# Math 160 – Survey of Calculus

515-294-7294

## Catalog description

MATH 160: Survey of Calculus

(4-0) Cr. 4. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry; or minimum of C- in MATH 140; or minimum of C- in MATH 143

Analytic geometry, derivatives and integrals of elementary functions, simple differential equations, 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 MATH 181 may be counted towards graduation.

## Textbook

Applied Calculus for the Managerial, Life and Social Sciences

Tan
bundled with WebAssign
ISBN: 9781285464640

## 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 trigonometric 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.)

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## Students with disabilities

Iowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at www.sas.dso.iastate.edu, by contacting SAS staff by email at accessibility@iastate.edu, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.