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Dec 13, 2024
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MATH& 153 - Calculus III
5.0 Credits Infinite sequences and series, vectors and vector functions, functions of several variable, and partial derivatives. Graphing calculator required (was MATH 153). Prerequisite: MATH& 152 (was MATH 152) or equivalent with a grade of 2.0 or higher.
Course Objectives Upon successful completion of this course, students will be able to:
- Identify the different types of sequences and series. [REASON]
- Determine when a sequence or series is convergent or divergent. [REASON]
- Perform basic convergence tests (including the ratio test, comparison test and integral test). [REASON]
- Compute the radius and interval of convergence for a power series. [REASON]
- Compute the Taylor Series expansion of a function. [REASON]
- Perform vector arithmetic computations. [REASON]
- Compute using vector components. [REASON]
- Perform vector operations (including dot product, cross product and projections). [REASON]
- Find an equation of a line and plane using vector notation. [REASON]
- Differentiate and integrate vector-valued functions. [REASON]
- Find tangent and unit tangent vectors to a smooth curve at a point. [REASON]
- Compute curvature. [REASON]
- Find the unit normal and binormal vectors of a smooth curve defined by a vector-valued function. [REASON]
- Determine the tangential and normal components of the acceleration vector. [REASON]
- Convert points and equations between rectangular coordinates and polar coordinates. [REASON]
- Recognize and sketch graphs of equations in polar coordinates. [REASON]
- Construct graphs, find domains and ranges, and analyze continuity and differentiability of functions with two or more independent variables. [REASON]
- Write expressions for partial derivatives using limits. [REASON]
- Calculate partial derivatives using formulas. [REASON]
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