| Spring 2024 MAT 303: Calculus 4 with applications | ||
| Schedule | MWF 9:00-9:53am Javits 111 | |
| Instructor | Robert Hough | |
| Office hours | F 1-2pm in Math Learning Center, F 2-4pm in Math Tower 4-118 | |
| TAs | Owen Mireles Briones and Yichen Cheng. | |
| Description | Homogeneous and inhomogeneous linear differential equations; systems of linear differential equations; series solutions; Laplace transforms; Fourier series. Applications to economics, engineering, and all sciences with emphasis on numerical and graphical solutions; use of computers. | |
| Prerequisites | C or higher in MAT 127 or 132 or 142 or AMS 161 or level 9 on the mathematics placement examination | |
| Textbook | Differential Equations and Boundary Value Problems (5th edition) by Edwards, Penney and Calvis | |
| Homework | Weekly problem sets will be assigned, and collected in recitation. Late homework is not accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class. | |
| Grading | Homework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%. | |
Accommodations for students with hearing and communication impairments:
Some students with hearing and communication impairments may need their instructor to wear a
clear mask for lip and facial expression purposes. If the student has registered with the Student
Accessibility Support Center (SASC) and has requested an accommodation for clear masks, SASC
will reach out to the students instructors and provide a clear mask for them to wear while teaching
and/or interacting with the student. If you have questions, please email sasc@stonybrook.edu or
call (631) 632-6748.
Software Requirements: We will use Mathematica, which is a computational software program developed by Wolfram Research and used in many scientific, engineering, mathematical and computing fields, based on symbolic mathematics. Mathematica has a comprehensive documentation: https://reference.wolfram.com/language. Stony Brook students can download the Windows/Mac/Linux version of Mathematica from Softweb (https://softweb.cc.stonybrook.edu). You need your Stony Brook netID and netID password to log in to Softweb. To obtain an Activation Key for Mathematica you must visit the Wolfram User Portal by following the link in Softweb. If it is your first time visiting the Wolfram User Portal, you must create a Wolfram ID and follow the steps in there to request an Activation Key. In addition, you can use any of the campus SINC sites, or you can access the Virtual SINC site.
Syllabus/schedule (subject to change)
| Mon 1/22 | 1. | Differential equations, models, integral solutions | 1.1-1.2 |
| Wed 1/24 | 2. | Slope fields, separable equations | 1.3-1.4 |
| Fri 1/26 | 3. | Linear first order equations | 1.5 Week 1 HW: 1.1 #6, 12 1.2 #7, 17 1.3 #21, 30 1.4 #11, 15, 23, 49 1.5 #13, 19 |
| Mon 1/29 | 4. | Substitution methods, exact equations | 1.6 |
| Wed 1/31 | 5. | Equilibrium solutions, stability | 2.1-2.2 |
| Fri 2/2 | 6. | Acceleration and velocity models | 2.3 Week 2 HW: 1.6 #17, 19, 33 2.1 #15, 23, 33 2.2 #21, 28 2.3 #6, 25 |
| Mon 2/5 | 7. | Euler's method | 2.4-2.5 |
| Wed 2/7 | 8. | Runge-Kutta method | 2.6 |
| Fri 2/9 | 9. | Second order, general linear equations | 3.1-3.2 Week 3 HW: 2.4 #8 3.1 #7, 11, 15, 25, 41 3.2 #5, 17, 33, 39 |
| Mon 2/12 | 10. | Homogeneous equations, mechanical vibrations | 3.3-3.4 |
| Wed 2/14 | 11. | Non-homogeneous equations undefined coefficients, forced oscillation, resonance | 3.5-3.6 |
| Fri 2/16 | 12. | Electrical circuits, endpoint problems, eigenvalues | 3.7-3.8 Week 4 HW: 3.3 #5, 14, 26, 35 3.4 #3, 5, 27 3.5 #9, 15, 23, 51 3.6 #3, 8, 22 3.7 #2, 13 3.8 #4, 16 |
| Mon 2/19 | Midterm 1 | ||
| Wed 2/21 | 13. | First order systems | 4.1 |
| Fri 2/23 | 14. | Method of elimination, numerical systems | 4.2-4.3 Week 5 HW: 4.1 #1, 5, 15, 25 4.2 #16, 3, 48 4.3 #5, 7, 12 |
| Mon 2/26 | 15. | Matrices and linear systems | 5.1 |
| Wed 2/28 | 16. | Eigenvalue method, gallery solution curves | 5.2-5.3 |
| Fri 3/1 | 17. | Second order systems | 5.4 Week 6 HW: 5.1 #9, 17, 27, 42, 43 5.2 #8, 19, 38 5.3 #17, 18, 21 5.4 #3, 14, 18 |
| Mon 3/4 | 18. | Multiple eigenvalue systems | 5.5 |
| Wed 3/6 | 19. | Matrix exponentials, linear systems | 5.6 |
| Fri 3/8 | 20. | Non-homogeneous linear systems | 5.7 Week 7 HW: 5.5 #8, 12, 27 5.6 #3, 15, 27, 33 5.7 #5, 11, 19, 33 |
| Mon 3/11 - Fri 3/15 | Spring break | ||
| Mon 3/18 | 21. | Stability, phase plane, linear and almost linear systems | 6.1-6.2 |
| Wed 3/20 | 22. | Ecological systems, nonlinear mechanical systems | 6.3-6.4 |
| Fri 3/22 | 23. | Chaos | 6.5 Week 8 HW: 6.1 #1, 17, 25 6.2 #5, 19, 34 6.3 #6, 12 6.4 #9, 13, 21 |
| Mon 3/25 | 24. | Laplace transform, inverse transform | 7.1 |
| Wed 3/27 | 25. | Transformation of initial value problems | 7.2 |
| Fri 3/29 | 26. | Translation and partial fractions | 7.3 Week 9 HW: 7.1 #14, 16, 32, 39 7.2 #13, 20, 34 b>7.3 #11, 20, 30 |
| Mon 4/1 | 27. | Derivatives, integrals, products of transforms | 7.4 |
| Wed 4/3 | 28. | Periodic and piecewise continuous input, impulses and delta functions | 7.5-7.6 |
| Fri 4/5 | Midterm 2 | Week 10 HW: 7.4 #10, 31, 38 7.5 #16, 29, 34 7.6 6, 15, 19 | |
| Mon 4/8 | 29. | Power series, series solutions | 8.1-8.2 |
| Wed 4/10 | 30. | Regular singular points, method of Frobenius | 8.3-8.4 |
| Fri 4/12 | 31. | Bessel's equations and functions | 8.5-8.6 Week 11 HW: 8.1 #7, 11, 25 8.2 #9, 33 8.3 #5, 23, 38 8.4 #4, 18 8.5 #3, 24 8.6 #9 |
| Mon 4/15 | 32. | Periodic functions, Fourier series | 9.1-9.2 |
| Wed 4/17 | 33. | Fourier series, applications | 9.3-9.4 |
| Fri 4/19 | 34. | Heat equation | 9.5 Week 12 HW: 9.1 #13, 17, 23 9.2 #8, 19 9.3 #4, 13 9.4 #8, 15 9.5 #8, 17, 18 |
| Mon 4/22 | 35. | Wave equation | 9.6 |
| Wed 4/24 | 36. | Laplace equation | 9.7 |
| Fri 4/26 | 37. | Sturm-Liouville equation | 10.1 Week 13 HW: 9.6 #4, 10, 17 9.7 #1, 4, 16 10.1 #3, 14, 17 |
| Mon 4/29 | 38. | Eigenfunction expansions | 10.2 |
| Wed 5/1 | 39. | Steady periodic solutions, natural frequencies | 10.3 |
| Fri 5/3 | 40. | Cylindrical coordinates, higher-dimensional phenomena | 10.4-10.5 |
Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.stonybrook.edu and search Fire safety and Evacuation and Disabilities.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, and/or inhibits students' ability to learn.