General Information

Introduction to the fundamentals of numerical analysis: error analysis, approximation, interpolation, numerical integration. In the second half of the course, the above are used to build approximate solvers for ordinary and partial differential equations. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is required to test the theoretical concepts throughout the course.

Prerequisites

MATH 2210, MATH 2230-MATH 2240, or MATH 2940 or equivalent and one additional mathematics course numbered 3000 or above.

Students will be expected to be comfortable writing proofs and have knowledge of programming. MATH 4250/CS 4210 and MATH 4260/CS 4220 provide a comprehensive introduction to numerical analysis; these classes can be taken independently from each other and in either order.

Topics Covered

  • Error analysis
  • Approximation
  • Interpolation
  • Numerical integration
  • Building approximate solvers for ordinary and partial differential equations using the above techniques
  • Advantages, disadvantages, and limits of applicability for all the covered techniques

Workload

Heavy. Weekly problem sets with a take-home midterm and final (iirc near the end it was loosened to about 1.5 weeks/pset?). [Fall 2022]

General Advice

Definitely not for the faint of heart. Would be very wise to be familiar with ODEs and PDEs and comfortable with coding in MATLAB. Start psets early. Like, seriously. [Fall 2022]

Testimonials

“Will preface everything I say that the course is quite professor dependent.

The first course in the numerical analysis “sequence” (in quotes because can be taken independently). This one is typically taught by a math professor and a majority of the people in the class are math majors. It’s a very good class to take if you’re interested in computational math. Course ramps up seemingly exponentially in difficulty. Problem sets/exams are a very nice blend of proofs and implementation; writeups tend to have a very “lab report” style, where you present a lot of figures and analysis about the results of your implementations (and honestly quite open to interpretation). (When I took it) Fantastic professor with very clear and lucid lecturing style. Lots of my computer science compatriots describe it as one of the hardest classes they’ve taken (just shy of compilers if that means anything to you). Rating: 4/5.” [Fall 2022]

Past Offerings

Semester Professor Median Grade Course Page
Fall 2020 Alexander Vladimirsky A-  
Fall 2022 Alexander Vladimirsky B+?