MAT 370 - Numerical Analysis

Spring 2024 Syllabus

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 Intro to Python and Jupyter Notebooks 0.1 + 0.2 != 0.3
2		Binary and Floating Point Numbers	HW 1
3		Crash course in numerical Python
4		Colab, Python, and LaTeX Workshop
5	A Reminder on Linear Systems	Gaussian Elimination	HW 2
6		LU Decomposition
7		Symmetric and Banded Coefficient Matrices	HW 3
8		Pivoting
9	A Reminder on Interpolation and Curve Fitting	Polynomial Interpolation	HW 4
10		Cubic Splines
11		Least Squares
12		Catch-Up Day
13		Unit Problem Set I, Day 1
14		Unit Problem Set II, Day 2
15	A Reminder on Root-Finding	Root Finding: Incremental Search and the Bisection Method	HW 5
16		Root Finding: Linear Interpolation Methods
17		Root Finding: Simultaneous Systems
18		Catch-Up Day
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		Unit Problem Set II, Day 1
26		Unit Problem Set II, Day 2
27/28		Reflections

---

Back to Hompage