Chapter 12
Interpolation
In Chapter 11, we considered data that we wished to approximate using a specified
function. In this chapter, we consider the case in which we want to construct a
function that exactly matches the given data. Such instances arise i
# Point) (40(1)? LAM/"1M0 Im/MC L k EH?!"
5, z
9. \ VQgj i; k: a 001 )
3 2- 9.mrPsons \] L 1 k cfw_7.15 CL)
ml: 3 s i '2.
q 3 P59 3/2. 2 25 11 31. E 005')
eat 3 3 b 3
EXMPG 13,;
th 1415 wen: 0) J 3"(1WJOL 5&3 Tar, 5"1504 'I, J "a m/ elm/J:
O
tile r.
Ti 1.
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Chapter 7: Initial Value Problems
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall
MAE 376: Applied Mathematics for MAE
Errors in Computations
Dr. Ehsan T. Esfahani
October 4th and 6th, 2016
Approximation and Round-Off Errors
For many engineering problems, we cannot obtain
analytical solutions.
Numerical methods yield approximate resu
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Chapter 6: Finite Difference
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016
MAE 340: Homework 7
Name and Section:
For each of the following characteristic equations,
a) Draw the root locus plot for 0 K , using the graph provided
b) Find the range of K (if any) that results in a stable system
c) Find the range of K (if any) that r
Lab 10: Non-linear Systems
Due: December 2, 2016, 11:59 PM, submitted to UB Learns ONLY
The goal of this programming project is to study the behavior of a simple mechanical system.
Consider the system shown in Figure 1. The bars are rigid and connected to
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Chapter 4: Numerical Methods for Solving Linear Equations
Review: LU Decomposition
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Example.
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Chapter 4: Numerical Methods for Solving Linear Equations
Review: Analytical evaluation of existence and uniqueness of the solution
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Numerical Method 1: Gauss
Chapter 13
Numerical Integration
The integration of functions is a common task in engineering applications. However,
we do not always have the luxury of functions that can be analytically integrated.
We may not even have analytical functions to begin with
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Chapter 3: Differential Equations
Classification of Differential Equations
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Notations:
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Solution of Ordinary D
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Chapter 2: Eigen Problem
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Example:
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Applications:
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Partial Differential Equations (PDE)
(Wave Equation)
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class Notes (MAE 376 Fall 2016)
Ehsan T Esfahani
Class
MAE 376: Applied Mathematics for MAEs
Dr. Paul T. Bauman, Dr. Ehsan Esfahani, Dr. Abani K. Patra
with contributions from Dr. Souma Chowdhury
Fall Semester 2016
c 2015 Paul T. Bauman, Ehsan Esfahani, Abani K. Patra
All rights reserved.
This work is intende
MAE 376:
Applied Mathematics for
Mechanical and Aerospace Engineers
Lecture 24
Ehsan T Esfahani, Ph.D.
Department of Mechanical and Aerospace Engineering,
University at Buffalo, The State University of New York
Fall 2016
Summary of Last Lectures
Solution
MAE 376:
Applied Mathematics for
Mechanical and Aerospace Engineers
Lecture 22
Ehsan T Esfahani, Ph.D.
Department of Mechanical and Aerospace Engineering,
University at Buffalo, The State University of New York
Fall 2016
NONLINEAR ALGEBRAIC EQUATIONS
Goal