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Master Course Outline
MATH& 151
Calculus I

Credits: 5
Clock Hours per Quarter: 50

AA Discipline: [Quantitative] [Natural Sciences]

Lecture Hours:50

The first in a sequence of four courses for students who are planning to major in engineering, mathematics, or the sciences. Graphical analysis of concepts is emphasized through the use of technology. Topics include limits and continuity, derivatives and their applications. Prerequisite: Grade of C- or higher in MATH& 142 or permission of the Mathematics Department. Formerly MATH 124, Calculus with Analytic Geometry I.

Intended Learning Outcomes
  • Analyze the following families of functions. Special attention should be give to each function's individuality: the shape of its graph, characteristic properties, comparative growth rates, and general uses.
    a. Linear functions.
    b. Power and root functions.
    c. Exponential and logarithmic functions.
    d. General polynomial functions.
    e. Rational functions.
    f. Trigonometric functions.
    g. Inverse functions.
  • Successfully apply the following actions to functions from each family listed above.
    a. Read graphs and think graphically.
    b. Read tables and think numerically.
    c. Algebraic skills.
    d. Modeling the real world.
  • Successfully apply the following actions to functions from each family listed above both in an algebraic context as well as graphical context.
    a. The arithmetic operations addition, subtraction, multiplication, and division.
    b. Function composition.
    c. Transformations and translations of the type A f(b x + C) + D where f is a function from the families listed above and A,B,C, & D are real numbers.
  • Successfully apply the concept of a derivative to each of the families of functions listed above.
    a. Find derivatives numerically (by taking arbitrarily find difference quotients).
    b. Visualize derivatives graphically as the slope of the graph.
    c. Interpret the meaning of the first and second derivatives in various applications.
    d. Understand local linearity.
    e. Recognize the derivative as a function in its own right.
  • Successfully apply the symbolic methods of differentiation to each of the families of functions listed above.
    a. Formulas for derivative functions.
    b. Powers and polynomials.
    c. Product rule.
    d. Quotient rule.
    e. Chain rule.
    f. Implicit differentiation
  • Successfully apply the derivative in solving problems.
  • "Going backward" from a derivative to the original function, first graphically and numerically, then analytically.
  • Technological skills integrated into the course include, but are not limited to, the following:
    Effectively use computer graphing software or graphing calculators to explore graphs of functions, to analyze their basic characteristic and properties, and to become more successful in problem solving.
  • Optional:
    a. Successfully develop a practical understanding of the definite integral (OPTIONAL).
    b. Limit of Riemann sums.
    c. Connection between derivative and the definite integral.
    d. Compute the definition integral numerically.
    e. Properties of the definite integral and its interpretation as area.

  • Syllabi Listing See ALL Quarters
    Year Quarter
    MATH& 151
    Fall 2014
    Eric Schulz
    MATH& 151
    Fall 2014
    Julianne Sachs
    MATH& 151
    Fall 2013
    Megan Schoessler
    MATH& 151
    Fall 2012
    Julianne Sachs
    MATH& 151
    Fall 2011
    Gary Owsley

    Two Year Projected Schedule

    Year One* Year Two**

    *If fall quarter starts on an odd year (2003, 2005, etc.), it's Year One.
    If fall quarter starts on an even year (2002, 2004, etc.), it's Year Two.