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    Milwaukee School of Engineering
  Jan 18, 2018
2017-2018 Undergraduate Academic Catalog
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MA 137 - Calculus II

4 lecture hours 0 lab hours 4 credits
Course Description
This course is a continuation of MA 136  and an introduction to integral calculus. Topics include Newton’s method, differentials, basic integrals involving algebraic, trigonometric, exponential, logarithmic and inverse trig functions. Topics also include rectilinear motion, areas and volumes of revolution, integration techniques such as integration by parts and partial fractions, and numerical integration methods. (prereq: MA 136 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Use Newton’s method to approximate the zeros of a function
  • Find the differential of a function and use it to approximate error
  • Integrate algebraic, exponential, trigonometric, logarithmic and inverse trigonometric functions
  • Evaluate a definite integral by the limit of Riemann sums and by Fundamental Theorem of Calculus
  • Use method of substitution to find indefinite and definite integrals
  • Use method of integration by parts
  • Integrate products and powers of trigonometric functions
  • Integrate functions using partial fractions
  • Integrate functions by using trigonometric substitution
  • Find areas between curves
  • Find volumes of solids of revolution using disk and washer methods

Prerequisites by Topic
  • Graphing of functions
  • Derivatives of algebraic, exponential, trigonometric, inverse trig and logarithmic functions
  • Limits of algebraic and trigonometric functions
  • Implicit derivatives
  • Graphing using relative extrema

Course Topics
  • Newton’s method of approximating zeros of a function
  • Differentials
  • Area problem and indefinite integrals 
  • The definite integral as the limit of Riemann sums and the Fundamental Theorem of Calculus
  • Integration by substitution 
  • Areas between curves
  • Rectilinear motion
  • Volumes by disk and washers
  • Integration by parts
  • Integration of products and powers of trig functions
  • Integration using partial fractions
  • Integration using trigonometric substitutions
  • Integration using tables
  • Numerical integration

Yu Hin (Gary) Au

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