numerical analysis homework

Browse Course Material

Course info.

• Prof. Laurent Demanet

Departments

• Mathematics

As Taught In

• Applied Mathematics
• Computation

Learning Resource Types

Introduction to numerical analysis, assignments.

You are leaving MIT OpenCourseWare

Math 128A - Numerical Analysis

Uc berkeley, fall 2021, course website.

• The course is hosted on bCourses __________________________________________________________________________________________

Lecture Videos

• Pre-recorded Lecture Videos __________________________________________________________________________________________

Lecture Slides

• Chapter 1 - Mathematical Preliminaries and Error Analysis ( PDF , HTML )
• Chapter 2 - Solutions of Equations in One Variable ( PDF , HTML )
• Chapter 3 - Interpolation and Polynomial Approximation ( PDF , HTML )
• Chapter 4 - Numerical Differentiation and Integration ( PDF , HTML )
• Chapter 5 - Initial-Value Problems for Ordinary Differential Equations ( PDF , HTML )
• Chapter 6 - Direct Methods for Solving Linear Systems ( PDF , HTML ) __________________________________________________________________________________________

MATLAB Codes

All in-class MATLAB codes

Organized by textbook sections:

• Section 1.2: num2bin.m
• Section 2.1: bisection.m , bisection_table.m
• Section 2.2: fixedpoint.m , fixedpoint_table.m , fixedpoint_plot.m
• Section 2.3: newton.m , newton_table.m , newton_plot.m
• Section 2.5: steffensen.m , steffensen_table.m
• Section 2.6: horner.m , muller.m , muller_table.m , muller_plot.m
• Section 3.3: divideddifference.m
• Section 3.5: ncspline.m , ccspline.m , splineeval.m , diffsplineeval.m , splinedemo.m
• Section 4.1: diffdemo.m
• Section 4.2: richdemo.m
• Section 4.5: romberg.m
• Section 4.7: gaussquad.m
• Section 4.8: simpsondouble.m , gaussdouble_demo.m
• Section 4.9: laguerrequad.m
• Section 5.4: rk4.m
• Section 5.11: rk4stability.m
• Programming Assignment 3: pendplot.m
• Section 6.2: gausselim.m
• Section 6.5: lu_demo.m , mkM.m __________________________________________________________________________________________

Department of Mathematics

Math 448/548: numerical analysis.

• Job Opportunities

Numerical Analysis Resources

The principal reason we think we can do without a text this semester is that there is such an abundance of resources available free, or at low cost. Here is a list of a few of them. The appearance of a site on this list should not be taken as an endorsement of the material. The sheer volume of material available makes it difficult to vet everything as thoroughly as I would like. If you find mistakes or other infelicities, please let the instructor know.

Free Internet Resources

• Numerical Computing with Matlab , by Cleve Moler. You will need to register to download this text.
• Transforming Numerical Methods Education for the STEM Undergraduate has text materials as well as youtube lectures.
• A site at Cal Fullerton has a variety of resources, but what seemed most interesting was some animations of certain numerical methods.
• I question the strategy of covering elliptic PDEs before discussing methods for linear algebra, but a physicist at Oxford has produced a text that does so . It uses Maple, and appears to have useful information.
• MIT has a large number of online course materials, including some for Numerical Analysis for Engineers .
• MyMath has online software
• Octave is free Matlab lookalike software.

If you feel a need to have an actual book to look at, here are some. Since these are not required, if you choose to buy one you may pick any edition you like.

• Scientific Computing, An Introductory Survey, by Michael Heath, is a relatively new book that covers topics in a good order. I have not used this book, but I like its table of contents.
• Elementary Numerical Analysis: An Algorithmic Approach , Conte and DeBoor, is an old book that I have always liked. The order of the topics is not what I prefer, but it is written well at a good undergraduate level. I see that you can buy used copies for as little as $0.30. At that price, you cannot afford not to have this on your shelf.
• Numerical Analysis, by Richard Burden and J. Douglas Faires, is a text that has been used very broadly. It should be possible to pick up a cheap older edition.

Numerical Analysis

David gleich, purdue university, spring 2021, course number cs-51400, math-51400, online due to covid-19 pandemic, social distance, wear a mask., zoom, tuesday and thursday, 10:30-11:45, numerical analysis, announcements.

Numerical analysis is the study of computer-based numerical methods for working with common mathematical and scientific operations. The emphasis of the course is on numerical algorithms, represented as computer codes, their mathematical abstractions, represented as rigorously as possible, and the resulting approximation errors. This is a graduate class on these methods that would serve a fondation for students in computer science, mathematics, computational science and engineering, statistics, engineering, and releated fields that will use numerical algorithms and approximations in their work.

The topics we'll cover include:

• Computer-friendly representations of numbers including floating-point arithmetic
• Approximations to functions
• Numerical methods to differentiate and integrate functions
• Methods to solve non-linear equations (CS 51500 focuses on linear equations)
• Numerical solutions to ODEs

An undergraduate version of this course is available as CS314, and for students from disciplines other than CS and Mathematics, this might be more suitable depending on your previous knowledge of this material.

Books and reading materials

The following textbook is officially required. But you won't need it for any of the homework problems.

Walter Gautschi, Numerical Analysis 2nd Edition . Birkhauser/Springer, 2012 http://dx.doi.org/10.1007/978-0-8176-8259-0

See the readings page for additional references as well as a set of recommended readings associated with each lecture. These will be updated after the lecture and not before. There is a rough reading guide in the syllabus.

This is a lecture class. You (the student) will be expected to attend lectures and there will be regular homeworks. These will include writing computer codes in the Matlab or Julia languages. There will also be a midterm and a final. More detailed requirements are explained in the syllabus including the course policies.

• Course Home
• Readings & Lectures
• Brightspace

Assignments

• Intro video survey (html) (tex) (pdf)
• Homework 1 (html) (tex) (pdf)
• Homework 2 (html) (tex) (pdf)
• Homework 3 (html) (tex) (pdf)
• Homework 4 (html) (tex) (pdf)
• Homework 5 (html) (tex) (pdf)
• preamble.tex

Copyright © David F. Gleich 2021

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• Homework Assignments and due dates Homework Problem Set Homework Problem Set 1 Solutions Homework Problem Set 2 Solutions Homework Problem Set 3 Solutions Homework Problem Set 4 Solutions Homework Problem Set 5 Solutions Homework Problem Set 6 Solutions
• Project Ideas and Information
• Old Math 611 Final Exams Final Exam 1990 Final Exam 1996 Final Exam 1997 Final Exam 2000

Bisection    Bisection computer code in C Newton's Method    Newton's Method computer code in C Fixed Point Iteration Computer Code in C Secant Method Computer Code in C

Aitken & Steffenson Method    Aitken's and Steffensen's Methods Computer code in C Romberg Method    Romberg Method Computer code in C

Lagrange Interpolation    Lagrange interpolation Computer code in C

Right Rectangles Comparisons of Trapezoid, Simpson and Midpoint Methods Computer code in C

Taylor Series Comparison of One-Step ODE solvers Computer code in C Adam-Bashforth    Adams-Bashforth/Moulton Predictor-Corrector Computer code in C

   Gaussian Elimination Computer code in C