Math 1070 Fall Semester 2022

Numerical Mathematical Analysis
MWF 10:00-10:50, A522 Public Health-Crabtree

Aug 29, 2022 - Dec 9, 2022

Office Hours

MW 3:00 - 4:00, and by appointment (also via zoom)
Office: Thackeray 612
E-mail: trenchea@pitt.edu

This course is an introduction to modern numerical methods. Topics include polynomial and spline interpolation, numerical integration and differentiation, numerical solution of nonlinear equations and ordinary differential equations. Our goal will be to understand how and when the methods work. The concept of numerical error will be used to quantify the accuracy of approximation. We will also study the stability and the efficiency of the algorithms.

Computer assignments will use Matlab, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows in the university computing labs. The full set of manuals is on the web in html and also in Adobe PDF format. The "Getting Started" manual is a good place to begin and is available both in html format and in Adobe PDF format. The full reference manual as well as manuals for each of the many toolboxes are all available.

Course Delivery

Tutoring: The Mathematics Department offers a free tutoring service. The Math Assistance Center (MAC) is located on the second floor of the O’Hara Student Center. Tutoring services and tutoring hours will be posted outside the MAC as well as on the web at MAC.

Course materials

Textbook: Elementary Numerical Analysis, 3rd edition by Kendall Atkinson and Weimin Han.

  • Syllabus
  • Matlab Primer
  • Matlab Tutorial: Postscript; HTML
  • MATLAB computer lab exercises by Dr. John Burkardt.
  • Introduction to Matlab by Dr. Mike Sussman: Preliminaries; Beginning Matlab
    For useful material related to this course go to Kendall Atkinson's class web page

    Software

  • A collection of matlab codes accompanying the text
  • Some graphical user interfaces
    Additional references :
  • Numerical Mathematics, second edition, by A. Quarteroni, R. Sacco, F. Faleri. Book's Programs
  • Numerical Methods in Scientific Computing, volume I, by G. Dahlquist, A. Bjorck. SIAM.
  • Numerical Methods, by G. Dahlquist, A. Bjorck. Dover.

    Homework Assignments

  • Homework 1, Due September 9, 2022: Section 1.1 # 9, Section 1.2 #6, 9c, 15, 17
  • Homework 2, Due September 23, 2022: Section 2.2 #1b,d, 5b,c, 6f,h; Section 2.3 #9
  • Homework 3, Due September 30, 2022: Section 4.1 #7, 8a, 12-bonus, 23a, 25
  • Homework 4, Due October 12, 2022: Section 4.2 #1, 4; Section 4.3 #1, 11; Hermite interpolation problem
  • Homework 5, Due October 19, 2022: Section 5.1 #1, 11b,c, 16
  • Homework 6, Due October 26, 2022: Section 5.2 #1a, 7, 15, 19
  • Homework 7, Due November 2, 2022: Section 5.3 #2 - only do I-2, I-3 for 2a,b,c; #9; Section 5.4 #1a, #3 - only do a), #8, #9 - only do a)
  • Homework 8, Due November 9, 2022: Section 3.1 #1d, 9; Section 3.2 #2d, 3, 13 (extra credit); Section 3.3 #1d, 4
  • Homework 9, Due November 16, 2022: Section 3.4 #1, 5, 8, 11, 13a
  • Homework 10, Due November 23, 2022: Section 3.5 #1 (use the code from newton.m, error_bd = 1e-8, x0 = -1 and 1), 8
  • Homework 11, Due December 7, 2022

    Matlab Assignments

  • Matlab Exercise 1. Due September 9, 2022.
  • Matlab Exercise 2. Due October 24, 2022.
  • Matlab Exercise 3. Due November 16, 2022.
  • Matlab Exercise 4. Due December 7, 2022.

    Exams

  • Exam 1: October 7, 2022.
  • Exam 2: November 9, 2022.
  • Final Exam: 12/14/2022, Wednesday 2:00PM - 3:50PM 105 Alexander J. Allen Hall, December 14, 2022.

    Disability Resource Services

    If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services (DRS), 140 William Pitt Union, 412-648-7890, drsrecep@pitt.edu, (412) 228-5347 for P3 ASL users, as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

    Academic Integrity

    The University of Pittsburgh Academic Integrity Code is available at https://www.provost.pitt.edu/faculty/academic-integrity-freedom/academic-integrity-guidelines. The code states that "A student has an obligation to exhibit honesty and to respect the ethical standards of the academy in carrying out his or her academic assignments." The website lists examples of actions that violate this code. Students are expected to adhere to the Academic Integrity Code, and violations of the code will be dealt with seriously.

    On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.

    This is especially notable during this period. Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a zero score for the quiz, exam or paper in question. Additional sanctions may be imposed, depending on the severity of the infraction.
    Please note, in particular, that Pitt has a data sharing arrangement with Chegg.com that enables us to identify in- stances in which Chegg.com has been used to cheat on assessments. Consequences of being caught in this academic integrity violation have included zero scores on assessments and F grades for the course.

    Health and Safety

    In the midst of this pandemic, it is extremely important that you abide by public health regulations and University of Pittsburgh health standards and guidelines. While in class, at a minimum this means that you must wear a face covering and comply with physical distancing requirements; other requirements may be added by the University during the semester. These rules have been developed to protect the health and safety of all community members. Failure to comply with these requirements will result in you not being permitted to attend class in person and could result in a Student Conduct violation. For the most up-to-date information and guidance, please visit coronavirus.pitt.edu and check your Pitt email for updates before each class.

    Diversity and Inclusion

    The University of Pittsburgh does not tolerate any form of discrimination, harassment, or retaliation based on disability, race, color, religion, national origin, ancestry, genetic information, marital status, familial status, sex, age, sexual orientation, veteran status or gender identity or other factors as stated in the University's Title IX policy. The University is committed to taking prompt action to end a hostile environment that interferes with the University's mission. For more information about policies, procedures, and practices, see: https://www.diversity.pitt.edu/civil-rights-title-ix-compliance/policies-procedures-and-practices.

    Classroom Recording

    To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities not already recorded by the instructor, without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student's own private use.

    Lectures could be recorded by the instructor, and this may include student participation. Students are not required to participate in the recorded conversation. The recorded lecture may be used by the faculty member and the registered students only for internal class purposes and only during the term in which the course is being offered. Recorded lectures will be uploaded and shared with students through Canvas.

    Copyright

    Some of the materials in this course may be protected by copyright. United States copyright law, 17 USC section 101, et seq., in addition to University policy and procedures, prohibit unauthorized duplication or retransmission of course materials. See the Library of Congress Copyright Office and the University Copyright Policy.