MA427:

Introduction to Numerical Analysis I

This course forms the first part of a year-long exploration into the fascinating world of numerical analysis. This course sequence offers a comprehensive introduction to the essential methods and theories that underpin modern computational mathematics. Over the span of two semesters, you will engage with a wide spectrum of foundational topics, including the analysis and solution of both nonlinear and linear problems, as well as the development and implementation of practical algorithms that drive modern computation.

• General syllabus about this one-year sequence includes the following subjects (not necessarily in order.)
• The emphasis in MA427 will focus primarily on nonlinear problems, while MA428 emphasizes linear problems, ensuring a balanced and thorough exploration of the field. be on the nonlinear problems, whereas the emphasis in MA428 will be on the linear problems. 
• To gain a complete understanding of the diverse computational techniques presented, students are strongly encouraged to enroll in both semesters of the sequence.
• A working knowledge of programming is expected, as computational experiments and algorithmic implementation form an integral part of the learning experience.

Reading materials:

• Text book: My own lecture notes by subjects for this course are available on line.
• The following books are good references for this subject:
1. Introduction to Numerical Analysis, Third Edition, Stoer and Bulirschs.
2. Numerical Analysis, L. Ridgway Scott.
3. Numerical Analysis, 2^nd Edition, Tim Sauer.

Some useful tools:

• Unix Reference Desk
• Netlib: Numerical Analysis Library Network (Lots of library routines)
• AMS: American Mathematical Society (Math Review on line)
• NCSU Library: Enter it with an awesome heart and a humble attitude; out of it with a learned mind.
• Encyclopedia s and Dictionaries: Who says a mathematician doesn't need these?
• RBC: Something good for your souls
  

Grading Policy:

• final grade= (25% homework) + (50% projects) + (25% final exam)
• Homework and final exam are to be completed by individuals.

1. Homework will be assigned intermittently.
2. Homework is meant to supplement gaps in lectures, so do expect a quick turn-around.

• Projects may be worked on and turned in by study groups of up to 2 people per group.

1. All group members receive the same grade.
2. Projects are related to skills learned in class, but most topics require additional endeavors to investigate new territories.
3. Project papers require specific format. All reports and figures must be computer generated.

• The final examination will be administered in a take-home format and will comprehensively assess all topics covered throughout the course. Each student is required to complete the exam independently.

1. The test will be distributed during one of the last eight hours of class. Your attendance is tied to whether you will receive the individualized test, which must be submitted no later than 2:30 PM on Monday, 12/8/2025.

2. All responses should be typed and compiled into a single PDF document, identified by your specific LCG number and submitted via email.

University policies:

Statement for students with disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with the Disability Resource Office at Holmes Hall, Suite 304, 2751 Cates Avenue, Campus Box 7509, 919-515-7653. For more information on NC State’s policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (NCSU REG 02.20.01).

Digital Components: This course may require using digital tools including Moodle, WebAssign, email, Google Drive, Zoom, Gradescope, and Panopto. Please refer to the documentation for these tools for privacy and security information. Students may be required to disclose personally identifiable information to other students in the course, via digital tools, such as email or web-postings, where relevant to the course. Examples include online discussions of class topics and posting of student coursework. All students are expected to respect the privacy of each other by not sharing or using such information outside the course.

AI Policy: AI technology offers remarkable benefits, streamlining complex tasks, enhancing decision-making, and driving innovation across countless fields. However, it is essential to remember that using AI to generate answers for homework or projects undermines the integrity of your learning. Such misuse is considered academic dishonesty and will result in disciplinary consequences if discovered. Please use AI responsibly, as a support for your understanding, but not as a shortcut that compromises your education.

Additional Rules and Regulations: Students are responsible for reviewing the NC State University Policies, Rules, and Regulations (PRRs) which pertain to their course rights and responsibilities, including those referenced both below and above in this syllabus:

■ Equal Opportunity and Non-Discrimination Policy Statement https://policies.ncsu.edu/policy/pol-04-25-05 with additional referenc [sic] at https://equalopportunity.ncsu.edu/policies/

■ Code of Student Conduct https://policies.ncsu.edu/policy/pol-11-35-01.