Math 1510 – Calculus for Business and Social Science

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