Nov 22, 2024  
2014-2015 Undergraduate Academic Catalog 
    
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2014-2015 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 231 - Calculus for Engineers III

4 lecture hours 0 lab hours 4 credits
Course Description
This course is a continuation of MA 137  and an introduction to multivariable calculus. Topics include L’Hȏpital’s rule, improper integrals, applications of integrals to physics, parametric equations, polar coordinates, vector algebra and surfaces in three dimensions, and partial derivatives with applications. (prereq: MA 137  or MA 225 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
• Use L’Hȏpital’s Rule to evaluate a limit
• Evaluate improper integrals
• Find the length of the arc of a curve
• Find work, fluid pressure, and force
• Eliminate the parameter from parametric equations
• Draw graphs of parametric equations and determine the direction of travel for an increasing parameter
• Find first and second derivatives of parametric functions
• Find the arc length for parametric curves
• Convert between rectangular and polar coordinates
• Draw graphs of polar curves
• Find area and arc length in polar coordinates
• Perform operations using vector algebra
• Find dot products, cross products, and equations of lines and planes in three dimensions
• Sketch surfaces in three dimensions
• Find first and second partial derivatives
• Find the total differential of a function of more than one variable and use it to approximate error
• Use chain rules to find derivatives and partial derivatives
• Find implicit partial derivatives
• Determine the maximum, minimum, and saddle points on a surface
Prerequisites by Topic
• The basic principles of algebra
• The basic principles of trigonometry
• Differentiation and integration of algebraic and transcendental functions
• Limits
• Understanding of the definition of the definite integral
Course Topics
• L’Hȏpital’s Rule (2 classes)
• Improper integrals (3 classes)
• Arc length (1 class)
• Work (2 classes)
• Fluid pressure and force (2 classes)
• Parametric equations (24 classes)
• Polar coordinates and graphs (3 classes)
• 3-Space Vectors, lines, and planes (6 classes)
• Surfaces in three dimensions (3 classes)
• Functions of several variables (1 class)
• Partial derivatives (6 classes)
• Extrema of functions of two variables (2 classes)
• Review and exams (7 classes)
Coordinator
Yvonne Yaz


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