MATH& 153 - Calculus III
Sequences, series, power series, vectors, vector-valued functions, lines and planes in 3D, calculus with parametric equations and polar coordinates, and partial derivatives.
Prerequisite MATH& 152 with a minimum grade of 2.0.
Course-level Learning Objectives (CLOs)
Upon successful completion of this course, students will be able to:
- Identify the different types of sequences and series.
- Determine when a sequence or series is convergent or divergent.
- Perform basic convergence tests (including the ratio test, comparison test, and integral test).
- Compute the radius and interval of convergence for a power series.
- Compute the Taylor Series expansion of a function.
- Perform vector arithmetic computations.
- Compute using vector components.
- Perform vector operations (including dot product, cross product, and projections).
- Find an equation of a line and plane using vector notation.
- Differentiate and integrate vector-valued functions.
- Find tangent and unit tangent vectors to a smooth curve at a point.
- Compute curvature.
- Find the unit normal and binormal vectors of a smooth curve defined by a vector-valued function.
- Determine the tangential and normal components of the acceleration vector.
- Convert points and equations between rectangular coordinates and polar coordinates.
- Recognize and sketch graphs of equations in polar coordinates.
- Construct graphs, find domains and ranges, and analyze continuity and differentiability of functions with two or more independent variables.
- Write expressions for partial derivatives using limits.
- Calculate partial derivatives using formulas.
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