Math 5485
Welcome!
These are the lecture notes for Math 5485, Fall 2025. I encourage you to download and play around with the jupyter files available at github.
Please refer to the syllabus for information on the course.
Use the links on the side or navigate by chapter:
- Chapter 0: Introduction to Math 5485
- Chapter 1: An Introduction to Numerical Analysis,
- Chapter 2: Solving Nonlinear Equations in 1d,
- Chapter 3: Polynomial Interpolation,
- Chapter 4: Numerical Integration.
- Chapter 5: Linear systems of equations.
Presentation Prize:
Congratulations to Efosa Owie for winning the best presentation prize for his talk on “Cubic Spline Interpolation”
(The best presentation was voted for by the class)
Course Schedule:
Chapter 0: An Introduction to Math 5485
- Week 1: L1
Chapter 1: An Introduction to Numerical Analysis
- Week 2: L2 Floating point numbers, L3 Stability & Conditioning
Chapter 2: Solving nonlinear equations in 1d
- Week 3: L4 Solving nonlinear equations in 1d, L5 Exercises
- Week 4: L6-7 Solving nonlinear equations in 1d II & III
Chapter 3: Polynomial interpolation
- Week 5: L8 Polynomial Interpolation, L9 How to choose the set of interpolation nodes? & Barycentric formula
- Week 6: L10 Hermite Interpolation, L11 Exercises
Chapter 4: Numerical Integration
- Week 7: L12-13 Newton-Cotes quadrature
- Week 8: L14 Revision, L15 Midterm Exam
- Week 9: L16-17 Group Project: Integrating Differential Equations
- Week 10: L18-19 Gaussian quadrature
Chapter 5: Linear systems of equations
- Week 11: L20 Intro to matrices and Gaussian Elimination, L21 LU decomposition
- Week 12: L22, L23
- Week 13: L24, Wednesday: Class cancelled (Thanksgiving)
- Week 14: L25-26 Presentations
- Week 15: L27-28: Interesting non-examinable material, Exercises, Revision
December, 15 at 10:30: Final Exam (Keller Hall 3-125)
