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Nov 22, 2024
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MA 225 - Calculus II4 lecture hours 0 lab hours 4 credits
Course Description
This subject is a continuation of MA 128 . The topics covered include numerical integration, volumes of revolution, moments of inertia, work and fluid pressure, differentiation and integration of transcendental functions, L’Hȏpital’s rule, special integration techniques, parametric equations, and arc length. (prereq: MA 126 or equivalent, MA 128 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
• integrate the trigonometric, inverse trigonometric, exponential, and logarithmic functions which can be integrated by reversing the formula for differentiation
• integrate the trigonometric functions which require using the Pythagorean, half-angle, or double-angle relationships before either of the above methods can be used
• integrate by parts and by trigonometric substitution
• find the area between two curves
• find the approximate value of a definite integral using numerical integration
• find the volumes generated by rotating areas under curves and volumes of revolution
• find moments of inertia of areas about lines coincident with and parallel to the coordinate axes
• find work done by a variable force
• find the force against a vertically submerged surface
• find and simplify the derivatives of the trigonometric, inverse trigonometric, exponential, and logarithmic functions and use these derivatives in curve sketching and applied problems
• find limits by L’Hȏpital’s rule
• find parametric equations for and arc lengths of curves in two dimensions
Prerequisites by Topic
• Simplifying algebraic fractions
• Trigonometric identities
• Sketching curves in two-space
• Differentiation of algebraic functions
Course Topics
• Applications of integration (9 classes)
• Differentiation of transcendental functions (9 classes)
• L’Hȏpital’s Rule (1 class)
• Integration techniques (11 classes)
• Parametric equations and arc length (4 classes)
• Review and exams (6 classes)
Coordinator
Bruce O’Neill
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