Math 151 - Calculus for Business and Social Sciences

Course Coordinator

Jim Cliber (

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.


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


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  


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.


  • 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.

Old Exams

Fall 2013 Exam 1
Fall 2013 Exam 2
Fall 2013 Exam 3
Fall 2013 Final Exam

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, or 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