MAT 397

Calculus III

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Syllabus

You can find the link to the general syllabus, course syllabus below, and supplemental respect and Covid-19 policies below:

General Syllabus
Course Syllabus
Respect & Covid-19 Policy

 

University Related 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).

General Tutoring Resources: Visit the Free Academic Assistance List or Overall Tutoring Source List.

Past Final Exams: Click here to find past MAT 397 final exams.

Past MAT 397 Courses: You can find my past MAT 397 courses under the ‘Courses’ tab.
 

Other Resources

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.

Extra Book Problems: You can find extra recommended book problems at this link.

Other Lectures/Notes: There are a number of excellent sources of additional Multivariable Calculus lectures and notes. If you want or need more explanations or problems, I would recommend the following:

Multivariable Calculus 2007 (But especially the video lectures, found here)
Calculus 3: Professor Leonard
Paul’s Online Notes (Especially good for problems/solutions)
Multivariable Calculus 2010
Multivariable Calculus 2006
Calculus of Several Variables 2010
Multivariable Calculus (Khan Academy)
 

Handouts

Calculus III: Course Prerequisite ‘Bootcamp’

Derivative Flashcards

Integral Flashcards

Calculus I Shortsheet

Calculus I Review

Geometry True/False

Dot Product, Cross Product, Projections

 

Lectures, Course Notes, and Problem Book

The course lecture videos can be found on Blackboard. There is a textbook for this course. However, there is no single textbook which exactly addresses all the types of problems we will see in this course. Accordingly, I have written a workbook for the majority of problem types that we shall see in this course, this includes space for your notes for each topic. You can also find my lecture notes, as well as a student version of the notes with the problem solutions removed.

Workbook: Student Version
Workbook: Instructor Version

Course Lecture Notes
 

Applied Problems

What is the point of learning Calculus if you cannot apply it?! Below are applications of some of the topics from Multivariable/Vector Calculus that we will learn this semester. You need to complete and submit two of these ‘projects’ this semester. The due dates are found on Blackboard. Remember, these will only be graded on effort and completeness, not correctness. You may only choose one of 4, 5, 7, 8, 9, 12, 15.

	Course Topic	Application	Problems	Solutions	Due
1	Geometry	Measuring Global Distances	PDF	PDF	10/09
2	Vectors	Tension & Catastrophic Failure	PDF	PDF	10/09
3	Dot Product	Document Comparison	PDF	PDF	10/09
4	Cross Product	Torque	PDF *	PDF	10/09
5	Surfaces	Ideal Gas Law	PDF *	PDF	10/09
6	Vector Functions	Kinematic Equations	PDF	PDF	10/09
7	Arclength/Curvature	DNA	PDF *	PDF	10/09
8	Multivariable Functions	Meteorology	PDF *	PDF	10/09
9	Limits	Time Dilation	PDF *	PDF	10/09
10	Partials	Financial Mathematics	PDF	PDF	10/09
11	Differentials	Error Analysis	PDF	PDF	11/27
12	Chain Rule	Body Mass Index (BMI)	PDF *	PDF	11/27
13	Gradients	Gradient Descent & Machine Learning	PDF	PDF	11/27
14	Maxima/Minima	Biological Diversity	PDF	PDF	11/27
15	Lagrange Multipliers	Snell’s Law	PDF*	PDF	11/27
16	Vector Fields	Ocean Currents	PDF	PDF	11/27
17	Green’s Theorem	Planimeters	PDF	PDF	11/27

 

Quizzes

Quizzes will be submitted on Blackboard. However, you can download all the quizzes using the link below. Note that the due dates reflected in compiled quiz document may not reflect any course changes. So you should use the quiz due dates on Blackboard.

Compiled Course Quizzes

Below are the quiz solutions, which will be updated regularly.

Quiz Solutions
 

Exams

Exam 1: Problems  Solutions

Exam 2: Problems  Solutions
 

Wolfram Demonstrations

The Wolfram Demonstrations page contains over 12,000 different demonstrations of applications of Mathematica programs to dozens of fields, including Calculus. You can interact with these demonstrations by downloading the Wolfram CDF player for your browser. Feel free to use these to help you engage with course concepts, and explore other topics. You can find a list of particularly useful, relevant, or interesting demonstrations in the drop down tab below.

Demonstrations List