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Nov 21, 2024
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MA 3501 - Engineering Mathematics I4 lecture hours 0 lab hours 4 credits
Course Description
This course provides topics to bridge the technical calculus sequence to the university’s calculus sequence. Topics include vector algebra; review of single variable calculus, including differentiation of elementary functions, the mean value theorem, antiderivatives, and definite integrals; selected methods of integration including partial fractions decomposition; functions of several variables including partial differentiation and multiple integration in cylindrical and spherical coordinates. (prereq: one year of technical calculus or equivalent)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Differentiate and integrate elementary functions
- Evaluate improper integrals on an infinite interval
- Integration by partial fractions decomposition
- Evaluate partial derivatives of functions of multiple variables
- Use the chain rule to find derivatives of functions of multiple variables
- Evaluate the total differential to estimate change in a function of multiple variables
- Evaluate double integrals in rectangular and polar coordinates
- Evaluate triple integrals in rectangular, cylindrical, and spherical
- Perform operations using vector algebra
- Evaluate dot and cross products of vectors
- Find equations of planes in three dimensions
- Parameterize lines in three dimensions
- Solve geometric problems involving lines and planes
Prerequisites by Topic
- Differentiation of trigonometric, inverse trigonometric, exponential and logarithmic functions.
- Basic integration including substitution.
Course Topics
- Review of differentiation of elementary functions
- The mean value theorem
- Review of antiderivatives and basic integration techniques, definite integrals, and the fundamental theorem of calculus
- Improper integrals on an infinite interval
- Integration by partial fractions decomposition
- Functions of two or more variables
- Partial differentiation, the chain rule, and the total differential
- Double integrals in rectangular and polar coordinates
- Triple integrals in rectangular, cylindrical, and spherical
- Three-dimensional coordinate systems
- Vector algebra including dot and cross products of vectors
- Lines and planes in three-dimensional space
Coordinator
Dr. Anthony van Groningen
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