or virtually via Zoom (meeting ID info on Canvas Announcements)
Differential equations represent an important branch of mathematics. Many of their properties have been understood mathematically and they have a history of being successfully applied to important problems in all areas of science and engineering. This course will introduce primarily linear, first-order, and second-order differential equations. Solution techniques for separable equations and homogeneous and inhomogeneous equations as well as a range of modeling-based applications arising in the context of engineering, physics and chemistry will be presented. The application of Laplace transforms to differential equations, systems of linear differential equations, linearization of nonlinear systems, and phase plane methods will be covered. Fourier series, a useful tool in signal processing, will also be introduced, and we will discuss how the Fourier series arises in solving the famous heat equation by separation of variables. The idea of approximating and visualizing solutions using a computer, such as with Matlab, will be introduced early in the term and students are expected to use Matlab as a resource in their work for this course.
There is a link in Canvas which includes the purchase of the electronic version of the textbook onto your tuition statement if you do not `opt out'. This purchase offers more than what is necessary. The only requirement to this course is the textbook. Students may choose to use the first edition of the text or a used second edition, which may be available at a lower cost. If you wish to do that, you should choose the `opt out' option prior to the add/drop deadline and visit http://calculus.math.pitt.edu and click the Textbook information link.
Tutoring: The Mathematics Department offers a free tutoring service. The Math Assistance Center (MAC) is located on the second floor of the O’Hara Student Center. Tutoring services and tutoring hours will be posted outside the MAC as well as on the web at MAC.
12/16/2021, Thursday 4:00PM - 5:50PM, 104 Thaw Hall.
Evening sections will meet through final exam week, and the final exam will be given during the last one or two scheduled class periods.If any assessments will be administered online, proctoring might be done via ZOOM and a video connection will be required.
On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.
This is especially notable during this
period.
Cheating/plagiarism will not be tolerated.
Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a
zero score for the quiz, exam or paper in question.
Additional sanctions may be imposed, depending on the severity of the infraction.
Please note, in particular, that Pitt has a data sharing arrangement with Chegg.com that enables us to identify in- stances in which Chegg.com has been used to cheat on assessments. Consequences of being caught in this academic integrity violation have included zero scores on assessments and F grades for the course.
In the midst of this pandemic, it is extremely important that you abide by public health regulations and University of Pittsburgh health standards and guidelines. While in class, at a minimum this means that you must wear a face covering and comply with physical distancing requirements; other requirements may be added by the University during the semester. These rules have been developed to protect the health and safety of all community members. Failure to comply with these requirements will result in you not being permitted to attend class in person and could result in a Student Conduct violation. For the most up-to-date information and guidance, please visit coronavirus.pitt.edu and check your Pitt email for updates before each class.
Lectures could be recorded by the instructor, and this may include student participation. Students are not required to participate in the recorded conversation. The recorded lecture may be used by the faculty member and the registered students only for internal class purposes and only during the term in which the course is being offered. Recorded lectures will be uploaded and shared with students through Canvas.
Week 1
August 27:
Introduction to Differential Equations (DE)
1.1
Number 1-11. Homework: 1,2,5,7,11
Week 2
August 30: First Order Initial Value Problems
2.1
Number 1-6, 12-15. Homework: 1,3,5,12,13,15
September 1:
Numerical methods
and computer tools including Matlab for DEs
6.1
Number 1-5 Homework: 3,5
September 3:
Numerical Methods. Runge-Kutta Methods
6.2
Number 1-9. Homework: 5, 23
Solutions
Week 3
September 8:
Numerical Methods. Numerical Error.
6.3 Number 1-6, 11-13.
September 10
Separable Equations
2.2
Number 1-22, 23-29, 33-35 Homework: 3,5,9,33
Solutions
Week 4
September 13:
Models of Motion
2.3
Number 1-10 Homework: 9
September 15:
First Order Linear Equations
2.4
Number 1-21 Homework: 5,15,19
September 17:
Mixing Problems
2.5
Number 1-7, 9-10 Homework: 5, 9b
Solutions
Week 5
September 20:
Electrical Circuits
3.4
Number 1-19 Homework: 1,3,5,7,11
September 22:
Second Order Equations
4.1
Number 1-20, 26-30 Homework: 1,3,9,17
September 24:
Linear Homogeneous Equations with Constant Coefficients
4.3
Number 1-36 Homework: 1,9,17,35
Solutions
Week 6
September 27:
Harmonic Motion
4.4
Number 1-12, 14-16, 18 Homework: 1,7
September 29:
Inhomogeneous second order equations. Undetermined Coefficients
4.5
Number 1-29 Homework: 1,5,11
October 1:
Inhomogeneous second order equations. Undetermined Coefficients (continued)
4.5 (cont.) Number 1-29 Homework: 15,19
Solutions
Week 7
October 4:
Inhomogeneous Equations. Variation of Parameters
4.6
Number 1-10 Homework: 1,3,5
October 6:
Forced harmonic motion
4.7
Number 3-11 Homework: 3,11
October 8:
Review
Solutions
Week 8
October 11:
Midterm 1
October 13:
Laplace Transform
5.1
Number 1-29 Homework: 7,13,15,29
October 15:
Fall Break for students (No Classes)
Solutions
Week 9
October 18:
Laplace Transform. Basic properties
5.2
Number 1-41 Homework: 5,11,19,29
October 20:
The Inverse Laplace Transform
5.3
Number 1-36 Homework: 3,7,11,19
October 22:
Using the Laplace Transform to solve DEs
5.4
Number 1-26 Homework: 7,11,21
Solutions
Week 10
October 25:
Discontinuous Forcing Term
5.5
Number 1-25 Homework: 1,3,11,17
October 27:
The Dirac Delta Function
5.6
Number 1-9 Homework: 2,3,5,7
October 29:
Convolutions
5.7
Number 4-24 Homework: 6,8,10
Solutions
Week 11
November 1:
Introduction to Systems
8.1
Number 1-16 Homework: 5,7,13,15
November 3:
Systems (continued)
8.2
Number 1-6, 13-16 Homework: 11,13,15 (use pplane.jar)
November 5:
Systems of differential equations, Constant coefficient homogeneous 2x2 systems
8.3
Number 1-6 Homework: 1,3,5
Solutions
Week 12
November 8:
Linear Systems with Constant Coefficients
9.1
Number 1-8, 16-23 Homework: 3,5,17,19
November 10:
Planar Systems
9.2
Number 1-27, 58-61 Homework: 3,13,15,59
November 12:
Phase Plane Portraits
9.3
Number 20-23 Homework: 21
Solutions
Week 13
November 15:
Nonlinear Systems: Equilibria, Linearization
10.1
Number 1-16 Homework: 3,7,15
November 15:
Review
November 19:
Midterm 2
Solutions
Week 14
November 29:
Fourier series
12.1
Number 1-22 Homework: 5,7,13,17
December 1:
Fourier Cosine and Sine Series
12.3
Number 1-32 Homework: 3,7,19,31
December 3:
Heat Equation
13.1 Number 1-9 Homework: 3
Solutions
Week 15
December 6:
Separation of variables for the heat equation
13.2 Number 1-18
December 8:
Separation of variables for the heat equation (continued)
13.2 Number 1-18
December 10:
Review