MAT 370 - Numerical Analysis

Syllabus (Spring 2026)

Course Description: This course introduces basic techniques for the efficient numerical solution of problems in engineering, mathematics, and science. Topics covered may include: root finding methods, interpolation, numerical differentiation and integration, numerical solutions of differential equations, and matrix theory concepts such as QR factorization and singular value decompositions. Students will utilize industry-standard software for simulations.

Course Timeline and Notebooks

Below is a tentative timeline for our course. It includes preparatory work that should be done prior to each class meeting, a detailed set of notes corresponding to each class meeting, and assignments following each class meeting.

Class Meeting	Before Class	During Class	After Class
1	Review Syllabus Setup Google Colab	Introduction and What to Expect (Slides, PDF) Intro to Python and Jupyter Notebooks 0.1 + 0.2 != 0.3
2		Binary and Floating Point Numbers Companion Slides (HTML or PDF)
3		Python and Coding Foundations	HW 1
4		Crash course in numerical Python Companion Slides (HTML or PDF)
5		Colab, Python, and LaTeX Workshop Companion Slides (HTML or PDF)
6	A Reminder on Linear Systems	Gaussian Elimination Companion Slides (HTML or PDF)	HW 2
7		LU Decomposition Companion Slides (HTML or PDF)
8		Symmetric and Banded Coefficient Matrices Companion Slides (HTML or PDF)	HW 3
9		Pivoting Companion Slides (HTML or PDF)
10	A Reminder on Interpolation and Curve Fitting	Polynomial Interpolation Companion Slides (HTML or PDF)	HW 4
11		Cubic Splines Companion Slides (HTML or PDF)
12		Least Squares Companion Slides (HTML or PDF)
13		Catch-Up Day
14		Unit Problem Set I, Day 1
15		Unit Problem Set II, Day 2
16	A Reminder on Root-Finding	Root Finding: Incremental Search and the Bisection Method Companion Slides (HTML or PDF)	HW 5
17		Root Finding: Linear Interpolation Methods Companion Slides (HTML or PDF)
18		Root Finding: Simultaneous Systems
19	A Reminder on Differentiation and Function Approximation	Differentiation: Finite Difference Approximation	HW 6
20		Differentiation: Improving Estimates via Richardson Extrapolation and Derivatives via Interpolation for non-Equispaced or Noisy Observations
21	A Reminder on Numerical Integration Techniques	Integration: Newton-Cotes Formulae	HW 7
22		Integration: Romberg Integration
23	A Reminder on Initial Value Problems	IVPs: Euler’s Method	HW 8
24		IVPs: Runge-Kutta Methods
25		Reflection Project Overview
26		Unit Problem Set II, Day 1
27		Unit Problem Set II, Day 2
28		Debrief Interviews
29		Debrief Interviews

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