Montgomery College 2018-2019 Catalog 
    Sep 24, 2023  
Montgomery College 2018-2019 Catalog [ARCHIVED CATALOG]

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MATH 181 - Calculus I


MATH 181  and MATH 182  are intended primarily for students of the physical sciences, engineering, and mathematics. An introduction to major ideas of single variable calculus including limits, derivatives, and integrals of algebraic and transcendental functions; applications. PREREQUISITE(S): A grade of C or better in MATH 165 , appropriate score on mathematics assessment test, or consent of department. Assessment Level(s): ENGL 101 / ENGL 101A  or AELW 940 /ELAI 990 , READ 120  or AELR 930 /ELAR 980 . For computation of tuition, this course is equivalent to five semester hours. Five hours each week. Formerly MA 181.

4 semester hours

Course Outcomes:
Upon course completion, a student will be able to:

  • Determine when and how to apply the Fundamental Theorem of Calculus.
  • Evaluate limits graphically, algebraically, and numerically.
  • Explain and distinguish between average and instantaneous rates of change and be able to interpret each within the context of an applied problem.
  • Find a derivative directly from the definition of a derivative.
  • Identify and apply the appropriate rule(s) for symbolic differentiation.
  • Implicitly differentiate a function.
  • Interpret derivatives verbally in the context of an application.
  • Interpret limits verbally.
  • Interpret the definite integral as a limit of sums.
  • Interpret the indefinite integral as an inverse process of differentiation and evaluate indefinite integrals.
  • Set up and evaluate definite integrals to solve applied problems, such as problems involving area, motion, and net change.
  • Use derivatives to determine the extreme values of a function.
  • Use derivatives to model and analyze a variety of applications, such as problems involving optimization, related rates, and motion.
  • Use first and second derivatives to obtain information about the graph of a function and use the graph of a function to obtain information about its first and second derivatives.
  • Use technology to discover, explore, illustrate, and understand limits, derivatives, and integrals.

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