MATH& 163: Calculus 3

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Class Program
Mathematics
Distribution
Symbolic or Quantitative Reasoning,
Math/Science Non-Laboratory
Credits 5 Lecture Hours 55
This course will expand on the applications and techniques of differentiation learned in the first and second quarters. It will introduce the student to the calculus of sequences and series and the use of the MacLauren and Taylor series to approximate functions. It will introduce the student to the calculus of curvilinear functions and the concept of the vector and vector functions. It will also introduce the concept of a partial derivative and the maximization of functions given in more than one independent variable.

Prerequisites

MATH& 152 or instructor permission
Quarters Offered
Winter,
Spring
Course Outcomes

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

  1. Determine the convergence of series and sequences
  2. Use series to represent and model functions
  3. Apply calculus to functions in Cartesian, polar, cylindrical, and spherical coordinates
  4. Find extrinsic properties (E.G. curvature, arc length) of vector-valued functions
Institutional Outcomes
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
Course Content Outline
  1. Sequences
  2. Infinite Series
  3. Comparison and Integral Tests
  4. Ratio and Root Tests
  5. Alternating Series and Absolute Convergence
  6. Power Series
  7. Taylor and MacLaurin Series
  8. Calculations with Taylor Series
  9. Conic Sections and Quadratic Equations
  10. Parameterizations of Curves
  11. Calculus with Parameterized Curves
  12. Polar Coordinates
  13. Polar Graphs
  14. Polar Equations for Conic Sections
  15. Integration in Polar Coordinates
  16. Vectors in the Plane
  17. Cartesian (Rectangular) Coordinates and Vectors in Space
  18. Dot Products
  19. Cross Products
  20. Lines and Planes in Space
  21. Surfaces in Space
  22. Cylindrical and Spherical Coordinates
  23. Vector-Valued Functions and Space Curves
  24. Modeling Projectile Motion
  25. Arc Length and the Unit Tangent Vector
  26. Curvature
  27. Introduction to Differential Equations (Optional)
Department Guidelines

In order to give the instructor the greatest flexibility in assigning a grade for the course, grades will be based on various instruments at the instructor’s discretion. However, to maintain instructional integrity there must be four class exams or three class exams and a project. A final exam will be given if there are less than four exams or a project may be substituted for the final exam if there are four in-class exams. At least 60% of the grade will be based on quantifiable work (exams, homework, quizzes, etc.). The remaining portion of the grade may be based on quantifiable work, attendance, projects, journal work, etc., at the instructor's discretion.

The following is a compilation of acceptable grading instruments: In class exams and a final, attendance, homework or quizzes, research paper, modeling projects on the calculator or computer. Other projects or assignments may be assigned as deemed appropriate at the instructor's discretion.