MATH 1171 - Calculus for Business and Economics

Course Description

This course is intended for Business and Economics students. Students will learn about calculation and interpretation of derivatives, curve sketching for simple functions, optimization (applied to business and economics), and multivariable functions (including partial derivatives, optimization and Lagrange multipliers).

Learning outcomes

• Evaluate a given limit, or determine that the limit does not exist, using appropriate graphical, algebraic or numerical methods. Algebraic methods include simplifying, factoring, and rationalizing a numerator or denominator.
• Determine the points of discontinuity of a function defined by a graph or formula.
• State the definition of the derivative, and apply it to find derivatives of simple functions.
• Use differentiation rules to find derivatives of power, exponential, and logarithmic functions.
• Apply the Product Rule, Quotient Rule, and Chain Rule when appropriate.
• Interpret the derivative of a function as the slope of a tangent line to the graph of the function, and use this idea to obtain derivatives graphically.
• Find first derivatives of functions defined implicitly. Use implicit differentiation to differentiate inverse functions. Compute derivatives by logarithmic differentiation. Find the tangent line at a point on a curve defined implicitly.
• Find the critical numbers for a function defined by a formula. Find the absolute maximum and minimum values of a function on a closed, bounded interval. Solve optimization problems by using derivatives to find extreme values of appropriate objective functions (especially cost, revenue, and profit).
• Use the first derivative of a function to determine the intervals on which it is increasing or decreasing and its local maximum and minimum values. Use the second derivative of a function to determine the intervals on which it is concave up or concave down and to find its inflection points. Determine horizontal and vertical asymptotes when they exist. Use all of this information to graph a function without the help of a graphing device.
• Interpret derivatives as rates of change, and find marginal cost/revenue and/or profit. Find average functions.
• Find partial derivatives of multiple variable functions, and use them to find critical points and extrema. Interpret them in the context of applications in Business and Economics.

Course topics

• Unit 1: Limits
• Unit 2: Derivatives
• Unit 3: Curve Sketching
• Unit 4: Partial Derivatives 

Required text and materials

The following free, open educational resources are required for this course and will be available within the course:

1. Boroushaki, S. (2022). CLP-1 Differential calculus. CC BY NC SA 4.0
2. Boroushaki, S. (2022). CLP-1 Differential calculus exercises. CC BY-NC-SA 4.0
3. Calaway, S., Hoffman, D., & Lippman, D. (2014). Applied calculus. CC BY 3.0 US
4. Feldman, F., Rechnitzer, A., & Yeager, E. (2024). CLP-3 Multivariable calculus. CC BY NC SA 4.0
5. Feldman, F., Rechnitzer, A., & Yeager, E. (2024). CLP-3 Multivariable calculus exercises. CC BY NC SA 4.0

Assessments

To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course and 50% or higher on the mandatory final exam.

Note: The final exam for this course is only available as a paper exam and must be taken in person at an approved Testing Centre. Please email exams@tru.ca with any questions.

Recommended requisite(s)

Pre-calculus 12; or MATH 1001; or MATH 0633

Exclusions

MATH 1141

MATH 1157

MATH 1170