## Course coordinator

Alejandro Andreotti

aleand@iastate.edu

515-294-5128

## Catalog description

**MATH 1510: Calculus for Business and Social Sciences**

(2-1) Cr. 3. F.S.SS.

*Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry*

Differential calculus, applications to max-min problems, integral calculus and applications. Will not serve as prerequisite for MATH 2650 or MATH 2660. Only one of MATH 1510, MATH 1600, or the sequence MATH 1650-MATH 1660 may be counted towards graduation.

## Textbook

**Calculus with Applications (11th Edition)
**Lial, Greenwell, and Richey

## Course description

This calculus course is an introduction to differential and integral calculus which comprise the study of change. The course will cover limits, continuity, the derivative of explicit and implicit functions, applications of the derivative, the integral, and transcendental functions. Calculus emphasizes skills, theory, and applications. The emphasis will be on both theory and applications.

## Objectives

### We will cover most of Chapters R–7 from the textbook. Upon completion of the course, you will be able to:

- Find the domain and range of polynomial, rational, and radical functions.
- Identify the properties of polynomial, rational, and radical functions.
- Graph polynomial, rational, and radical functions using asymptotes when applicable.
- Identify exponential and logarithmic functions.
- Graph exponential and logarithmic functions.
- Solve exponential and logarithmic equations.
- Apply the concepts of doubling time, half-time, and interest rate models.
- Define the concepts of limits and continuity of functions.
- Compute limits using graphical and numerical methods.
- Compute limits using the rules of limits.•Identify situations where limits fail to exist.
- Define the average rate of change and instantaneous rate of change.
- Define the average velocity and instantaneous velocity.
- Apply the average and instantaneous rates of change to mathematical models.
- Define the derivative using the concept of limits.
- Define the derivative as the tangent line of a graph.
- Define the derivative as a rate of change.
- Compute derivatives using graphical methods.
- Compute derivatives using numerical methods.
- Compute derivatives using the limit definition of a derivative.
- Compute derivatives using the Power Rule.
- Compute derivatives using the Product Rule.
- Compute derivatives using the Quotient Rule.
- Compute derivatives using the Chain Rule.
- Compute the derivative of exponential functions.
- Compute the derivative of logarithmic functions.
- Apply derivatives to the business concepts of cost analysis, marginal costs, and rates of change.
- Define increasing and decreasing functions.
- Identify increasing and decreasing functions using graphs.
- Calculate the critical points of a function.
- Define relative extrema.
- Identify relative extrema using the First Derivative Test.
- Calculate higher derivatives using the Power, Product, Quotient, and Chain Rules.
- Identify concavity using the Second Derivative Test.
- Sketch curves of various functions.
- Apply curve-sketching techniques to optimization models.
- Compute the absolute extrema of functions.
- Find the implicit derivatives of equations.
- Calculate the related rates of application models.
- Calculate differentials and linear approximations.
- Define antiderivatives.
- Calculate the antiderivatives of functions using the Power Rule.
- Calculate the antiderivatives of functions using Substitution.
- Approximate the area under a curve using definite integrals.
- Evaluate definite integrals using the Fundamental Theorem of Calculus.
- Calculate the area between two curves.

## Course pacing

Times are loosely suggested based on a 15-week semester of 29 lecture meetings, allowing 4 days for review and exams. The final exam is departmental and is held during finals week.

**Weeks 1-3**- Algebra Review
- Chapters R, 1, 2

**Weeks 4-5**- Introduction to Limits & Derivatives
- Chapter 3

**Weeks 6-7**- Techniques for Finding Derivatives
- Chapter 4

**Weeks 8-11**- Extrema & Applications of Extrema
- Chapters 5 and 6

**Week 12**- Implicit Differentiation & Related Rates
- Chapter 6

**Weeks 13-15**- Integration
- Chapter 7