10/26/10
cs412: introduction to numerical analysis
Lecture 13: Cubic Hermite Spline Interpolation II
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Cubic Hermite Spline Interpolation
Recall in the last lecture we
09/14/10
cs412: introduction to numerical analysis
Lecture 2: Introduction Part II and Solving Equations
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw
Numerical Solution to Quadratic Equations
Recall from last lecture that we wanted
12/9/10
cs412: introduction to numerical analysis
Lecture 25: Numerical Solution of Dierential Equations Error Analysis
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Error Analysis for Solving IVP
For the last se
12/09/10
cs412: introduction to numerical analysis
Lecture 24: Systems of First Order Dierential Equations
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Systems of First Order IVP
In the last lecture, we discusse
12/07/10
cs412: introduction to numerical analysis
Lecture 23: Systems of Dierential Equations
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Review
For the last few lectures, we have discussed the solution of ini
12/7/10
cs412: introduction to numerical analysis
Lecture 22: Rules for Solving IVP
Instructor: Professor Amos Ron
1
Yunpeng Li, Pratap Ramamurthy,
Mark Cowlishaw, Nathanael Fillmore
Scribes:
Review
Recall that last time we discussed the numerical solutio
11/30/10
cs412: introduction to numerical analysis
Lecture 21: Numerical Solution of Dierential Equations
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Introduction
The last topic of this semester is numerical so
11/18/10
cs412: introduction to numerical analysis
Lecture 20: Numerical Integration III
Instructor: Professor Amos Ron
Scribes: Mark Cowlishaw, Yunpeng Li, Nathanael Fillmore
For the last few lectures we have discussed numerical approximations of the den
11/16/10
cs412: introduction to numerical analysis
Lecture 19: Numerical Integration II
Instructor: Professor Amos Ron
1
Scribes: Mark Cowlishaw, Nathanael Fillmore
Error Analysis of Simple Rules for Numerical Integration
Last time we discussed approximat
11/16/10
cs412: introduction to numerical analysis
Lecture 18: Numerical Integration
Instructor: Professor Amos Ron
1
Scribes: Mark Cowlishaw, Nathanael Fillmore
Numerical Integration
Recall that last lecture, we discussed numerical integration. Given an
11/9/10
cs412: introduction to numerical analysis
Lecture 17: Rectangular Systems and Numerical Integration
Instructor: Professor Amos Ron
1
Scribes: Mark Cowlishaw, Nathanael Fillmore
Review of Least Squares Solutions to Overdetermined Systems
Recall tha
11/4/10
cs412: introduction to numerical analysis
Lecture 16: Linear Algebra III
Instructor: Professor Amos Ron
Scribes: Mark Cowlishaw, Nathanael Fillmore
For the last few lectures we have discussed numerical solutions to linear systems of equations
Ax =
11/02/10
cs412: introduction to numerical analysis
Lecture 15: Linear Algebra II
Instructor: Professor Amos Ron
Scribes: Mark Cowlishaw, Nathanael Fillmore
Recall that last time, we were discussing the numerical solution of systems of linear equations.
Ax
10/26/10
cs412: introduction to numerical analysis
Lecture 14: Linear Algebra
Instructor: Professor Amos Ron
1
Scribes: Mark Cowlishaw, Nathanael Fillmore
Introduction
In the last few classes, we have discussed several methods for approximating the behavi
10/21/10
cs412: introduction to numerical analysis
Lecture 12: Cubic Hermite Spline Interpolation
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Review of Interpolation using Cubic Splines
Recall from last time th
10/19/10
cs412: introduction to numerical analysis
Lecture 11: Interpolation by Cubic Splines
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Review
Recall from last time the denition of a cubic spline.
Definition
10/12/10
cs412: introduction to numerical analysis
Lecture 10: Introduction to Splines
Instructor: Professor Amos Ron
1
Scribes: Mark Cowlishaw, Nathanael Fillmore
Review of Chebyshev Points
Last time we talked briey about using Chebyshev points for polyn
10/17/10
cs412: introduction to numerical analysis
Lecture 9: Polynomial Interpolation: Error Analysis and Introduction to Splines
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Error Analysis
Recall the error for
10/05/10
cs412: introduction to numerical analysis
Lecture 8: Polynomial Interpolation: Using Newton Polynomials and Error Analysis
Instructor: Professor Amos Ron
1
Scribes: Giordano Fusco, Mark Cowlishaw, Nathanael Fillmore
Review of Newton Polynomials
R
09/30/10
cs412: introduction to numerical analysis
Lecture 7: Newton Interpolation
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Motivation for Newton interpolation
Recall the polynomial interpolation problem we
09/28/10
cs412: introduction to numerical analysis
Lecture 6: Polynomial Interpolation II
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Polynomial Interpolation as a Linear Problem
Last time, we introduced the po
09/23/10
cs412: introduction to numerical analysis
Lecture 5: Solving Equations and Polynomial Interpolation
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
More on Newtons Method and the Secant Method
In the last
09/21/10
cs412: introduction to numerical analysis
Lecture 4: Solving Equations: Newtons Method, Bisection, and the Secant Method
Instructor: Professor Amos Ron
1
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Review of Fixed Point Iterations
In
09/14/10
cs412: introduction to numerical analysis
Lecture 3: Solving Equations Using Fixed Point Iterations
Instructor: Professor Amos Ron
Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore
Our problem, to recall, is solving equations in one variabl
Fall Semester 09-10
Akila Weerapana
Lecture 27: FIXED EXCHANGE RATES
I. OVERVIEW
In the last class, we discussed the basics of exchange rates and exchange rate determination.
The exchange rate describes the price of one currency in terms of another. In t
Fall Semester 09-10
Akila Weerapana
Lecture 26: International Finance
I. OVERVIEW
Earlier on in this class, we discussed how money serves as a medium of exchange that simplies
transactions between millions of people interacting in a marketplace. Even tho
Fall Semester 09-10
Akila Weerapana
Lecture 25: The Outlook For The U.S. Economy
I. OVERVIEW
In the last class, we discussed the policy options available for the U.S. economy, categorizing
them into scal, monetary and banking options.
The scal policy ne
Fall Semester 09-10
Akila Weerapana
Lecture 24: Policy Responses to The Recession of 2008/09
I. OVERVIEW
In the last lecture, we discussed the nancial crisis of 2008/09, a credit crunch precipitated
by a collapse of a bubble in the U.S. housing market th
Fall Semester 09-10
Akila Weerapana
Lecture 23: The Financial Crisis of 2008
I. OVERVIEW
Having just completed the midterm, and with it the bulk of the macroeconomic models we
learn in this class, I thought that this week would be a good one for applying
Fall Semester 09-10
Akila Weerapana
Lecture 22: Monetary Policy
I. OVERVIEW
In the last lecture, we took a closer look at what a good scal policy would be both when the
economy was in a recession, and when it was not.
We showed that after a negative spe