### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# BEG SCI COMPUTING AMATH 301

UW

GPA 3.59

### View Full Document

## 43

## 1

## Popular in Course

## Popular in Applied Mathematics

This 4 page Class Notes was uploaded by Mossie Pfannerstill V on Wednesday September 9, 2015. The Class Notes belongs to AMATH 301 at University of Washington taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/192280/amath-301-university-of-washington in Applied Mathematics at University of Washington.

## Reviews for BEG SCI COMPUTING

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/09/15

AMath 301 Final Review The exam is Thursday March 20 2008 at 830 am The material will be over the whole course with more emphasis on post midterm material No notes books or calculators allowed Bring your mind I will provide you a list of relevant MATLAB function calls if you need them In the exam you will be asked to both calculate by hand and ALSO write MATLAB code When you write code for the exam write it as if I will write a m le and run your code Along with the midterm review 0 Ordinary Differential Equations pages 50 78 in notes 7 Initial Value Problems Euler s Method and how to time step with it Local Truncation error of Euler s method 9 9 9 How to check the order of a time step method by reducing the stepsize and calcu lating the error Idea of Runge Kutta methods Heun s method Writing a higher order differential equation as a rst order system Implementation of MATLAB s ode solver 0de45 Understand output from MATLAB s ode solver 0de45 9 99 7 Boundary Value Problems Idea of the shooting method for a linear second order problem see handout ldea and implementation of shooting method for nonlinear problems Direct solve method 0 Partial Differential Equations pages 89 105 7 Solving PDE with spatial discretization Solving a PDE using spatial discretization and time stepping Know how to represent a rst den39uatz39ue operator as a centered second order matrix operation 9 Know how to represent a second derivative operator as a centered second order matrix operation spdiags command in MATLAB How the spatial discretization converts the PDE into a system of ODEs Implementing MATLAB code to solve the PDE using spatial discretization 7 Solving a PDE spectrally fft ifft commands and what they do The relation of a Fourier Transform of a spatial derivative of some function to the Fouier Transform of that function Taking the Fourier Transform of a PDE How taking the Fourier Transform of a PDE converts it to an ODE for the transform of the function you want 9 9 9 9 Timestepping the transformed equation to obtain a solution Idea of periodic boundary conditions Example Problems 1 Consider the approximation to the second derivative dz g 1 A95 7 21 f90 A95 dmz Am Using a Taylor series approximation7 obtain the leading order truncation error in this approximation 2 Consider the ordinary differential equation dzu du 3 W a u 7 0 a Write this second order ODE as a rst order system 10 Write a MATLAB code that uses ODE45 to solve for Use a tspan 07 10 7 140 17 and uO 0 Include your rhsm le AMath 301 Final Review The exam is Monday June 4 2007 at 830 am The material will be over the whole course with more emphasis on post midterm material No notes books or calculators allowed Bring your mind I will provide you a list of relevant MATLAB function calls if you need them In the exam you will be asked to both calculate by hand and ALSO write MATLAB code When you write code for the exam write it as if I will write a m le and run your code Along with the midterm review 0 Numerical Differentiation and Integration page 38 50 in notes Round off error and how it can effect computations idea Taylor series and how they are used to approximate derivatives Be able to check the order of a certain approximation Optimal step size to reduce error 7 Composite Trapezoidal rule integrating some function 7 MATLAB trapz cumtrapz quad commands 0 Ordinary Differential Equations pages 50 78 in notes 7 Initial Value Problems Euler s Method and how to time step with it Local Truncation error of Euler s method How to check the order of a timestep method by reducing the step size and calcu lating the error Idea of Runge Kutta methods Heun s method Writing a higher order differential equation as a rst order system Implementation of MATLAB s ode solver 0de45 Understand output from MATLAB s ode solver 0de45 9 99 9 7 Boundary Value Problems Idea of the shooting method Direct solve method 0 Partial Differential Equations pages 89 105 7 Solving PDE with spatial discretization 9 9 Solving a PDE using spatial discretization and timestepping Know how to represent a rst derivative operator as a centered second order matrix operation Know how to represent a second den39uatz39ue operator as a centered second order matrix operation spdiags command in MATLAB How the spatial discretization converts the PDE into a system of ODEs Implementing MATLAB code to solve the PDE using spatial discretization 7 Solving a PDE spectrally 9 9 9 fft7 ifft commands7 and what they do The relation of a Fourier Transform of a spatial derivative of some function to the Fouier Transform of that function Taking the Fourier Transform of a PDE How taking the Fourier Transform of a PDE converts it to an ODE for the transform of the function you want Timestepping the transformed equation to obtain a solution Idea of periodic boundary conditions Example Problems 1 Consider the approximation to the second derivative 121 dmz N fA2f A N Am2 Using a Taylor series approximation7 obtain the leading order truncation error in this approximation 2 Consider the ordinary differential equation a Write this second order ODE as a rst order system b Write a MATLAB code that uses ODE45 to solve for Use a tspan 0107 140 17 and uO 0 Include your rhsm le

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.