Numerical Analysis I

MATH 345 : Fall 2023

Department of Mathematics - SUNY Geneseo

Course Description

This course provides an introduction to numerical methods and the analysis of these methods. Topics include floating point arithmetic, error analysis, solution of non-linear equations, interpolation and approximation, numerical differentiation and integration, and the solution of linear systems.


Cesar Aguilar, South Hall 325A

Office Hours

Tue 8:30-9:30, 10:45-11:45
Thu 10:45-11:45

Class Meetings

Tue & Thu, 12:30-1:45, Welles 121


Anaconda Python
64-bit graphical installer

Final Exam

Tuesday, December 19, 12:00-2:30PM, Welles 121

Textbook and Resources

  1. Numerical Analysis by Cesar Aguilar
  2. Numerical Analysis by Burden and Faires, 8th edition or higher
  3. Whirlwind Tour of Python (good book)
  4. Python Data Science Handbook (good book)
  5. Official Python Tutorial

Student File Upload

  Upload your homework, test, lab


The current week content will be displayed here during the semester. For now, see the Schedule tab.


Title Due Date Week No.
Homework 1 - Taylor's Theorem and Errors Sep 8, 2023 1
Homework 2 - Bisection Method Sep 19, 2023 3
Homework 3 - Fixed Point Iteration Oct 1, 2023 4
Homework 4 - Lagrange Interpolation Oct 26, 2023 7
Homework 6 - Divided Differences Nov 7, 2023 10
Homework 7 - Numerical Differentiation Nov 20, 2023 11
Homework 8 - Numerical Integration Dec 3, 2023 13


Week 1  Aug 28 - Sep 01
Python, Calculus, Round-Off Error
Topics: Python, Calculus, Round-Off Error
What to Read: 1.1, 1.2
Aug 28 First day of classes
Week 2  Sep 04 - Sep 08
Algorithms, Bisection Method
Topics: Algorithms, Bisection Method
What to Read: 1.3, 2.1
Sep 04 Labor Day: No Classes
HW DUE HW 1DUE: Sep 08
Week 3  Sep 11 - Sep 15
Bisection Method, Convergence
Topics: Bisection Method, Convergence
What to Read: 2.1
Files: Lab #1
Week 4  Sep 18 - Sep 22
Fixed-Point Iteration, Newton's Method
Topics: Fixed-Point Iteration, Newton's Method
What to Read: 2.2, 2.3
HW DUE HW 2DUE: Sep 19
Week 5  Sep 25 - Sep 29
Error Analysis, Test #1
Topics: Error Analysis, Test #1
What to Read: 2.4
NEXT WEEK Test 1 on Oct 3, 12:30 PM – 1:45 PM
Week 6  Oct 02 - Oct 06
Lagrange Interpolation
Topics: Lagrange Interpolation
What to Read: 3.1
HW DUE HW 3DUE: Oct 01
TEST 1 Oct 3, 12:30 PM – 1:45 PM
Week 7  Oct 09 - Oct 13
Chebyshev Polynomials
Topics: Chebyshev Polynomials
What to Read: 3.2
Oct 09-10 Fall Break: No Classes
Week 8  Oct 16 - Oct 20
Divided Difference
Topics: Divided Difference
What to Read: 3.3
Week 9  Oct 23 - Oct 27
Hermite Polynomials
Topics: Hermite Polynomials
What to Read: 3.4
HW DUE HW 4DUE: Oct 26
Week 10  Oct 30 - Nov 03
Cubic Splines, Test #2
Topics: Cubic Splines, Test #2
What to Read: 3.5
NEXT WEEK Test 2 on Nov 9, 12:30 PM – 1:45 PM
Week 11  Nov 06 - Nov 10
Topics: Differentation
What to Read: 4.1
HW DUE HW 6DUE: Nov 07
TEST 2 Nov 9, 12:30 PM – 1:45 PM
Week 12  Nov 13 - Nov 17
Topics: Integration
What to Read: 4.2
Week 13  Nov 20 - Nov 24
Integration, Review
Topics: Integration, Review
What to Read: 4.2
Nov 22-24 Thanksgiving Break: No Classes
HW DUE HW 7DUE: Nov 20
Week 14  Nov 27 - Dec 01
Gaussian Elimination
Topics: Gaussian Elimination
What to Read: 5.1
Week 15  Dec 04 - Dec 08
LU Decomposition
Topics: LU Decomposition
What to Read: 5.2
HW DUE HW 8DUE: Dec 03
Week 16  Dec 11 - Dec 15
Topics: N/A
Dec 11 Last day of classes


Learning Outcomes

Upon successful completion of MATH 345 - Numerical Analysis I, a student will be able to:

    Grading Scheme

    Below is the tentative course grading scheme. The grading scheme may change during the semester at the discretion of the instructor. Any changes to the grading scheme will be announced in class before the final exam. If homework assignments are done in groups, then a student must achieve a passing grade in all individual assessments (e.g., tests and final exam) to pass the course.

    E< 60

    Tests and Exam

    There will be 3-4 tests scheduled evenly throughout the semester. The final exam is scheduled for Tuesday, December 19, 12:00-2:30PM, Welles 121. The final exam will be cumulative, that is, any topic covered in the course could be tested in the final exam. There will be no make-up for a missed test or final exam under any circumstances. If a student misses a test and can present evidence of an extenuating circumstance then the weight of the missed test will be redistributed to the final exam weight. Having the cold or flu is not an extenuating circumstance. Examples of extenuating circumstances include a medical emergency, a serious prolonged illness, or the death of a member of your immediate family.


    There will be approximately 10 homework assignments throughout the semester. You will be given approximately 5 days to submit your solutions to the homework problems. Homework solutions should be written in Python using a .py file extension and your .py file should be uploaded using the file upload link. I encourage you to collaborate with your colleagues on your assignments/labs but your final submitted work should be your own (see Academic Dishonesty statement below).

    Textbook and Resources

    1. Numerical Analysis by Cesar Aguilar
    2. Numerical Analysis by Burden and Faires, 8th edition or higher
    3. Python Data Science Handbook (supplement)
    4. Official Python Tutorial


    We will be using the general purpose programming language Python for this course. Download and install Python here.

    Office Hours and Math Learning Center

    I encourage you to come to my office (South Hall 325A) whenever you are having trouble with any part of the course material, seeking academic advice, or you just want to chat about mathematics in general. If you want to meet with me outside of my office hours, you will need to make an appointment, preferably via email. I also encourage you to visit the Math Learning Center located in South Hall 332 where you can receive free tutoring on a walk-in basis by highly qualified upper level students. Access to in-person office hours and to the MLC will depend on social distancing guidelines set by the College.

    Email Communication

    I will do my best to reply to student email regarding the logistics of the course within 24 hours during the working week (Mon-Fri). However, due to the potential large volume of emails, inquiries regarding homework problems and/or specific course content should be made during office hours or after class.

    Academic Dishonesty and Plagiarism

    Please read, and follow, Geneseo's Academic Dishonesty and Plagiarism policy. Below is the definition of plagiarism and its consequences as described in SUNY Geneseo's Academic Dishonesty and Plagiarism statement:

    Plagiarism is the representation of someone else's words or ideas as one's own, or the arrangement of someone else's material(s) as one's own. Such misrepresentation may be sufficient grounds for a student's receiving a grade of E for the paper or presentation involved or may result in an E being assigned as the final grade for the course.

    If there is sufficient evidence of academic dishonesty on a homework assignment, all students involved will receive a zero score on the homework assignment and I will provide the department chairperson, the dean of academic planning and advising, and the student(s) with a written report of the violation, the penalty imposed and the counseling provided to the students involved. A second instance of academic dishonesty on a homework assignment will result in a final grade of E for the course for all students involved. Academic dishonesty on a test/final exam will result in a final grade of E for the course.

    Academic Accommodations

    SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility (OAS) will coordinate reasonable accommodations for persons with disabilities to ensure equal access to academic programs, activities, and services at Geneseo.

    Students with approved accommodations may submit a semester request to renew their academic accommodations. Please visit the OAS website for information on the process for requesting academic accommodations.

    Questions? Contact the OAS by email, phone, or in-person:

    Office of Accessibility Services
    Erwin Hall 22