Computational BME

Undergraduate TAsHamza Ahmed(ha8xf@virginia.edu)Godwin Oluwafemi(goo4qe@virginia.edu)Jack Pessaud(hmb8xg@virginia.edu)Chloe Ulsh(cju9fky@virginia.edu)Olivia Gubbay(kvc7rp@virginia.edu)
Office hours: HamzaThursday 2:15-3:15 PM: Thornton StacksGodwinWednesday 6-8 PM: Alderman (134)JackWednesday 3-4 PM: Thornton StacksChloeThursday 4-5 PM: MR5 Room 2005OliviaFriday 11 AM - 12:30 PM: Shannon 318 F

BME2315 - Spring 2024

Computational & numerical methods in engineering

Syllabus: link

Live meeting times: Tuesdays, Thursdays 12:30pm-1:45 pm, MR5 1041

Please complete quizzes accompanying each video (or group of videos) before the corresponding times (Quizzes are due Tuesday 9pm each week, see details below). These quizzes will help you keep up with and summarize the main topics of each lecture. Each quiz can be taken two times before due.

Homework is due every Friday at 5:00pm; detailed instructions for each homework can be found below.

Instructor: Prof. Gustavo Rohde, gustavo@virginia.edu
- Office hour: Wed 1:30-2:30pm, MR5 1115
Graduate TA: James Gentry (jg9zk@virginia.edu)
- Office hour: Thursday 10:30-11:30am, Wilsdorf 201H

Zoom link: https://virginia.zoom.us/j/96337640365?pwd=eFV3MmYzQklWNERHeEtZS1Y4dGZBZz09

Pre-requisites:

APMA 2120 (differential equations), CS 1110 (programming)

Grade distribution

Quizzes 10%, Homeworks 40%, Class participation 5%, Midterm Exam 1 15%, Midterm Exam 2 15% Final Exam 15%

Homework Instructions

Homework assignments due on Fridays 5pm. Two-day extensions are possible, with a penalty of 10% of the grade per day. Students will be allowed to drop one homework assignment. For instructions on homework assignments, click here. Students are required to upload a single .pdf file (ComputingID_HWXX.pdf) containing solutions to the written problems and a single .m file (ComputingID_HWXX.m) containing solutions to the MATLAB coding problems. Before submission, please rename both these files using your own computing ID and the homework number.

Extra Credit: Getting started with Matlab (2%)

Complete this Matlab Fundamentals course by Mar 20 (and upload certificate to "Matlab fundamentals certificate (Extra Credit)" under Assignments in Collab) to get familiar with Matlab programming and earn extra credits. In addition, this online course will also prepare you for the programming tasks in the homework as well as your own applications. See a short introduction to Matlab and get access to the download page from link.

Quiz policy: 10%

Students can drop 2 quizzes. Late quizzes will not be accepted, no make ups.

Final exam: 15%

Take home exam, cumulative, submitted online.

Class participation: 5%

Participation is required. A QR code will be displayed during each class for students to confirm their presence. Absence of 4 lectures is allowed.

Matlab, and 1D calculus Assignments

Week 1: Introduction and logistics (Jan 18)

Introduction [slides], [the math you will need] Reading: Syllabus

Week 2: Matlab bootcamp (Jan 22)

Matlab basics: [video] Matlab programming: [video] quiz 1 (Due 9:00pm Jan 23)Matlab arrays: [video]Data I/O: [video]Data visualization: [video] quiz 2 (Due 9:00pm Jan 23)Debugging: [video][Codes], [Slides], [Recitation]Reading: Chapter 2 HW1 (Due 5:00pm Jan 26)

Week 3: Differentiation and Integration (Jan 29)

Numerical integration: [video], [slide]Numerical differentiation: [video], [finite difference], [slide], [note] quiz 3 (Due 9:00pm Jan 30) [Recitation], [code]Reading: Chapter 19.1--19.6, 4.3.4, 21.1, 21.2 HW2 (Due 5:00pm Feb 2)

Week 4: Root finding and 1D minimization (Feb 5)

Univariate function roots: [video], [matlab], [slide], [slide2] 1D minimization: [video]Examples : [video], [slides] quiz 4 (Due 9:00pm Feb 6) [Recitation],[convergence]Reading: Chapter 5.3, 5.4, 6.2, 6.3 HW3 (Due 5:00pm Feb 9)

Week 5: Exam 1 (Feb 12)

Review (Feb 13)Exam (Due Feb 15), [sample exam]

Linear algebra & applications Assignments

Week 6: Matrices, vectors and linear system of equations (Feb 19)

Examples of linear systems [video], [slides] Matrices & vectors [video], [slides], (optional) [video]Matrix determinant, rank & inverse [video] quiz 5 (Due 9:00 pm Feb 20)Geometry & interpretation [video], [extra slide] Solving linear systems with Matlab [video], [code] quiz 6 (Due 9:00 pm Feb 20)[Recitation] Reading: Chapter 8.1--8.3, 9.1 HW4 (Due 5:00 pm Feb 23)

Week 7: Linear algebra continuation (Feb 26)

Linear systems, column space, span [video]Gaussian elimination, Condition number [video] [slide] quiz 7 (Due 9:00pm Feb 27)(optional) Eigenvalues, eigenvectors [video] [Recitation]Reading: Chapter 9.2--9.3, 11.2 HW5 (Due 5:00pm Mar 1)

Spring Break (Mar 4)

Week 8: Interpolation & Linear Regression (Mar 11)

Interpolation: [why], [polynomial],[splines],[Lagrange], [matlab], [code], [notes] quiz 8 (Due 9:00 pm Mar 12)Linear least squares:[why], [example1], [example2],[linear model],[regression], [matlab],[code] quiz 9 (Due 9:00 pm Mar 12) [Recitation], [code]Reading: Chapter 17.1--17.3, 18.1-18.2 HW6 (Due 5:00pm Mar 15)

Week 9: Nonlinear root finding and optimization (Mar 18)

Multivariate roots: [video][example] quiz 10 (Due 9:00pm Mar 19)Gradient descent, Newton's method: [video], [slide] Matlab: [video], [code]Nonlinear regression example: [video], [slide] quiz 11 (Due 9:00pm Mar 19)Recitation: [Multivariate root finding], [Multivariate optimization] Reading: 5.4, 6.2, 6.3, 7.1 HW7 (Due 5:00pm Mar 22)

Week 10: Exam 2 (Mar 25)

Review (Mar 26)Exam (Due Mar 28), [sample exam]

Differential equations Assignments

Week 11: Ordinary differential equations I (Apr 1)

Introduction: [video], [slide] Euler's method: [video], [code], [slide] quiz 12 (Due 9:00pm Apr 2) [Recitation], [code] Reading: Chapter 22.1-22.2, 22.5.1 HW8 (Due 5:00pm Apr 5)

Week 12: Ordinary differential equations II (Apr 8)

Runge-Kutta methods: [video], [slide] Adaptive time stepping: [video], [slide] Higher order ODEs: [video] quiz 13 (Due 9:00pm Apr 9)COVID 19 modeling: [video], [slide], [code][Recitation], [code], [two body] HW9 (Due 5:00pm Apr 12) Reading: Chapter 22.3.2, 22.4, 23.1, 23.3

Week 13: Partial differential equations (Apr 15)

Intro and Nomenclature [video], [slides] Examples and boundary conditions [video] More intuition: [video] quiz 14 (Due 9:00pm Apr 16)[Recitation] Reading: part 1-2 of note1, part 1.1-1.2 of note2

Week 14: Partial differential equations (Apr 22)

Overview [video], [slide] Heat equation [video], [note]Wave equation [video], [note] quiz 15 (Due 9:00 pm Apr 23) [Recitation], [code]Reading: additional reference HW10 (Due 5:00 pm Apr 26)

Week 15: Summary and review (April 29)

Summary and Review (April 30)[sample exam]