# 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

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.