# Past Exam for MATH 203 - Calculus III at Northeastern Illinois University (NEIU)

## Exam Information

 Material Type: Exam 2 Professor: Staff Class: MATH 203 - Calculus III Subject: Mathematics University: Northeastern Illinois University Term: -- Keywords: DifferencesCalculatorsDefinitionsRectangularCoordinate SystemsCoordinate System

## Sample Document Text

Math203, Demo Exam #2 (Chapters 15-17) Directions: Answer all of the questions. The problems will have their weights assigned next to them. Show all work and reasoning for maximum credit. No notes, cellular phones, pagers, calculators, books or friends. Good luck. 1)Definitions. a. Describe how you would find all of the potential maxima and minima for f(x,y). How could you distinguish between a maximum, minimum, or a saddle? b. Describe the differences between the rectangular, cylindrical, and spherical coordinate systems. When are times when a particular coordinate system is a better choice than the other two. Provide an example of each. c. Describe what a Jacobian is. Then use it to derive the φρ sin2 Jacobian in the spherical system. d. Define a gradient field. Describe how you would draw one. Describe what it means. Provide an example. e. Provide a sample parameterization of motion in 3 dimensional space. Also describe how you would find the velocity and total distanc...

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