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Aug 04, 2024
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# MATH& 163 Calculus 3 (5 credits)

Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Prerequisite MATH& 152  with a grade of 2.0 or higher or instructor permission.

Course Description
Sequences and series, multi-variable functions and their graphs, vector algebra and vector functions, partial differentiation.

Student Outcomes
Sequences and Series
1. Generate the terms of a sequence from an explicit or recursive equation.
2. Determine the formulas for simple sequences (geometric, arithmetic, power).
3. Determine the limit of a sequence, if it exists.
4. Determine the convergence of simple series (e.g., harmonic series) by comparing to improper integrals.
5. Explore the convergence of series and sequences using technology.
6. Determine the convergence of a geometric series and find its sum if it exists.
7. Determine the radius of convergence of a power series using the ratio test.
8. Represent appropriate functions via geometric series and Taylor series.
9. Differentiate and integrate power series.

Vectors
10. Determine the distance between points in three dimensional space.
11. Determine the equation of a sphere centered at a given point and of a given radius.
12. Determine the magnitude of a vector.
13. Perform basic computations with vectors numerically and graphically.
14. Compute the dot product of two vectors.
15. Determine the angle between two vectors.
16. Compute the projection of one vector onto another.
17. Compute the cross product of two vectors.
18. Determine the area of the parallelogram spanned by two vectors via the magnitude of the cross product.

Vector Functions and Space Curves
19. Determine the parametric equation of a line given sufficient information (e.g., a point and a parallel vector, two points).
20. Determine the scalar equation of a plane given sufficient information (e.g., three points, a point and a normal vector, a point and two non-parallel vectors).
21. Sketch the graph of a vector valued function (parameterized curve).
22. Identify the graphs of standard space curves (e.g., line, parabola, circle, helix).
23. Integrate and differentiate vector valued functions.
24. Determine tangent lines to space curves.
25. Determine the arc length of a space curve.

Functions of Several Variables and 3D Surfaces
26. Evaluate functions of several variables numerically, graphically, and symbolically.
27. Use the technique of level curves to sketch the graph of a function of two variables.
28. Graph functions of several variables utilizing technology as appropriate.
29. Identify the graphs of standard surfaces (e.g., sphere, paraboloid, ellipsoid, cylindrical surfaces).
30. Compute limits of functions of several variables.
31. Determine the domain and continuity of a function of several variables.

Partial Derivatives
32. Utilize the definition of the partial derivative of a function of several variables to solve rate of change problems.
33. Compute partial derivatives symbolically utilizing the basic techniques from single variable calculus.
34. Determine implicit and parametric equations for the tangent plane to a surface that is defined by the graph of a function.
35. Compute partial derivatives via the chain rule and through implicit differentiation.
36. Apply directional derivatives to solve rate of change problems in arbitrary directions. Determine the direction of maximal and minimal change of a function of several variables.
37. Apply techniques of partial derivatives to solve problems in the sciences and engineering.

General Content
38. Solve application problems in the sciences, including determining position, velocity, and acceleration of an object moving along a given trajectory.
39. Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation and appropriate language.
40. Link graphical, numeric, and symbolic approaches when interpreting situations and analyzing problems.

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