College in High School Course Syllabus
Mathematics 0120
Business Calculus
(4 Credits)
This course is an introduction to calculus for students in business, economics, and other social sciences. Application of concepts is stressed throughout the course.
A rigorous high school algebra that includes exponentials and logarithmic functions or precalculus is a prerequisite for the course. Proficiency in algebraic manipulation is essential.
The grade is determined by the student's performance on three exams and a comprehensive final.
The recommended text for this course is Brief Applied Calculus by Berresford, third edition (Houghton Mifflin).
The following topics are covered in the Math 0120 course:
1. Derivatives
- Limits
- Introduction to limits
- Approaching infinity
- One-sided limits
- Continuity
- Tangents as rate of change
- Definition of derivatives
- Rules for derivatives
- Polynomials
- Products
- Quotients
- Chair rule
- Powers
- Implicit
- Marginal analysis in business
- Related rates
2. Application of the Derivative
- Graphing using:
- First derivative
- Second derivative
- Asymptotes and intercepts
- Absolute extreme on a given domain
- Optimizing problems
- Differentials
3. Exponential and Logarithmic Functions
- Review
- Graphs
- Values
- Algebraic laws
- Constant e and continual
- Compounding interest
- Derivatives
- Chain rule
- Elasticity of demand
4. Integration
- Indefinite integral
- Procedures for integrating
- Polynomials
- Powers
- Exponentials/logarithmic
- By substitution
- Growth and decay equations
- Definite integral
- Area
- Under the curve
- Between curves
- Definite integral as a limit of a sum
- Using trapezoidal and Simpson's rule
- Applications
- Average value of a function
- Continuous income stream
- Consumer and producer's surplus
- Equilibrium price
- Integration by parts
- Improper integrals
- Integration tables
- Differential equations/separation of variables
5. Multivariable Calculus
- Functions of several variables
- Partial derivatives
- Maxima and minima
- LaGrange multipliers
Optional:
- Method of least squares
- Double integrals over rectangular regions
- Trigonometric functions
- Review of basic trigonometric values, graphs, and laws
- Derivatives
- Integrals
- Arithmetic and geometric progressions