
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
 Threedimensional coordinate systems
 Vector algebra including dot and cross products of vectors
 Lines and planes in threedimensional space
Coordinator Dr. Bruce O’Neill
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