Business Calculus

Explore the fundamentals of business calculus through a comprehensive 9-hour course. Delve into functions, relations, and algebraic concepts before progressing to limits, continuity, and rates of change. Master derivatives, including product and quotient rules, chain rule, and implicit differentiation. Learn integration techniques, from indefinite integrals to integration by parts, and their applications in calculating areas and volumes. Apply calculus concepts to business and economics, covering optimization, consumer and producer surplus, annuities, and money streams. Gain proficiency in multivariable calculus, including partial derivatives and double integrals, to analyze complex business scenarios.

1.1 Introduction to Functions and Relations.
1.2 Algebra and Composition of Functions.
1.3 Slope, Rates of Change, and Linear Functions.
4.1, 4.2 The Exponential and Logarithmic Functions.
1.4 Introduction to Limits.
1.5 Functions and Continuity.
1.6 Average and Instantaneous Rates of Change.
7.1 Functions of Several Variables.
2.1 The Derivative of a Function and Two Interpretations.
2.2 Differentiating Products and Quotients.
2.3 Higher-Ordered Derivatives.
2.4 The Chain Rule and General Power Rule.
4.3, 4.4 Differentiating the Natural Logarithm & Exponential Functions.
2.5 Implicit Differentiation.
7.2 Partial Derivatives.
5.1 Antidifferentiation and the Indefinite Integral.
5.2 Integration by Substitution.
5.3 The Definite Integral.
5.4, 6.1 Area of Regions in the Plane.
5.6 Integration by Parts.
7.6 Double Integrals as Volume.
3.3 Applications of the Derivative Optimization.
3.4 Applications of the Derivative in Business and Economics.
6.2 Consumer's and Producer's Surplus.
6.3 Annuities and Money Streams.
7.7 The Average Value of a Function.