Math 160 - Survey of Calculus

Course Coordinator

Mark Hunacek (mhunacek@iastate.edu)


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.


Textbook

book cover

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


Syllabus

  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)

Objectives

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.

Differentiation

  • 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.

Integration

  • 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)


Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.


Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.

More information about disability resources in the Mathematics Department can be found at http://www.math.iastate.edu/Undergrad/AccommodationPol.html.