MATH 151 - Calculus for Management

Department Syllabus

Description

Elementary calculus and its applications in business, economics, life and social sciences. Functions, limits and continuity. The derivative, applications in marginal analysis, optimization, differentials and error estimation. Antiderivatives, area under a curve and definite integrals. Exponential and logarithm functions; applications to growth and decay problems. Improper integrals. No credit toward a major or minor in mathematics. (4 credits)

For Legacy General Education, this course may be taken for general education credit (D for all majors, G2 for non-math and non-science majors), and satisfies the Foundations for Lifelong Learning Mathematics Requirement.

For Gateway General Education, this course may be taken for Cornerstone-Quantitative Literacy (QL) credit.

Credit will not be granted for more than one course from MATH 151, 161 or 163H. These courses are considered equivalent and will be processed as repeat credit.

Prerequisites

C- or better in MATH 101 or math placement testing/evaluation before registration.

Course Objectives

Students will become proficient in applying the techniques of calculus to problem solving situations.  By the conclusion of this course the successful student will be able to:

  • evaluate limits algebraically, graphically and numerically,
  • solve problems involving the derivative, its definition, its relationship to limits, and its application to finding slopes of curves and rates of change, requiring the explanation of information presented in mathematical forms, and express quantitative evidence in support of the mathematical/statistical argument or purpose of the work (in terms of what evidence is used and how it is formatted, presented, and contextualized),
  • solve problems involving the fundamental formulas and techniques of differential calculus, such as optimization problems that require the student to convert relevant information into various mathematical forms, and to make judgments and draw appropriate conclusions based on the quantitative analysis of data and/or mathematical models of phenomena or processes, while recognizing the limits of this analysis,
  • solve problems involving the indefinite integral including problems requiring u-substitution,
  • solve problems involving the definite integral, its relationship to limits, and its application to finding areas,
  • solve problems involving differentiating and integrating functions including polynomial, rational, exponential and logarithmic functions, requiring the explanation of information presented in mathematical forms
  • solve problems involving the development of applications of the theoretical underpinnings of calculus, to make and evaluate important assumptions in estimation, modeling, and data analysis, and to express quantitative evidence in support of the mathematical/statistical argument or purpose of the work (in terms of what evidence is used and how it is formatted, presented, and contextualized),
  • demonstrate understanding the notions of limits and continuity, some of the key formulas of calculus, and of some major theorems of calculus.

Assessment

Assessment of student achievement of the course objectives will vary from one instructor to another.  Typical assessment will be made through work in class, homework, and examinations.

Use of Technology

Students are required to have access to a graphing calculator, preferably one supported by the department (the TI 83/83+, 84, or 86).

Topics

  • Review of foundational topics
  • Real numbers
  • Equations of lines
  • Nonlinear inequalities
  • Functions
    • Linear, Quadratic, Polynomials, Rational
  • Limits and Continuity
  • Concept of Limit
  • Definition of Limit
  • Evaluating limits, algebraically, graphically and numerically
  • Continuity
  • Rates of Change and Derivatives
  • Definition of the derivative
  • Rules of Differentiation: power rule/product rule/quotient rule
  • Higher Order Derivatives
  • Non-differentiable functions
  • Related Rates
  • Applications of Derivatives
  • Graphing
  • Optimization
  • Marginal analysis and differentials
  • Business and economics applications
  • Exponential and Logarithmic Functions
  • Definitions/Derivatives
  • Exponential growth and decay
  • Applications
  • Integration
  • Antiderivatives and indefinite integrals
    • General power rule
    • u-substitution
  • Definite Integrals
  • Fundamental theorem of calculus
  • Area

Applications

Recently Used Textbooks

Brief Calculus, An Applied Approach, Tenth Edition by Larson,  Cengage Learning, 2017