Undergraduate TAsBrenna McGahan(bom9arp@virginia.edu)Gina BrownMadison Myott (mgm2gd@virginia.edu)Caroline Davis
(cnd7cy@virginia.edu)

Office hours: Mon 2pm-4pm
HSL 1329
Wed 10am-12pm
HSL 1324

BME2315 - Spring 2022

Computational & numerical methods in engineering

Syllabus: link

Live meeting times: Tuesdays, Thursdays 12:30pm-1:45 pm, see Collab for the zoom link for our first couple of weeks we will be online.

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

Homework is due every Thursday, detailed instructions for each homework can be found below.

  • Instructor: Prof. Gustavo Rohde, gustavo@virginia.edu
    • Office hour: Tue 1:50-2:50pm
    • Location (zoom), see collab for link
  • Graduate TA: Yanjun Xie, yx7pt@virginia.edu
  • 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 11pm. 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 10 (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 on live Tuesday recitations is required. A QR code will be displayed during tuesday sessions for students to confirm their presence. Absence of 3 lectures is allowed.


Matlab, and 1D calculus Assignments

Week 1: Introduction and logistics (Jan 20)

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

Week 2: Matlab bootcamp (Jan 25 )

Matlab basics: [video] Matlab programming: [video] quiz 1 (Due 11:50pm Jan 24)Matlab arrays: [video]Data I/O: [video]Data visualization: [video] quiz 2 (Due 11:50pm Jan 26)[Codes], [Slides] [Recitation]Reading: Chapter 2 HW1 (Due 11:59pm Jan 27)

Week 3: Differentiation and Integration (Feb 1)

Numerical integration: [video], [slide]Numerical differentiation: [video], [finite difference], [slide], [note] quiz 3 (Due 11:50pm Feb 4) [Recitation][code]Reading: Chapter 19.1--19.6, 4.3.4, 21.1, 21.2 HW2 (Due 11:59pm Feb 3)

Week 4: Root finding and 1D minimization (Feb 8)

Univariate function roots: [video], [matlab], [slide], [slide2] 1D minimization: [video]Examples : [video], [slides] quiz 4 (Due 11:50pm Feb 11) [Recitation]Reading: Chapter 5.3, 5.4, 6.2, 6.3 HW3 (Due 11:59pm Feb 10)

Week 5: Exam 1 (Feb 15)

Review (Feb 15)Exam (Due Feb 17), [sample exam]

Linear algebra & applications Assignments

Week 6: Matrices, vectors and linear system of equations (Feb 22)

Examples of linear systems [video], [slides] Matrices & vectors [video], [slides], (optional) [video]Matrix determinant, rank & inverse [video] quiz 5 (Due 11:50 pm Feb 25)Geometry & interpretation [video], [extra slide] Solving linear systems with Matlab [video], [code] quiz 6 (Due 11:50 pm Feb 27)[Recitation] Reading: Chapter 8.1--8.3, 9.1 HW4 (Due 11:59 pm Feb 24)

Week 7: Linear algebra continuation (Mar 1)

Linear systems, column space, span [video]Gaussian elimination, Condition number [video] [slide] quiz 7 (Due 11:50 pm Mar 4)(optional) Eigenvalues, eigenvectors [video] [Recitation]Reading: Chapter 9.2--9.3, 11.2 HW5 (Due 11:59 pm Mar 3)

Spring Break (Mar 8)

Week 8: Interpolation & Linear Regression (Mar 15)

Interpolation: [why], [polynomial],[splines],[Lagrange], [matlab], [code], [notes] quiz 8 (Due 11:50 pm Mar 18)Linear least squares:[why], [example1], [example2],[linear model],[regression], [matlab],[code] quiz 9 (Due 11:50 pm Mar 20) [Recitation][code]Reading: Chapter 17.1--17.3, 18.1-18.2 HW6 (Due 11:59 pm Mar 17)

Week 9: Nonlinear root finding and optimization (Mar 22)

Multivariate roots: [video][example] quiz 10 (Due 11:50 pm Mar 25)Gradient descent, Newton's method: [video], [slide] Matlab: [video], [code]Nonlinear regression example: [video], [slide] quiz 11 (Due 11:50 pm Mar 27) Recitation: [Multivariate root finding] [Multivariate optimization] Reading: 5.4, 6.2, 6.3, 7.1 HW7 (Due 11:59 pm Mar 24)

Week 10: Exam 2 (Mar 29)

Review (Mar 29)Exam (Due Mar 31), [sample exam]

Differential equations Assignments

Week 11: Ordinary differential equations I (Apr 5)

Introduction: [video], [slide] Euler's method: [video], [code], [slide] quiz 12 (Due 11:50 pm Apr 6) [Recitation] [code] Reading: Chapter 22.1-22.2, 22.5.1 HW8 (Due 11:59 pm Apr 7)

Week 12: Ordinary differential equations II (Apr 12)

Runge-Kutta methods: [video], [slide] Adaptive time stepping: [video], [slide] Higher order ODEs: [video] quiz 13 (Due 11:50 pm Apr 13) COVID 19 modeling: [video], [slide], [code][Recitation][code] HW9 (Due 11:59 pm Apr 14) Reading: Chapter 22.3.2, 22.4, 23.1, 23.3

Week 13: Partial differential equations (Apr 19)

Intro and Nomenclature [video], [slide] Examples and boundary conditions [video] More intuition: [video] quiz 14 (Due 11:50 pm Apr 20)[Recitation] Reading: part 1-2 of note1, part 1.1-1.2 of note2

Week 14: Partial differential equations (Apr 26)

Overview [video], [slide] Heat equation [video], [note]Wave equation [video], [note] quiz 15 (Due 11:50 pm Apr 27) [Recitation][code] Reading: additional reference HW10 (Due 11:59 pm Apr 28)

Week 15: Summary and review (May 3)

Summary and Review (May 3)[sample exam]