# Math 151 - Calculus for Business and Social Sciences

## Course Coordinator

Jim Cliber (jcliber@iastate.edu)

## Catalog Description

MATH 151. Calculus for Business and Social Sciences.
(2-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 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 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

Lial/Greenwell/Richey, 10th ed.
Calculus with Applications
bundled with MyMathLab Plus access code
ISBN: 9781269372275

## Syllabus

Chapter and Section references are from Calculus with Applications, 10th Edition, by Lial/Greenwell/Richey.

Times are suggested based on a 15-week semester of 29 lecture meetings, allowing 4 days for review and exams.

Three evening midterm exams are scheduled during weeks 5, 9, and 13.

The final exam is departmental and is held during finals week.

Chapter & Sections Topics Time
Chapter 2 – Nonlinear Functions 3 days
2.4 Exponential Functions
2.5 Logarithmic Functions
2.6 Applications: Growth and Decay; Mathematics of Finance

Chapter 3 – The Derivative 4 days
3.1 Limits
3.2 Continuity
3.3 Rates of Change
3.4 Definition of the Derivative

Chapter 4 – Calculating the Derivative 5 days
4.1 Techniques for Finding Derivatives
4.2 Derivatives of Products and Quotients
4.3 The Chain Rule
4.4 Derivatives of Exponential Functions
4.5 Derivatives of Logarithmic Functions

Chapter 5 - Graphs and the Derivative 3 days
5.1 Increasing and Decreasing Functions
5.2 Relative Extrema
5.3 Higher Derivatives, Concavity, and the Second Derivative Test

Chapter 6 – Applications of the Derivative 4 days
6.1 Absolute Extrema
6.2 Applications of Extrema
6.4 Implicit Differentiation
6.5 Related Rates

Chapter 7 – Integration 5 days
7.1 Antiderivatives
7.2 Substitution
7.3 Area and the Definite Integral
7.4 The Fundamental Theorem of Calculus
7.5 The Area Between Two Curves

Chapter 8 – Further Techniques and Applications of Integration 1 day
8.1 Integration by Parts

## Objectives

### Nonlinear Functions

• Rewrite an exponential equation as a logarithmic equation and vice versa.
• Solve equations involving exponential and logarithmic functions.
• Apply properties of logarithms.
• Solve application problems such as compound interest, exponential growth, and carbon dating.

### The Derivative

• Use graphical and numerical evidence to estimate limits and to identify situations where limits fail to exist.
• Apply rules to calculate limits.
• Use the limit concept to determine where a function is continuous.
• Calculate average rates of change of a function and use them to estimate the value of the derivative.
• Find the derivative of a function using the limit definition of the derivative.

### Calculating the Derivative

• Calculate derivatives with a pencil and paper using:
• Power rule
• Linearity properties (Constant Multiple, Sum, and Difference rules)
• Product and Quotient rules
• Chain rule
• Calculate derivatives of exponential functions.
• Calculate derivatives of logarithmic functions.

### Graphs and the Derivative

• Find critical points of a function and use them to determine where the function is increasing and decreasing.
• Use the First Derivative Test to locate relative extreme values of functions.
• Calculate the second derivate of a function and use it to determine where the function is concave up and concave down.
• Use the Second Derivative Test to classify relative extreme values of functions.

### Applications of the Derivative

• Locate absolute extreme values of functions.
• Solve optimization (“max/min”) problems.
• Use implicit differentiation to calculate derivatives of functions defined implicitly.
• Solve “related rates” problems.

### Integration

• Find antiderivatives of basic functions.
• Calculate elementary integrals using the method of “u-substitution”.
• Use sigma notation and finite sums to estimate the area under the graph of a function.
• Use the Fundamental Theorem of Calculus to evaluate definite integrals.
• Find the area between the graphs of two functions.
• Evaluate integrals using integration by parts.

## 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.