Math 427K: Advanced Calculus for Applications IUnique Number 55160Fall Semester 2011Where am I?You are in Associate Professor Dan Knopf’s Math 427K class. Your TA is Chris White.Lectures meet 9:30–10:45 Tuesdays and Thursdays in JGB 2.216.Problem sessions meet 5:00–5:50 Mondays and Wednesdays in WRW 102.Why am I here?Ordinary and partial differential equations are fundamental tools used by modern science and engineering.In these disciplines, differential equations are applied to produce mathematical models of complex physicalphenomena. Consequently, it is seldom enough merely to know that a differential equation has solutions. Itis more important to know when these solutions are unique and how to understand and approximate theirbehaviors, so that one can gain insight into the physical processes the differential equation is supposed tomodel. This course will introduce you to a variety of important techniques used to find and qualitativelyanalyze solutions of differential equations, with emphasis on those that arise in applications.What are the prerequisites for this course?The prerequisite is Math 408D or 408L (or equivalent) with a grade of at least C.What materials should I have?Elementary Differential Equations and Boundary Value Problems, Ninth Edition, by William E. Boyceand Richard C. DiPrima. John Wiley & Sons, Inc.How can I get extra help?• The contact information for your professor and TA is below. We encourage you to come to us forindividualized help if needed!Name E-mail Office Phone Office hoursDan Knopf [email protected] RLM 9.152 471.8131 3:00–5:00 TuesdaysChris White [email protected] RLM 11.130 475.9598 3:00–5:00 Thursdays & 12:00–2:00 Fridays• This course will use Blackboard. Class announcements will be posted there, and we will maintaina discussion board, called MathChat, where you may submit questions and share answers. Your TAand I will check these frequently, answering your questions as promptly as possible.• The syllabus will be updated during the semester as exam room scheduling becomes known. Acurrent version will always be available on Blackboard, as well as through a link from my home page:http : //www.ma.utexas.edu/users/danknopf• Contact information for the Mathematics Advising Center may be found at:http : //www.ma.utexas.edu/academics/undergraduate/advising/• The University of Texas at Austin provides, upon request, appropriate academic accommodationsfor qualified students with disabilities. For more information, contact the Division of Diversityand Community Engagement, Services for Students with Disabilities (phone 471.6259, video phone866.329.3986). Their website is:http : //www.utexas.edu/diversity/ddce/ssd/If you fall under the University’s Learning Disability Policy, it is your responsibility todeliver the SSD certification of that fact to me at least one week prior to the first exam.How will the course be graded?There will be quizzes on homework, two midterm exams, and a cumulative final. There will also be one(and only one!) opportunity for extra credit.By UT Austin policy, if you must miss an assignment or exam in order to observe a religious holy day,you must notify me at least two weeks prior to that day. You will be given an opportunity to complete themissed work within a reasonable time after your absence.• Homework/Quizzes: There will be eleven homework assignments. Each assignment will be postedon Blackboard approximately one week before it is due. Assignments will be due on most Wednes-days; see schedule below. The main purpose of the homework is learning, not assessment. So thehomework itself will not be graded. But to assess how well you learned its contents, there will be ashort quiz during discussion session each Wednesday that homework is due. Each quiz will consistof one or two homework problems from that week — verbatim. So if you have worked diligently onthe homework, you will be prepared to get good quiz grades.– The lowest two quiz scores will be dropped, to allow for illness, emergencies, and othervalid nonacademic excuses.– The remaining nine scores will be averaged to determine 15% of your overall grade.– There will be no make-up quizzes. A missed quiz counts as a zero, hence qualifies as oneof your two dropped scores. (The sole exception is a conflict with a religious holy day, in whichcase you must contact me at least two weeks in advance; see above.)• In-class exams: There will be two in-class exams. (See schedule below.) Each will count for 25%of your overall grade.– No exam scores are dropped.– If you miss an exam, you must contact me before the exam and provide a valid written seriousexcuse in order to be allowed to take a make-up.• Final exam: The final will determine 35% of your overall grade.– The final exam time and location is set by the Registrar. (See schedule below.) You may requestan alternate time for your final exam only for a very serious reason, such as hospitalization.• Extra credit: You will each receive an email asking you to participate in a pilot online assessmentproject using Quest, a computerized Learning and Assessment system maintained by the Collegeof Natural Sciences. The assessment is an hour-long online quiz to be taken between 12:00 noon onFriday, August 26 and 10:00 AM on Monday, August 29. Your score in this pilot assessment willcount towards 1% extra credit in the course (i.e. up to 1 point added to the 100-point scale below).Your overall grade will be computed according to a scale at least as generous as this:F D- D D+ C- C C+ B- B B+ A- A0–50 51–55 56–63 64–65 66–67 68–75 76–77 78–79 80–87 88–89 90–91 92–1002Can you give me some tips for the course?• Attend problem sessions. Because I must introduce new concepts during lectures, there simplyisn’t time to work as many examples as would be pedagogically ideal. Problem sessions offer manymore opportunities to learn from examples, clarify ideas, and practice using new concepts. Problemsessions are valuable resources for learning and review. Note in particular that the problem sessionimmediately before an exam reviews the exam topics, while the problem session immediately afteran exam reveals the correct exam answers.• Ask questions — in lecture, during problem sections, and on Blackboard.• Do the homework. No students, no matter how talented, can learn mathematics without workingexamples themselves. The most important component of success in