Course Resources

1. Yourself!  -- One of the most important things for doing well in a challenging course is to actively view yourself as being responsible for your own learning.  Take the initiative to:  set an appropriate, sufficient, but realistic study schedule for yourself; be honest with yourself about how thoroughly you are learning the material; identify when things are not going as they should; and be responsible for taking action to fix things that need to be fixed.  Don't wait for your instructor to do these sorts of things!
    
2. Textbook, class notes -- You should read the appropriate sections of the book before coming to class.  It is not expected that you will fully understand everything that you read; but that initial exposure will help you get more out of the lecture by saving you from having to spend valuable class time with the more superficial aspects of the presentation, and allowing you more time to think about the deeper parts.
   
   You should also read again after each class, as soon as possible, along with any notes you may have taken in class.  This will allow you to straighten out some of the ideas you were not entirely clear on during class, while those ideas are still pretty fresh in your mind. 
   
   Note also that not all of the material for the course will be covered in the class meetings!  The instructor will have to make tough decisions about how best to use class time, and as part of that process some ideas and examples will be left to the student to read.  Going in to any of the exams, you are responsible for everything from all course resources -- the lectures, the book, the notes, the homework exercises,... 
    
3. Instructor(s) (and TAs if any) -- We want to be as much help to you as we can, within the constraints of the circumstances.  Of course your attendance in all class meetings is fundamental to our being able to help you.  NB attendance at all class meetings is required and your attendance record is part of your course grade.  (If you miss a class meeting, excused or not, it is your responsibility to catch up on the missed material.  You should keep in mind that in this course, the material builds on itself; if you miss some of the material, subsequent lectures will seem more difficult to you.)
   
   It is also very likely to be helpful to re-watch the recorded lectures (if available from your instructor) after you have had a chance to study and discuss the material, pausing it as often as you like, to think about things you might not have understood immediately, or when you need to figure something out, before hitting "play" again and keep going.
   
   You are invited to all of the office hours of the course; they are all listed on the Office Hours page of this website.  Even though office hour time is shared with other students it can still be a very effective use of your time.
   
   Importantly, note that instructors are listed third on this list of resources.  (There is just no substitute for self-motivated and focused study with the book and the notes!)
   
   
4. Help Room -- This semester, the Mathematics Department is staffing a Help Room for students taking multivariable calculus.  Here is the schedule:  https://math.duke.edu/undergraduate/help-tutoring/help-rooms
   
   The Help Room staffers are experienced undergrads who have taken and done very well in these courses.  You can ask for help on specific exercises, and you can also ask for help with general ideas in the course material.  All in all this is a fantastic resource if you are having trouble, and is available for many hours each week. 
    
5. Classmates -- We are big believers in study groups!  If you know people in the course that you think you can work with effectively, we strongly encourage you to do so.  You should also consider the Study Connect resource from the ARC as a great way to find other students to work with.
    
6. Of course it is great to be able to get help from other students when needed, but it is arguably even more valuable to give help -- because it will force you to explain through language the ideas that you think you understand, and this process is both surprisingly difficult and also surprisingly effective in revealing aspects of one's understanding that are actually not entirely polished yet. 
   
   Working together on homework is fine, but an even more effective use of study groups is simply to create dialogue, one way or another.  This creates opportunities for each speaker to test their understanding through their expression as noted above, and also the dialogue will naturally focus around whatever some two students see differently, in which case the resolution of the disagreement is that at least one gets their understanding improved.  You can create dialogue in different ways, such as having members of your group try to make confident statements about topics they think they understand, and then letting the group critique them. 
   
   Of course, it should go without saying that any work that you turn in must be your own.  See a more detailed discussion of what this means in the Academic Integrity section of the General Policies page.
    
7. Past Exams -- Clark Bray's past Math 219 exams (first taught in Spring 2022) might be useful as study material.  For example you might use the blanks to administer for yourself a mock exam, and then when you are done compare you work with that in the solutions. 
   
   You might also find it useful to work from Clark Bray's old semester Math 212 midterm exams.  Also of possible interest are the related midterm exams from Clark Bray's offerings of this course taught in summer terms (very similar but slightly different content due to use of a different textbook).  Of course Math 212 is not the same course as Math 219, but the material covered and the level of expectation are very similar, so these should still be a good resource.
    
8. ARC resources -- Check the ARC's website for possible resources that ARC might be offering this term, possibly including peer tutoring, small group tutoring, or study groups.  Consider especially their Study Connect program, noted above!
   
   
1. For 2023 Fall, from ARC: 
   

   SAGE Learning Communities:

   The STEM Advancement Through Group Education (SAGE) program is a resource offered in conjunction with the Academic Resource Center. These groups meet weekly with a trained undergraduate Peer Facilitator and engage with content closely correlated with the course. SAGE students are highly motivated, want to establish a critical foundation for STEM learning at Duke, and are interested in learning in a community with other students. SAGE helps students learn effective STEM study strategies, provides extra support for the challenging material in the course, and fosters a collaborative community of learners.

   Sign-ups will begin after the drop/add period. Information about how to sign up & more details about the program can be found here: https://arc.duke.edu/sage