MATH 331
Spring 2023
Ordinary Differential Equations
for Scientists and Engineers
See the directory below for relevant links for the class. All these links can also be found on Moodle.
ALL information can be found on the Moodle page. This includes pre-recorded video lectures to help you catch up if you miss class.
This is where you will submit online homework, and also where you can find an online copy of the textbook.
This is where you will submit written homework.
Contains a rearranged version of the information you can find on the Moodle page, including the pre-recorded video lectures.
Outstanding Questions
If you have a question about the logistics of the course, first take the time to double check that your question is not answered on any of these sites, and especially on the syllabus. If you cannot find an answer to your question, please shoot an e-mail to your instructor. If you are in Sections 05+07, that would be me ksackel@umass.edu. Send a follow-up e-mail only if I do not respond within 24 hours.
Lecture Schedule (Sections 05+07)
Days listed in black have already occurred.
Days listed in orange are tentative, since they have not yet occurred.
Exams are listed in blue.
Holidays and breaks are listed in pink. (Note that I have only listed holidays as they affect this class, not all holidays on the academic calendar.)
Logistical matters are written in green.
* * * * * * * * * * * * * * * * * * *
Lecture 1 (Tu, Feb 7): Course Policy, Start Chapter 1 Introduction, 1.1 Some Basic Mathematical Models; Direction Fields
Lecture 2 (Th, Feb 9): 1.2 Solutions of Some Differential Equations, 1.3 Classification of Differential Equations
M, Feb 13: Last day to add/drop with no record
Lecture 3 (Tu, Feb 14): Start Chapter 2 First-Order Differential Equations, 2.1 Linear Differential Equations; Method of Integrating Factors
Lecture 4 (Th, Feb 16): 2.2 Separable Differential Equations
Lecture 5 (Tu, Feb 21): 2.3 Modelling with First-Order Differential Equations
Lecture X (Th, Feb 23): SNOW DAY!
Lecture 6 (Tu, Feb 28): (Recorded over snow day) 2.5 Autonomous Differential Equations and Population Dynamics
Lecture 7 (Th, Mar 2): (Substitute) 2.4+2.8 The Existence and Uniqueness Theorem, Start 2.7 Numerical Approximations: Euler's Method
Lecture 8 (Tu, Mar 7): Finish 2.7 Numerical Approximations: Euler's Method, 2.6 Exact Differential Equations and Integrating Factors
Lecture 9 (Th, Mar 9): Start Chapter 3 Second-Order Linear Differential Operators, 3.1 Homogeneous Differential Equations with Constant Coefficients, Start 3.2 Solutions of Linear Homogeneous Equations; the Wronskian
Spring Recess: No class Mar 14, 16
Lecture 10 (Tu, Mar 21): Finish 3.2 Solutions of Linear Homogeneous Equations; the Wronskian
Lecture 11 (Th, Mar 23): 3.3 Complex Roots of the Characteristic Equation
Lecture 12 (Tu, Mar 28): 3.4 Repeated Roots; Reduction of Order, Start 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
Lecture 13 (Th, Mar 30): Review
MIDTERM EXAM (Th, Mar 30): 7-9 PM, up to Section 3.2
Lecture 14 (Tu, Apr 4): 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
Lecture 15 (Th, Apr 6): Finish 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
M, Apr 10: Last day to drop with "W" and select "P/F"
Lecture 16 (Tu, Apr 11): 3.7 Mechanical and Electrical Vibrations
Lecture 17 (Th, Apr 13): 3.8 Forced Periodic Vibrations
Patriot's Day Holiday: No class Apr 18
Lecture 19 (Th, Apr 20): Start Chapter 6 The Laplace Transform, 6.1 Definition of the Laplace Transform
Lecture 20 (Tu, Apr 25): 6.2 Solution of Initial Value Problems, Start 6.3 Step Functions
Lecture 21 (Th, Apr 27): Finish 6.3 Step Functions, Start 6.4 Differential Equations with Discontinuous Forcing Functions
Lecture 22 (Tu, May 2): Finish 6.4 Differential Equations with Discontinuous Forcing Functions, 6.5 Impulse Functions
Lecture 23 (Th, May 4): Start Chapter 7 Systems of First-Order Linear Equations, 7.1 Introduction, Start 7.2 Matrices
Lecture 24 (Tu, May 9): Finish 7.2 Matrices, Start 7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
Lecture 25 (Th, May 11): Finish 7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors, 7.4 Basic Theory of Systems of First-Order Linear Equations, Start 7.5 Homogeneous Linear Systems with Constant Coefficients
Lecture 26 (Tu, May 16): Finish 7.5 Homogeneous Linear Systems with Constant Coefficients
FINAL EXAM (Tu, May 23): 3:30-5:30 PM, Totman Gym, cumulative (but focusing on material from after the midterm)