Computational BME

Undergraduate TAsMichelle Wu, mw3ef@virginia.eduCaroline Davis, cnd7cy@virginia.eduEmma Wolcott, ew2fv@virginia.edu
Office hours: Sun 3-5pm, Mon 5-6pm

BME2315 - Spring 2021

Computational numerical methods

Syllabus: link

Live meeting times: Tuesdays 11:00am-12:15 pm, see Collab for the zoom link

Please complete quizzes accompanying each video (or group of videos) before the corresponding Mondays or Fridays (see details below). These quizzes will help you keep up and summarize the main topics of each lecture. Each quiz can be taken unlimited times before due.

Homework is due every Thursday, detailed instructions for each homework can be found in Assignments Section of the course Collab page

Instructor: Prof. Gustavo Rohde, gustavo@virginia.edu
- Office hour: Wed 10-11 am
Co-Instructor: Shiying Li, sl8jx@virginia.edu
- Office hour: Mon 9-10 pm
Graduate TA: Shifat E. Rabbi, mr2kz@virginia.edu
- Office hour: Wed 5-6:30 pm
see Collab site for zoom links of office hours

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 Thursdays at 11am. One day extensions are possible, with a penalty of 20% of the grade. 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 28 (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.

Quizz policy: 10%

Students can drop 2 quizzes. Late quizzes will not be accepted.

Final exam: 15%

Take home exam, cumulative, submitted online.

Class participation: 5%

Participation on live Tuesday recitations is required. Absence of 2 lectures is allowed.

Matlab, linear algebra & applications Assignments

Week 1: Introduction and logistics (Feb 2)

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

Week 2: Matlab bootcamp (Due: 10am Feb 9 )

Matlab basics: [video] Matlab programming: [video] quiz 1 (Due 11:50pm Feb 5)Matlab arrays: [video]Data I/O: [video]Data visualization: [video] quiz 2 (Due 11:50pm Feb 8)[Codes], [Slides] [Recitation]Reading: Chapter 2 HW1 (Due 11am Feb 11)

Week 3: Matrices, vectors and linear system of equations (Feb 16)

Examples of linear systems [video], [slides] Matrices & vectors [video], [slides], (optional) [video]Matrix determinant, rank & inverse [video] quiz 3 (Due 11:50pm Feb 12)Geometry & interpretation [video], [extra slide] Solving linear systems with Matlab [video], [code] quiz 4 (Due 11:50pm Feb 15) [Recitation]Reading: Chapter 8.1--8.3, 9.1 HW2 (Due 11am Feb 18)

Week 4: Linear algebra continuation (Feb 23)

Linear systems, column space, span [video]Gaussian elimination, Condition number [video] [slide] quiz 5 (Due 11:50pm Feb 22)(optional) Eigenvalues, eigenvectors [video] [Recitation]Reading: Chapter 9.2--9.3, 11.2 HW3 (Due 11am Feb 25)

Week 5: Interpolation & Linear Regression (Mar 2)

Interpolation: [why], [polynomial],[splines],[Lagrange], [matlab], [code], [notes] quiz 6 (Due 11:50pm Feb 26)Linear least squares:[why], [example1], [example2],[linear model],[regression], [matlab],[code] quiz 7 (Due 11:50pm Mar 1) [Recitation][code]Reading: Chapter 17.1--17.3, 18.1-18.2 HW4 (Due 11am Mar 4)

Week 6: Break, Exam

Break (Mar 9)Exam (Due Mar 11), [sample exam]

Integration, differentiation, nonlinear equations Assignments

Week 7: Numerical integration & differentiation (Mar 16)

Numerical integration: [video], [slide]Numerical differentiation: [video], [finite difference], [slide], [note] quiz 8 (Due 11:50pm Mar 15) [Recitation][code]Reading: Chapter 19.1--19.6, 4.3.4, 21.1, 21.2 HW5 (Due 11:59pm Mar 19)

Week 8: Nonlinear root finding (Mar 23 )

Univariate function roots: [video], [matlab], [slide], [slide2] Multivariate roots: [video][example] quiz 9 (Due 11:50pm Mar 22) [Recitation with blanks] [Recitation]Reading: Chapter 5.4, 6.2, 6.3 HW6 (Due 11am Mar 25)

Week 9: Optimization (Mar 30)

Introduction to optimization: [video], [slide]Gradient descent, Newton's method: [video], [slide] quiz 10 (Due 11:50pm Mar 26)Matlab: [video], [code]Nonlinear regression example: [video], [slide] quiz 11 (Due 10:50am Mar 30) [Recitation] [code] Reading: Chapter 7.1 HW7 (Due 11am Apr 1)

Week 10: Exam

Exam (Due Apr 6) [sample exam]

Differential equations Assignments

Week 11: Ordinary differential equations I (Apr 13)

Introduction: [video], [slide] Euler's method: [video], [code], [slide] quiz 12 (Due 11:50pm Apr 12) [Recitation] [code] Reading: Chapter 22.1-22.2, 22.5.1 HW8 (Due 11am Apr 16)

Week 12: Ordinary differential equations II (Apr 20 )

Runge-Kutta methods: [video], [slide] Adaptive time stepping: [video], [slide] Higher order ODEs: [video] quiz 13 (Due 11:50pm Apr 19) COVID 19 modeling: [video], [slide], [code][Recitation][code] HW9 (Due 11am Apr 22) Reading: Chapter 22.3.2, 22.4, 23.1, 23.3

Week 13: Partial differential equations (Apr 27)

Intro and Nomenclature [video], [slide] Examples and boundary conditions [video] More intuition: [video] quiz 14 (Due 11:50pm Apr 26)[Recitation] Reading: part 1-2 of note1, part 1.1-1.2 of note2

Week 14: Partial differential equations (May 4)

Overview [video], [slide] Heat equation [video], [note]Wave equation [video], [note] quiz 15 (Due 11:50pm May 3) [Recitation][code] Reading: additional reference HW10 (Due 11am May 6)