**Undergraduate TAs**Brenna 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 m****eeting 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- Office hour: Wed 5-7pm
- Zoom link

- see Collab site for
**zoom links**

**Pre-requisites:**

**Pre-requisites:**

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

**Grade distribution**

**Grade distribution**

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

**Homework Instructions**

**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%)

**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%

**Quiz policy**: 10%

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

**Final exam**: 15%

**Final exam**: 15%

Take home exam, cumulative, submitted online.

**Class participation**: 5%

**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 ) **

**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) **

**(Feb 1)**

**Numerical integration: [**video

**], [**slide

**]**

**Numerical differentiation: [**video

**], [**finite difference

**], [**slide

**], [**note

**]**

**quiz**

**3**

**(**

**Due 1**

**1**

**:**

**5**

**0p**

**m**

**Feb 4**

**)**[Recitation][code]

*Reading:*Chapter 19.1--19.6, 4.3.4, 21.1, 21.2

**HW**

**2**

**(Due**

**11:59**

**pm**

**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 1**

**1**

**:**

**5**

**0p**

**m**

**Feb 11**

**)**[Recitation]

*Reading:*Chapter 5.3, 5.4, 6.2, 6.3

**HW**

**3**

**(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****) **

**(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 F**

**eb 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

**HW**

**4**

**(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

**HW**

**5**

**(Due 11:59 p**

**m 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

**HW**

**6**

**(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) **

**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) **

**(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) **

**(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 (Ma**

**y 3**

**)**

**[**sample exam

**]**