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MATH W128A Numerical Analysis (Summer 2022)


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Use the floating Syllabus Navigation menu (above and to the side) to navigate through this syllabus.

See the Course Schedule for a weekly outline.

See the Course Summary below for a list of due dates (use the link at the top right of this page to "jump to today"). All times listed are Pacific Time. If you prefer, you can set your own time zone    (https:/community.canvaslms.com/t5/Student-Guide/How-do-I-set-a-time-zone-in-my-user- account-as-a-student/ta-p/414)  to display throughout bCourses.

Course Description

This course has the same content as the in-person version of Math 128A. The official description in the course catalog is as follows:

Basic concepts and methods in numerical analysis: Solution of equations in one variable; Polynomial interpolation and approximation; Numerical differentiation and integration; Initial-value problems for   ordinary differential equations; Direct methods for solving linear systems.

Course Objective

By the end of this course, you will be able to demonstrate understanding of the basic notions of numerical analysis that are needed in mathematics, science, and engineering.

Prerequisites

Math 53 and 54 or equivalent. It is helpful to have some basic programming skills, e.g. Math 98, Math 124, CS61A, Engin 7, or equivalent. It is recommended to view the "MATLAB Introduction" videos on the MATLAB page at the beginning of this course.

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Instructor Information, Office Hours, & Communication

Course Instructor

, persson@berkeley.edu

(mailto:persson@berkeley.edu)

Graduate Student Instructor (GSI)

, andrewshi@math.berkeley.edu (mailto:andrewshi@math.berkeley.edu)

While the instructor will interact with the whole class and will oversee all activities and grading, as      well as being available to resolve any issues that may arise, the GSI will be your main point of           contact. Your GSI is responsible for assisting you directly with your questions about assignments and course requirements, as outlined in the Assignments and Calendar. The GSI will also facilitate           ongoing discussion and interaction with you on major topics in each module.

Office Hours & Discussions

The course instructors will offer one-on-one office hours via Zoom. Book an appointment for an         individual session via one of the calendars at the bottom of the Live Sessions & Office Hours page   (linked in left navigation and on the homepage). Discussions will take place asynchronously via Ed   Discussion, and synchronously via the instructors' live Q&A sessions. While office hours are optional they can be valuable for discussion, answering questions, and reviewing for exams.

Ed Discussion

Ed Discussion (linked in course navigation on the left) will be used for discussions about the material. It is primarily intended for discussions between the students, but the instructors will also be there to   help answer questions (although perhaps not as frequently as other students). If you need more        direct communication with the instructors, please attend the scheduled office hours and live Q&A       sessions.


Course Materials and Technical Requirements

Required Materials

R. L. Burden and J. D. Faires, Numerical Analysis, 10th edition, Cengage Learning, 2015. ISBN-13: 978-1305253667 (Errata (https://sites.google.com/site/numericalanalysis1burden/module-5))

Note: The 9th edition is also supported

Technical Requirements

This course is built on a Learning Management system (LMS) called Canvas and you will need to

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2022/6/28 00:37                                                                                  Syllabus for Numerical Analysis (Summer 2022)

meet the computer specifications listed in bCourses to participate within this online platform.

MATLAB Requirements

The MATLAB programming language will be used for homework and programming assignments. There are various alternatives for using it:

You can download MATLAB (https://www.mathworks.com/academia/tah-portal/berkeley-

731130.html) for free through the UC Berkeley campus license.

Only the basic MATLAB functionality is needed for the course.

We recommend this option, if your computer supports it.

Alternatively, any computer with a browser can be used with MATLAB Online

() .


For students on the UC Berkeley campus, MATLAB is available in the computer lab B3A Evans

during drop-in hours. Check availability on the Evans-Comp Lab-B3A Google calendar ( cid=YmVya2VsZXkuZWR1XzcyNjU3MzZmNzU3MjYzNjUyZDMxMzgzOUByZXNvdXJjZS5jYWxlbmRhci5

.

The free alternative Octave (http://www.octave.org)has some limitations, but is sufficient for all

exercises in the class.

Recommended: view the "MATLAB Introduction" videos on the MATLAB bCourses page at the beginning of this course.

Technical Support

Neither the GSI, nor the professor can assist you with technical problems. You must call or email tech support and make sure you resolve any issues immediately. In your course, click on the Help” button on the bottom left of the global navigation menu. Be sure to document (save emails and transaction   numbers) for all interactions with tech support. Extensions and late submissions will not be accepted  due to technical difficulties.”


Learning Activities

VERY IMPORTANT

You won’t be able to access your course material until you read and make your pledge to Academic Integrity in the Orientation Module. You are expected to fully participate in all the course activities    described here.

1. Read the assigned sections of the textbook.

2. Watch and listen to the lecture presentations.


2022/6/28 00:37                                                                                  Syllabus for Numerical Analysis (Summer 2022)

3. Answer the Check Your Understanding” questions after each lecture segment.

4. Complete homework assignments, quizzes, and programming assignments.

5. Read announcements posted during the course.

6. (Optional but strongly recommended) Participate in office hours and live Q&A sessions.

7. (Optional but strongly recommended) Participate in discussions on Ed.

8. Complete the midterm and final exams.

Modules

Chapter 1: Introduction to the course. Review of MATLAB. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence.

Chapter 2: Solutions of Equations in One Variable: The Bisection Method, Fixed-Point Iteration, Newton’s Method and Its Extensions, Error Analysis for Iterative Methods, Accelerating             Convergence, Zeros of Polynomials and Müller’s Method.

Chapter 3: Interpolation and Polynomial Approximation: Interpolations and the Lagrange Polynomial, Divided Differences, Hermite Interpolation, Cubic Spline Interpolation.

Chapter 4: Numerical Differentiation and Integration: Numerical Differentiation, Richardson’s   Extrapolation, Elements of Numerical Integration, Composite Numerical Integration, Romberg Integration, Adaptive Quadrature Methods, Gaussian Quadrature, Multiple Integrals, Improper Integrals.

Chapter 5: Initial-Value Problems for Ordinary Differential Equations: The Elementary Theory of        Initial-Value Problems, Euler’s Method, Higher-Order Taylor Methods, Runge-Kutta Methods, Higher- Order Equations and Systems of Differential Equations, Error Control and the Runge-Kutta-Fehlberg Method, Multistep Methods, Stability, Stiff Differential Equations.

Chapter 6: Direct Methods for Solving Linear Systems: Linear Systems of Equations, Pivoting       Strategies, Linear Algebra and Matrix Inversion, The Determinant of a Matrix, Matrix Factorization, Special Types of Matrices.

Reading Assignments

Each chapter includes assigned readings from the textbook that correspond to the section/lecture    titles on the chapter pages. Please complete the assigned readings in addition to reviewing the lecture videos.

Lectures and Self-Check Questions

There will be a number of short video lectures each week. Each lecture segment will be followed by  one or more multiple-choice questions to check your understanding of the material, with instant         feedback and explanations of the answers. To receive a participation grade for the self-check            questions, you must answer the questions correctly, but you have as many attempts as needed to do so.

Gradescope

Gradescope will be used for submission of the homework, programming assignments, and midterm   and final exams. All Gradescope assignments are linked in bCourses. For instructions on how to scan and upload on Gradescope, see this video on submitting PDF homework () and this handout with recommended scanning apps () . Note in particular, that you are expected to produce a clear and readable PDF of your assignments, and to    mark which page each problem can be found on (as described on page 3 of the Gradescope handout above).

Homework Assignments

The weekly homework (a total of 7 assignments) is due on Tuesdays at 11:59pm Pacific Time, the     week after it is set (e.g., Homework 1 is due on the Tuesday of Week 2). These will be graded only    based on completeness, with each homework submission receiving a score of 0, 1, or 2 depending    on the effort. Note that the correctness is not evaluated, and it is highly recommended that students   study the official solutions when they are posted. Collaboration on homework with fellow students is   permitted, as long as each student writes their own solutions independently. The homework grade is  determined by the percentage of homework assignments that are completed on time. Late homework will not be accepted, but the lowest score will be dropped when computing the grade.

Quizzes

The weekly quizzes (a total of 7) are due on Tuesdays at 11:59pm (Pacific Time). The first quiz is due on Tuesday of the second week. The quizzes will be available on Gradescope for a 24-hour period,    from 11:59 pm (Pacific Time) on Mondays until 11:59 pm (Pacific Time) on Tuesdays. Quizzes will be similar to homework, except that they will be shorter and will be graded with a more detailed rubric in Gradescope. There is a 40-minute time limit: 30 minutes for completing the quiz and an extra 10        minutes for scanning and uploading your solutions. Thus, after a quiz is started, it must be submitted within 40 minutes. The quizzes will be “open book”: the textbook and course materials may be used.  However, no collaboration is allowed and the internet and electronic devices may not be used except as needed to access the course materials. There will be no make-up quizzes, but the quiz with lowest score will be dropped when computing the grade.

Programming Assignments

There will be a total of four programming assignments. Detailed PDF reports must be submitted,      including MATLAB code, plots, and comments. These will be graded with detailed rubrics in              Gradescope. Collaboration on the programming assignments with fellow students is permitted, as    long as each student writes their own solutions, computer codes, and reports independently. All four programming assignments count towards the course grade.

Solutions

Solution files for the homework, quizzes, and programming assignments will be made available on the Solutions page.

Participation


The participation grade is determined by the percentage of self-check questions that are answered correctly before the end of the course. You will have unlimited attempts on each question.

Discussion Forums

Students are encouraged to use Ed to discuss questions of general interest regarding the course    content. Messages not tied to any specific homework assignment should be posted with the tag      “General Q and A” . The GSI and the professor will periodically check in and help answer questions.

Midterm Exam

The midterm exam will take place remotely on Thursday July 21, 2022. Further details can be found on the Midterm Exam Review page, under "Midterm Exam Information."

Final Exam

The final exam will take place remotely on Thursday August 11, 2022. Further details can be found on the Final Exam Review page, under "Final Exam Information."