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MAT 1236 Calculus III

MAT 1236 Calculus III. Exam 1 Info. http://myhome.spu.edu/lauw. Tutoring record. Turn in your record Get a new one for Exam 2. Exam 1. Date and Time 4/28 Monday Sections 10.1-10.4, 12.1-12.5,14.1-14.3 Total Points 60 points Time 1:50-3:00. Possible Problem Types.

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MAT 1236 Calculus III

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  1. MAT 1236Calculus III Exam 1 Info http://myhome.spu.edu/lauw

  2. Tutoring record • Turn in your record • Get a new one for Exam 2

  3. Exam 1 • Date and Time 4/28 Monday • Sections10.1-10.4, 12.1-12.5,14.1-14.3 • Total Points 60 points • Time 1:50-3:00

  4. Possible Problem Types • Computational (>75%) • Non-computational • State Definitions, theorem, formula, … • Explain concepts • Derive formula e.g. • Derive the formula for the area of the parallelogram determined by vectors a and b. • Derive the formula for length of a parametric curve

  5. Derive formulas • We have done quite a few of these in the last 3 weeks. • 10.2 - , , Area • 10.4 - Area formula (polar) • 12.3 - Angle between 2 vectors, vector projection • 12.4 - Area of the parallelogram

  6. Parametric Equations • t is the parameter • The curve defined by a parametric equation is called a Parametric Curve

  7. Conversion • We can convert a parametric equation into the corresponding Cartesian equation by eliminating the parameter. • Pay attention to the range of the parameter.

  8. Tangent Lines

  9. Areas

  10. Areas This formula only works for regions given by

  11. 11.2 Length of Curve

  12. 11.2 Surface Area is rotated about the x-axis

  13. Polar Coordinates • Familiar with polar coordinate system • Need to know how to find the slope of tangent lines when polar equations are given.

  14. Polar Equations • Need to know how to find area of regions enclosed by curves given by polar equations. • Need to know how to find arc length of curves given by polar equations.

  15. Vector Operations

  16. Properties

  17. Vector Operations

  18. Vector Operations

  19. Other Properties

  20. Vector Operations

  21. Special Vectors

  22. Equations of Lines

  23. Equations of Planes

  24. Reminder • Points will not be given to steps involving taking cross product randomly. • You must give a reason why you are taking the cross product.

  25. Limits

  26. Partial Derivatives

  27. Important Notice • It is extremely important that you use logical formats and show the necessary details. Answers alone or without proper support arguments will be given no points.

  28. Important Notice • Points will be taken off for bad or incorrect notations

  29. Warning • Do not look at your neighbor’s paper.

  30. General Info • Absolutely no share of calculators. Bring extra batteries, extra calculators. It is your responsibility to bring a workable calculator. • You are expected to use correct notations. • You are expected to make your arguments very carefully.

  31. General Info • Make sure you put down the details of the solutions. No points will be given to answers alone. Make sure your work is neat, clear and easily readable or you will receive NO credits. • Points will be taken off for bad notations or omission of notations. The same mistake can be penalized for multiple times.

  32. General Info • No points will be given to graphs or graphical solutions. • Make sure your solutions are complete and logically presented. • Check and Recheck your solutions. Be sure to cross out any scratch works or unwanted materials.

  33. General Info • If more than one solution is given, no points will be given. • DO NOT store any information in your calculator.

  34. Practice Problems Disclaimer • This practice exam has no direct relations with the real exam. • You need to understand that the problems in the real exam may not resemble the homework problems or the problems in this practice exam.

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