1 Harmonic Oscillators V F=-kx or V=cx 2. Arises often as first approximation for the minimum of a potential well Solve directly.
Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:
7.8 Equations Involving Radicals. Solving Equations Involving Radicals :  1. the term with a variable in the radicand on one side of the sign.  2. Raise.
Multiplying Decimals Unit 3.5 Pages x 320 = x 800 = 3.3,806 x 10 = 27, ,400 38,060 Warm Up Problems Multiply.
Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. Find a percent using the percent equation.
Translating Word Problems into Equations. Avoid the nervousness! Follow these steps: Read the problem carefully and figure out what it is asking you to.
3.5 Solving systems of equations in 3 variables
HPC 1.4 Notes Learning Targets: - Solve equations using your calculator -Solve linear equations -Solve quadratic equations - Solve radical equations -
The Height Equation. h= ending height g = gravity constant (32 if feet, 9.8 if meters) v 0 = initial velocity h 0 = initial height t = time.
Substitution Method: 1. Solve the following system of equations by substitution. Step 1 is already completed. Step 2:Substitute x+3 into 2 nd equation.
Boundary Value Problems l Up to this point we have solved differential equations that have all of their initial conditions specified. l There is another.
3.6 Solving Absolute Value Equations and Inequalities
7:4. SIMPLE MODEL FOR NEUTRON SCATTERING LENGTHS CHAPTER 7 – NEUTRON SCATTERING THEORY 7:1. SOLUTION OF THE SCHRODINGER EQUATION 7:2. SCATTERING CROSS.
Using Equations to Solve Percent Problems
Time-independent Schrodinger eqn QM Ch.2, Physical Systems, 12.Jan.2003 EJZ Assume the potential V(x) does not change in time. Use * separation of variables.
Notes – 2/13 Addition Method of solving a System of Equations Also called the Elimination Method.
Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 271 Boundary-Value.
Perfect squares: 1, 4, 9, __, __, __, __, __, __, __,…
Solving Linear Systems by Substitution
Chapter 5: Quantum Mechanics
Differential Equations Linear Equations with Variable Coefficients.
 y’ = 3x and y’ = x are examples of differential equations  Differential Form dy = f(x) dx.
SYSTEMS OF EQUATIONS. SYSTEM OF EQUATIONS -Two or more linear equations involving the same variable.
Objectives: Use the quadratic formula to solve a quadratic equation Use quadratic models for real-life situations.
10/9/2015PHY 711 Fall Lecture 201 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 20: Introduction/review.
EXAMPLE 2 Graph a linear inequality in two variables Graph the inequality y > 4x – 3. STEP 2 0 > 4(0) – 3 ? Test (0, 0) in y > 4x – 3. SOLUTION Graph the.
EXAMPLE Ordering Real Numbers Order the numbers 0.47, 0.474, 0.47, and 0.23 from least to greatest. SOLUTION STEP 1 Write each decimal out to six.
 Given a quadratic equation in standard form, the value of x can be found by using the quadratic formula:
Identities, Contradictions and Conditional Equations.
MATH 685/ CSI 700/ OR 682 Lecture Notes Lecture 11. Ordinary differential equations. Boundary value problems.
Objective The student will be able to:
Computational Physics (Lecture 13)
Algebra 2 Test 1 Review Trivia
Warm Up Use scalar multiplication to evaluate the following:
Solving Schrodinger Equation: ”Easy” Bound States
SE301: Numerical Methods Topic 8 Ordinary Differential Equations (ODEs) Lecture KFUPM (Term 101) Section 04 Read , 26-2, 27-1 CISE301_Topic8L4&5.
Week 7- 2nd 6 Weeks.
WARMUP 1. y > – x – 4 y < 2x + 2.
Solve a system of linear equation in two variables
3.5 Solving systems of equations in 3 variables
Lesson 8-10 Nonlinear Systems
Civil Engineering Majors Authors: Autar Kaw, Charlie Barker
Ordinary differential equaltions:
Converting Repeating Decimals to Fractions
Industrial Engineering Majors Authors: Autar Kaw, Charlie Barker
7.4 Solving factored polynomials
3.8 Solving Equations Involving Absolute Value
The Quadratic Formula CA 19.0, 20.0.
Investigating the Behavior of Electrons in Different Quantum Systems
32 – Applications of the Derivative No Calculator
Humanities Matching Final
SECTION 2-4 : SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES
Gaussian Wavepacket in an Infinite square well
Tough AP Physics 1 standard Question…
Boundary Value Problems
Determine the graph of the given function. {image}
Boundary value problems:
Humanities Matching Final
Electrical Engineering Majors Authors: Autar Kaw, Charlie Barker
Numerical Computation and Optimization
Section Day 3 Solving
Chemical Engineering Majors Authors: Autar Kaw, Charlie Barker
Trigonometric Equations
f(x) = exp(ikx) and C = -k2 f(x) = x3 and C = 6
One-step addition & subtraction equations: fractions & decimals
A student tries to solve
Linear boundary value problems:
Presentation transcript:

Boundary value problems workshop A ball is thrown upwards with speed v such that after 1 second the ball is 1m high. Using a shooting algorithm, 2nd Runge-Kutta, find v to 3 decimal places. Compare with the analytic solution 2) Using the rescaled variables, find the three lowest eigenfunctions and eigenvalues of the Schrodinger equation for a harmonic potential. Do this using the shooting method. 3) Repeat question 2 but this time use the matching method, investigate how your answers change as xi and xf are altered.