Calculus III
Syllabus
You can find the link to the general syllabus and the recitation syllabus below:
General Syllabus
Professor Yeroskin’s Syllabus
Recitation Syllabus
Student Help Resources
Mental Health Resources: Click here to find a list of mental health resources available to you at Syracuse University as well as national hotlines. Never hesitate to make use of these services if you need them. If you know someone in distress, say something and be sure to make them aware of these resources.
Mathematics Help Resources: Click here to find Mathematics help offered through the Mathematics Department and click here to find Mathematics help offered through CLASS (Center for Learning and Student Success).
Past Final Exams: Click here to find past MAT 397 final exams.
Handouts
Challenge Integrals: A collection of difficult integrals and series. Solving these problems could result in prizes!
Symbolab: Symbolab is a useful online computational device, which will not only integrate but show steps. This can be a useful study tool, but be careful how you use it!
WolframAlpha: WolframAlpha is a useful online computation device. WolframAlpha takes written commands, interprets the input, and performs the computations. WolframAlpha is an online ‘watered down’ version of Mathematica, which at this time is offered to Syracuse University students for free! However, WolframAlpha will take many Mathematica commands, as I outline in this document.
Reference Tables: I created a reference table which is not just useful for Calculus, but most of the more applied mathematics courses you could take as an undergraduate.
Nash’s’ Problem – The Beautiful Mind Problem: You may recall this scene from the 2001 film ‘A Beautiful Mind’. If you have not seen the film, it is an Academy Award winning film about the mathematician John Nash—who tragically died in 2015. Depending on how you read what is written on the board in the film, the problem can be ‘easy’ or very difficult. Attached as ‘The Beautiful Mind Problem’ is an explanation that might help you solve this problem. To read more about this problem and its relation to more advanced Mathematics, you might want to read a bit at this link, at this link, and at this link.
Extra Resources
Here are two links that might be of use when trying to visualize multidimensional surfaces: Parametric Surfaces and Desmos
You can find lectures on this course material (though much more focused on theory), exams, quizzes, notes, et cetera from the OCW.MIT course taught by Dr. Dennis Auroux at this link.
If you wanted extra practice problems for different topics you will see throughout the semester, you might find this packet a rather good place for problems.
Quizzes
Lanzani
Quiz 1 — Geometry: Problems Solutions
Quiz 2 — Vectors/Tension: Problems Solutions
Quiz 3 — Vectors/Vector Functions: Problems Solutions
Quiz 4 — Vector Functions: Problems Solutions
Quiz 5 — Limits/Partial Derivatives: Problems Solutions
Quiz 6 — Tangent Planes/Linearization: Problems Solutions
Quiz 7 — Lagrange Multipliers/Double Integrals: Problems Solutions
Quiz 8 — Double Integrals: Problems Solutions
Quiz 9 — Triple Integrals: Problems Solutions
Quiz 10 — Line Integrals/Conservative Fields: Problems Solutions
Quiz 11 — Line Integrals/Conservative Fields/Green’s Theorem: Problems Solutions
Yeroskin
Quiz 1 — Vectors: Problems Solutions
Quiz 2 — Vectors/Lines: Problems Solutions
Quiz 3 — Arclength/Vector Functions: Problems Solutions
Quiz 4 — Limits/Partial Derivatives: Problems Solutions
Quiz 5 — Tangent Planes/Partial Derivatives: Problems Solutions
Quiz 6 — Max/Mins: Problems Solutions
Quiz 7 — Double Integrals: Problems Solutions
Quiz 8 — Mass/Volume: Problems Solutions
Quiz 9 — Mass: Problems Solutions
Quiz 10 — Gradient Fields: Problems Solutions
Quiz 11 — Green’s Theorem: Problems Solutions
Exams
Yeroskin
Exam 2: Problems
Exam 2 Extra Credit: Problems