Math 160 - Survey of Calculus

Course Coordinator

Mark Hunacek (

Catalog Description

MATH 160. Survey of Calculus.
(4-0) Cr. 4. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry
Analytic geometry, derivatives and integrals of elementary functions, partial derivatives, and applications. Will not serve as a prerequisite for MATH 265 or MATH 266. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.


book cover

Applied Calculus for the Managerial, Life and Social Sciences  
bundled with WebAssign
ISBN: 9781285464640 (hardcover)


  1. Precalculus review, equations of straight lines. (Chapter 1)
  2. Functions and graphs. (Sections 2.1 -- 2.2)
  3. Limits and continuity. (Sections 2.4 - 2.5)
  4. Introduction to differentiation and basic rules for differentiation. (Sections 2.6, 3.1 - 3.3)
  5. Implicit differentiation and related rates. (Section 3.6)
  6. Use of derivatives to find relative and absolute maxima/minima and to sketch graphs of functions. (Chapter 4)
  7. The constant e and continuously compounded interest. (Sections 5.1 – 5.3)
  8. Integration: indefinite integrals and anti-differentiation, definite integrals and the Fundamental Theorem of Calculus, area between curves, integration by parts. (Sections 6.1 – 6.6, 7.1)


Functions, Limits and Continuity

  • Understand what a function is, and the relationship of a function to its graph
  • Understand intuitively what the limit of a function is
  • Apply rules to calculate simple limits
  • Understand the intuitive meaning of continuity of a function at a point
  • Use the limit concept to determine where a function is continuous.
  • Use the Intermediate Value Theorem to identify an interval where a continuous function has a root.


  • Use the limit definition to calculate a derivative, or to determine when a derivative fails to exist.
    • Understand and use rules for the derivative of sums, products, and quotients
    • Understand and use the chain rule for computing the derivative of a composite function
    • Rules for computing derivatives of logarithmic and exponential functions
    • Rules for inverse functions, including logarithms and inverse trignometric functions.
  • Use the derivative to find tangent lines to curves.
  • Calculate derivatives of functions defined implicitly.
  • Interpret the derivative as a rate of change.
  • Solve problems involving rates of change of variables subject to a functional relationship (“related rates”)

Applications of Derivatives

  • Find critical points, and use them to locate maxima and minima.
  • Use critical points and signs of first and second derivatives to sketch graphs of functions:
    • Use the first derivative to find intervals where a function is increasing or decreasing.
    • Use the second derivative to determine concavity and find inflection points.
    • Apply the first and second derivative tests to classify critical points.
  • Use calculus to solve simple optimization problems in business and economics (marginal profit, etc.)
  • Use Differential Calculus to solve other kinds of optimization problems.


  • Find antiderivatives of functions.
  • Use antiderivatives to solve simple differential equations (variables separable)
  • Understand the concept of area under a curve, and the connection with antiderivatives given by the Fundamental Theorem of Calculus
  • Apply the Fundamental Theorem of Calculus to evaluate definite integrals
  • Evaluate definite integrals by certain simple rules (substitution, integration by parts, etc.)

Old Exams

(if there are any)

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