Math 53
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Page Table of Contents |
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Course DescriptionDifferential equations arise in quantitive modeling throughout the natural sciences, engineering, finance, computer graphics, machine learning, and many other areas. This course give a thorough introduction to modern methods of studying such equations. This includes both solving the equations, as well as understanding the behavior of solutions and their implications for models in the above areas. Some differential equations have solutions with explicit formulas that can be found using techniques based on calculus and linear algebra; often, however, there are no formulas for solutions and analysis focuses on more qualitative understanding (e.g. does the system modeled approach an equilibrium? How can the solution be approximated using computers, and how does one ensure the output of such a program is correct?). This course will cover both situations. There are many tools/techniques to study differential equations. All ultimately rely on calculus and linear algebra (albiet sometimes rather clever combinations of these). We will introduce techniques methodically, one by one; each technique will be accompanied by the necessary mathematical background, as well as real-world examples of systems whose behavior can be understood using that technique. Developing these techniques occupies the first portion of the course. After that, we will learn about algorithms that can be used to solve differential equations on computers, and their advantages and disadvantages. Finally, we will introduce Fourier series and use it to reduce problems in the multivariable setting (partial differential equations) to problems that can be solved with the techniques we have already learned. By the end of this course, you should be able to: The rest of the pages gives detailed information about the course policies. For the schedule, see schedule page. The same information is available here. Per University policy, your decision to take the course implies that you agree to these requirements and to the grading policies spelled out here; so be sure to read everything on these pages. |
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Instructors
Teaching Assistants
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Office HoursYou are encouraged to attend anyone's office hours, regardless of what lecture or TA section you are enrolled in. No appointment is necessary, just drop in at the scheduled office hours with your questions! | ||||||||
TextbookThe course textbook can be found here. The textbook was designed by the math department with input from several other departments. It is filled with interesting applications of all kinds. Please read the introduction! It contains an overview of the class and a guide for how to read the rest of the book. You will also find an email there for sending any feedback you may have. The book has been made with all of you in mind, so giving feedback can be very constructive! I will post my (handwritten) lecture notes on Canvas after each class. My notes are precisely what is covered in lecture and cover the key concepts in every chapter. Be aware, however, that these notes are written with myself as the target audience in order to deliver the lectures, and as such they may contain typos, shorthand, skipped steps, etc. All such omissions can be filled in by reading the corresponding material in the textbook. |
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Attending Lecture and SectionAttendance is not required at lecture, but regular attendance is important to your success in this class. A student who misses class is responsible for finding out what was discussed and learning the material that was covered on that day. Discussion sessions are a great additional resource we have in Math 53. Held at various times on Tuesdays and Thursdays this term, they will provide opportunities to see more guided examples and try your hand at exercises with a member of the teaching team present. Although the problems are not graded, the additional exposure to and practice with the material will greatly aid to your learning. Note that the discussion sessions will begin on Tuesday, January 7th. In the (hopefully unlikely) case that a class has to be held online, we will notify you and a Zoom link will be provided on Canvas. |
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Pre-class reading assignmentsThere will be a short assignment due on Mondays and Fridays at 9:30 am (delayed 24 hours if Monday is a University holiday, and in week 1 the Monday assignment will be due Wednesday);. This will involve answering a few questions pertaining to the previous lecture and a selection of reading for the upcoming lecture. These questions are meant to (1) reinforce and gauge your understanding of the previous lecture, and (2) to encourage you to engage a bit with the material of the next lecture beforehand. This will help you get more out of the lecture! The questions will take the form of a quiz posted on Canvas. Only the question pertaining to the previous lecture is graded for correctness. The other questions are graded for effort. The selection of reading can be found on each assignment as it is released. |
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General GuidanceIn order to learn the material, attending lecture is not enough. Struggling with the material yourself is a very important (probably the most important!) part of the process, so don't get discouraged if something is confusing! The weekly homeworks, pre-class reading assignments, and worksheet sections will give you practice with the material yourself. Meanwhile, in lecture, the instructor will describe the material and work through examples. You will get much more out of lectures if you are engaging with the material, and the pre-reading assignments encourage you to do so! You are also encouraged to attend office hours for help with the homework, additional information about topics from lecture, etc. |
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Grade breakdownYour grade will be based on the following components:
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HomeworkThere will be weekly homework posted on the course Canvas. For details about handing in your homework, see the homework page. No late homework will be accepted. The lowest two homework grades will be dropped in final average calculations. Homework and the Honor CodeYou are bound by the Stanford Honor Code for all work submitted for Math 53, including the homework assignments. For homework, we encourage you to use your book and all your notes, come to office hours, talk with any tutor(s) you have, and collaborate with your peers. We believe that thinking about math and conversing about math is an important part of the learning process. However, we expect that the work you submit is work you have written yourself and reflects your understanding of the problem and how to solve it. If you work on a problem with someone else, DO NOT copy their solution and instead, write it up on your own. Finding a solution on of the internet, copying it without thought onto your homework, and then submitting it for credit is a violation of the Stanford Honor Code and will be treated as such. |
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Exam conflictsPlease determine if you have any exact conflicts as quickly as possible! The exam information can be found under the Exams tab. If you have exam conflicts, please email your instructor and fill out the form found here to schedule an alternate exam sitting on the same day. In order to make sure that the logistics can be properly handled, this should be done at least two weeks before an exam! |
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Access and AcommodationsStanford is committed to providing equal educational opportunities for disabled students. Disabled students are a valued and essential part of the Stanford community. We welcome you to our class.If you experience disability, please register with the Office of Accessible Education (OAE). Professional staff will evaluate your needs, support appropriate and reasonable accommodations, and prepare an Academic Accommodation Letter for faculty. To get started, or to re-initiate services, please visit the OAE website. If you already have an Academic Accommodation Letter, please use the Google form found here to upload it and detail the specific accommodations you will need in this course. Letters are preferred by the end of week 2, and at least two weeks in advance of any exam, so we may partner with you and OAE to identify any barriers to access and inclusion that might be encountered in your experience of this course. New accommodation letters, or revised letters, are welcome throughout the quarter; please note that there may be constraints in fulfilling last-minute requests. |
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Academic Integrity Working GroupThis course is participating in the proctoring pilot overseen by the Academic Integrity Working Group (AIWG). The purpose of this pilot is to determine the efficacy of proctoring and develop effective practices for proctoring in-person exams at Stanford. To find more details on the pilot or the working group, please visit the AIWG’s webpage. |
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Course disruptionsStanford as an institution is committed to the highest quality education, and as your teaching team, our first priority is to uphold your educational experience. To that end we are committed to following the syllabus as written here, including through short- or long-term disruptions, such as public health emergencies, natural disasters, or protests and demonstrations. However, there may be extenuating circumstances that necessitate some changes. Should adjustments be necessary, we will communicate clearly and promptly to ensure you understand the expectations and are positioned for successful learning. |
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Other important policies
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