Integrating Discrete Functions

Slides:

Advertisements

Similar presentations

Numerical Methods.  Polynomial interpolation involves finding a polynomial of order n that passes through the n+1 points.  Several methods to obtain.

Advertisements

Circular Motion Example Problem 3: a t = f(t) A bead moves along a circular wire. Its speed increases at a = 2t – 4 m/s 2. Its initial (at t = 0) position.

Selected from presentations by Jim Ramsay, McGill University, Hongliang Fei, and Brian Quanz Basis Basics.

Direct Method of Interpolation

Particle Straight Line Kinematics: Ex Prob 2 This is an a = f(t) problem. I call it a “total distance” problem. Variations: v = f(t), s = f(t)…. A particle.

Fitting a Function to Data Adapted from Walch Education.

EXAMPLE 3 Use a quadratic model Fuel Efficiency

Reading Between the Lines

9/19/2015http://numericalmethods.eng.usf.edu1 Introduction to Scientific Computing Major: All Engineering Majors Authors: Autar Kaw, Luke Snyder

Plot and interpret position-time graphs A position time graph shows an objects change in position over a period of time.

Welcome to EML3041: Computational Methods. SIT IN FIRST FOUR ROWS ONLY My name is Dr. Kaw. Introduce yourself to the person on your left and right! Say.

1 Interpolation. 2 What is Interpolation ? Given (x 0,y 0 ), (x 1,y 1 ), …… (x n,y n ), find the value of ‘y’ at a.

1 Lagrangian Interpolation Major: All Engineering Majors Authors: Autar Kaw, Jai Paul

Numerical Methods For Slides Thanks to Lecture 6 Interpolation

Quadratic Spline Interpolation Part 1 of 2

9-4 Quadratic Equations and Projectiles

1 Newton’s Divided Difference Polynomial Method of Interpolation Major: All Engineering Majors Authors: Autar Kaw,

Integration This is not your father’s area?. Ask me what I should already know The pre-requisite questions.

1 Direct Method of Interpolation Major: All Engineering Majors Authors: Autar Kaw, Jai Paul

Distance, Speed and Time

1 INTERPOLASI. Direct Method of Interpolation 3 What is Interpolation ? Given (x 0,y 0 ), (x 1,y 1 ), …… (x n,y n ), find the value of ‘y’ at a value.

Gravity, Technology, Quadratic Like Equations. An object near the surface of earth is under the influence of gravity We can model this by using a quadratic.

Kinematics: Linear Motion in One Dimension Class 1.

1 Spline Interpolation Method Major: All Engineering Majors Authors: Autar Kaw, Jai Paul

1 NUMERICAL METHOD. 2 Introduction Definition : The study of approximation techniques for solving mathematical problems, taking into account the extent.

PHYSIC S. Think back to GCSE 1.Write down the definition of velocity Speed in a given direction 2.Write down the calculation for velocity But that is.

1D Kinematics Equations and Problems. Velocity The rate at an object changes position relative to something stationary. X VT ÷ x ÷

Physics Section 1.3 Identify types of variation from graphs Data and graphs volume (cm 3 ) | mass (g) 10 | | | | 50 m = kv Graph is a.

Solving Quadratic Equations by Graphing (9-2) Objective: Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing.

Graphs of a falling object And you. Objective 1: Graph a position –vs- time graph for an object falling from a tall building for 10 seconds Calculate.

Checking for understanding

This is not your father’s area?

Introduction to Numerical Methods Mathematical Procedures

22. Use this table to answer the question.

Introduction to Scientific Computing

EXAMPLE 4 Solve a multi-step problem

Describing Motion The graphs Part II….

This is not your father’s area?

Reading Between the Lines

Introduction to Scientific Computing

Spline Interpolation Method

Spline Interpolation Method

Unit 6 – Fundamentals of Calculus Section 6

Spline Interpolation Method

Computational Methods Autar Kaw University of South Florida

Computational Methods EML3041

9-4 Quadratic Equations and Projectiles

Nonlinear Equations Your nonlinearity confuses me

Considering air resistance

Integration As thy a difficult a problem as

CALCULATING EQUATION OF LEAST SQUARES REGRESSION LINE

Total Distance Traveled

Section Net Change in Position/Distance Traveled

Integration As thy a difficult a problem as

Nonlinear Equations Your nonlinearity confuses me

Day 23 10/5/10 TOPIC: Converting an xt Graph to a vt Graph

Section 9.4 – Solving Differential Equations Symbolically

Section Net Change in Position/Distance Traveled

Bring it together.

Direct Method of Interpolation

This is not your father’s area?

Reading Between the Lines

u - initial velocity (m/s) v - final velocity (m/s)

Computational Methods EML3041

a = v2 – v1 t a = 8 m/s s a = 8 m/s2 a = 36 m/s – 4 m/s 4 s #6 d

Newton’s Divided Difference Polynomial Method of Interpolation

Lagrangian Interpolation

Presentation transcript:

Integrating Discrete Functions http://numericalmethods.eng.usf.edu 1

Integrating Discrete Functions Spline Method http://numericalmethods 2

Problem Statement The upward velocity of a rocket is given as a function of time. Using quadratic splines, find the distance covered between t=11 and t=16 seconds. t v(t) s m/s 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 3

Data and Plot t v(t) s m/s 10 227.04 15 362.78 20 517.35 22.5 602.97 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 4

Solution 5

Distance from Velocity Profile 6

Distance from Velocity Profile 7

END http://numericalmethods.eng.usf.edu

Integrating Discrete Functions Regression Method http://numericalmethods.eng.usf.edu

Trunnion Shrink Fit into Hub

Is the Contraction Enough? Magnitude of contraction needed in the trunnion was 0.015” or more.

How do we find the contraction? T(oF) α (μin/in/oF) -340 2.45 -300 3.07 -220 4.08 -160 4.72 -80 5.43 6.00 40 6.24 80 6.47 Ta = 80oF Tc = -108oF D = 12.363"

Regression Model -340 2.45 -300 3.07 -220 4.08 -160 4.72 -80 5.43 6.00 T(oF) α (μin/in/oF) -340 2.45 -300 3.07 -220 4.08 -160 4.72 -80 5.43 6.00 40 6.24 80 6.47

Estimating the Contraction

Calculating the contraction Ta = 80oF, Tc = -108oF, D = 12.363" Magnitude of contraction needed in the trunnion was 0.015” or more.

THE END http://numericalmethods.eng.usf.edu