MATH 2250-04 — Differential Equations and Linear Algebra


Fall 2019


Instructor: Akil Narayan
Email: akil(-at-)sci.utah.edu
Office phone: +1 801-581-8984
Office location: WEB 4666, LCB 116
Office hours: Akil Narayan: Monday, Wednesday 10:00am-11:30am (WEB 4666)
Junpeng Jiao: Wednesday 10am-12pm (WEB 1705)
Catherine Warner: Monday, Tuesday 9:30am-10:30am (WEB 1705)


Class meeting time: Monday, Tuesday, Wednesday, Thursday (lab section), Friday 8:35am - 9:25am (MTWF lecture).
Labs (sections 05-08) are held at various times on Thursdays
Class meeting location: JWB 335 (MWF), JFB 103 (Tu)
Textbook (required): H. C. Edwards and D. E. Penney and D. Calvis, Differential Equations and Linear Algebra (4th edition), Pearson (2017), ISBN-13: 978-0-13-449718-1, ISBN-10: 0-13-449718-X.

NOTE: Unless you opt-out, you will be charged for electronic access to the text through the Inclusive Access program on Canvas. You may opt out by following the instructions here.


This is a hybrid course which teaches the allied subjects of linear algebra and differential equations. These topics underpin the mathematics required for most students in the Colleges of Science, Engineering, Mines & Earth Science.


Engineering students interested in pursuing further mathematics courses can elect to earn a minor in Mathematics by taking 2-4 additional courses. More details are available on this PDF flier. Please consult with your Engineering advisor for further information.

The course syllabus is here: PDF

The Department of Mathematics provides drop-in tutoring services for this course. Please see https://www.math.utah.edu/undergrad/mathcenter.php for details. Note that you should schedule your visit during a time when a knowledgable tutor is available who can address your questions. Each tutor's specialties and schedule are shown on the webpage above.

Graded assignments


Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.



Homework assignments


Homework will be collected in-class on Thursdays. Late work will not be accepted without advance approval from the instructor.

Problem set description Due date Homework
1 : Basics of differential equations August 29, 2019 PDF
L1 : Lab Assignment 1 August 29, 2019 PDF
2 : First-order linear equations and equilibrium solutions September 5, 2019 PDF
L2 : Lab Assignment 2 September 5, 2019 PDF
3 : Numerical methods and linear systems September 19, 2019 PDF
L3 : Lab Assignment 3 September 19, 2019 PDF
4 : Matrix manipulations September 26, 2019 PDF
L4 : Lab Assignment 4 September 26, 2019 PDF
5 : Vector spaces October 3, 2019 PDF
L5 : Lab Assignment 5 October 3, 2019 PDF
6 : Second order equations October 24, 2019 PDF
L6 : Lab Assignment 6 October 24, 2019 PDF
7 : Nonhomogeneous equations October 31, 2019 PDF
L7 : Lab Assignment 7 October 31, 2019 PDF
8 : Laplace transforms November 7, 2019 PDF
L8 : Lab Assignment 8 November 7, 2019 PDF
9 : Eigenvalues November 21, 2019 PDF
L9 : Lab Assignment 9 November 21, 2019 PDF
10 : Systems of DEs December 5, 2019 PDF
L10 : Lab Assignment 10 December 5, 2019 PDF



Miscellaneous handouts


The following are various relevant handouts.

Description Posting date Download
Lecture 00 slides: Introduction August 15, 2019 PDF
Lecture 01 slides: Models and differential equations August 15, 2019 PDF
Lecture 02 slides: Integrating differential equations August 15, 2019 PDF
Lecture 03 slides: Slope/direction fields August 15, 2019 PDF
Midterm 1 practice August 20, 2019 PDF
Midterm 1 practice solutions Septebmer 4, 2019 PDF
Midterm 1 Septebmer 25, 2019 PDF
Lecture 04 slides: Separable equations August 25, 2019 PDF
Lecture 05 slides: First-order linear DE's August 25, 2019 PDF
Lecture 06 slides: Applications August 25, 2019 PDF
Lecture 07 slides: Equilibrium solutions and stability August 25, 2019 PDF
Lecture 08 slides: Acceleration and velocity models September 8, 2019 PDF
Lecture 09 slides: Numerical methods September 8, 2019 PDF
Lecture 10 slides: Introduction to linear systems September 8, 2019 PDF
Lecture 11 slides: Gaussian elimination September 15, 2019 PDF
Lecture 12 slides: Reduced Echelon form September 15, 2019 PDF
Lecture 13 slides: Matrix arithmetic September 15, 2019 PDF
Lecture 14 slides: Matrix inverses September 16, 2019 PDF
Instructions to install Python with the Anaconda distribution September 17, 2019 PDF
Lecture 15 slides: Matrix determinants September 23, 2019 PDF
Lecture 16 slides: The vector space R3 September 24, 2019 PDF
Lecture 17 slides: The vector space Rn September 24, 2019 PDF
Midterm 2 practice September 25, 2019 PDF
Lecture 18 slides: Linear independence and span September 26, 2019 PDF
Lecture 19 slides: Basis and dimension September 26, 2019 PDF
Vector space terminology and glossary October 3, 2019 PDF
Lecture 20 slides: Second order linear equations October 13, 2019 PDF
Lecture 21 slides: Higher order linear equations October 13, 2019 PDF
Lecture 22 slides: Constant coefficient homogeneous equations October 13, 2019 PDF
Lecture 23 slides: Mechanical vibrations October 20, 2019 PDF
Lecture 24 slides: Undetermined coefficients October 20, 2019 PDF
Lecture 25 slides: Forcing and resonance October 20, 2019 PDF
Lecture 26 slides: Laplace Transforms October 25, 2019 PDF
Lecture 27 slides: DE's and Laplace transforms October 31, 2019 PDF
Laplace transforms table November 1, 2019 PDF
Lecture 28 slides: Laplace transform manipulations November 3, 2019 PDF
Lecture 29 slides: More Laplace transform properties November 10, 2019 PDF
Lecture 30 slides: Step functions and temporal shifts November 11, 2019 PDF
Lecture 31 slides: Eigenvalues and eigenvectors November 14, 2019 PDF
Lecture 32 slides: Matrix diagonalization November 17, 2019 PDF
Lecture 33 slides: Systems of DE's November 17, 2019 PDF
Lecture 34 slides: DE system properties November 23, 2019 PDF
Lecture 35 slides: Eigenvalue methods for DE systems November 23, 2019 PDF
Midterm 2 December 2, 2019 PDF
Midterm 3 December 2, 2019 PDF
Laplace transforms table (full) December 2, 2019 PDF



Software


The following are links to software used during class demonstrations.

Description Language Download
Lab 4 code IPython notebook + matlab github
All code below Python + IPython notebook github
Plotting slope fields Python slopefield.ipynb
Numerical methods utilities Python numerical_utils.py
Euler's method (requires numerical_utils.py) Python euler_demo.ipynb
Improved Euler's method (requires numerical_utils.py) Python improved_euler_demo.ipynb
Runge-Kutta methods (requires numerical_utils.py) Python runge_kutta_demo.ipynb
Convergence of numerical methods (requires numerical_utils.py) Python numerical_convergence.ipynb



Resources

IPython + Jupyter
Python