4 credits
Blue Book Description: Business Calculus is a critical component in the education of any business, financial, or economics professional who uses quantitative analysis. This course introduces and develops the mathematical skills required for analyzing change, and the underlying mathematical behaviors that model real-life economics and financial applications. The primary goal of our business calculus courses is to develop the students’ knowledge of calculus techniques, and to use a calculus framework to develop critical thinking and problem solving skills. The concept of a limit of a function/model is central to differential calculus; MATH 110 begins with a study of this concept, its geometric and analytical interpretation, and its use in the definition of the derivative. Differential calculus topics include: derivatives and their applications to rates of change, related rates, optimization, and graphing techniques. Target applications focus mainly on business applications, e.g. supply/demand models, elasticity, logistical growth, and marginal analysis within Cost, Revenue, and Profit models. Integral Calculus begins with the Fundamental Theorem of Calculus, integrating the fields of differential and integral calculus. Antidifferentiation techniques are used in applications focused on finding areas enclosed by functions, consumer and producer surplus, present and future values of income streams, annuities, and perpetuities, and the resolution of initial value problems within a business context. Students may only take one course for credit from MATH 110, 140, 140A, 140B, and 140H.
Pre-requisites: MATH 22 or MATH 40 or MATH 41 or satisfactory performance on the mathematics placement examination.
Pre-requisite for: Math 111, Math 220
Bachelor of Arts: Quantification
General Education: Quantification (GQ)
GenEd Learning Objective: Crit and Analytical Think
GenEd Learning Objective: Key Literacies
Suggested Textbook:
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach 10th Edition, by Soo T. Tan published by Cengage.
Check with your instructor to make sure this is the textbook used for your section.
Topics:
Chapter 1 Preliminaries
1.1 Precalculus Review I
1.2 Precalculus Review II
1.3 The Cartesian Coordinate System
1.4 Straight Lines
Chapter 2 Functions, Limits, and the Derivative
2.1 Functions and Their Graphs
2.2 The Algebra of Functions
2.3 Functions and Mathematical Models
2.4 Limits
2.5 One-Sided Limits and Continuity
2.6 The Derivative
Chapter 3 Differentiation
3.1 Basic Rules of Differentiation
3.2 The Product and Quotient Rules
3.3 The Chain Rule
3.4 Marginal Functions in Economics
3.5 Higher-Order Derivatives
3.6 Implicit Differentiation and Related Rates
3.7 Differentials
Chapter 4 Applications of the Derivative
4.1 Applications of the First Derivative
4.2 Applications of the Second Derivative
4.3 Curve Sketching
4.4 Optimization I
4.5 Optimization II
Chapter 5 Exponential and Logarithmic Functions
5.1 Exponential Functions
5.2 Logarithmic Functions
5.3 Compound Interest
5.4 Differentiation of Exponential Functions
5.5 Differentiation of Logarithmic Functions
5.6 Exponential Functions as Mathematical Models
Chapter 6 Integration
6.1 Antiderivatives and the Rules of Integration
6.2 Integration by Substitution
6.3 Area and the Definite Integral
6.4 The Fundamental Theorem of Calculus
6.4 Evaluating Definite Integrals
6.5 Area Between Two Curves
6.6 Applications of the Definite Integral to Business and Economics
Chapter 7 Additional Topics in Integration
7.1 Integration by Parts