MA 121 Syllabus

Mathematics Department
Indiana University of Pennsylvania
Indiana, PA 15705
Course Number: Math 121

Course Title: Calculus I for Business, Natural, and Social Sciences

Credits: 4 semester hours

Prerequisite: MA 105 or MA 110 or equivalent high school preparation

Textbook: Applied Calculus (fourth edition), by Soo Tang Tan,

Brooks/Cole Publishing Company, 1998.

Revised: April 1999

Catalog Description: This course introduces the non-Mathematics major to analytic geometry, elementary functions (including exponential and logarithmic functions), central ideas of the calculus (limit, continuity, derivative, and integral), and applications of derivatives to business, social, and natural sciences.

Course Outline:

  1. Preliminaries
    1. Precalculus Review I
    2. Precalculus Review II
    3. The Cartesian Coordinate System
    4. Straight Lines
  1. Functions, Limits, and the Derivative
    1. Functions and Their Graphs
    2. The Algebra of Functions
    3. Functions and Mathematical Models
    4. Limits
    5. One-Sided Limits and Continuity
    6. The Derivative
  1. Differentiation
    1. Basic Rules of Differentiation
    2. The Product and Quotient Rule
    3. The Chain Rule
    4. Marginal Functions in Economics
    5. Higher-Order Derivatives
    6. Implicit Differentiation and Related Rates
    7. Differentials
  1. Applications of the Derivative
    1. Applications of the First Derivative
    2. Applications of the Second Derivative
    3. Curve Sketching
    4. Optimization I
    5. Optimization II
  1. Exponential and Logarithmic Functions
    1. Exponential Functions
    2. Logarithmic Functions
    3. Compound Interest
    4. Differentiation of Exponential Functions
    5. Differentiation of Logarithmic Functions
    6. Exponential Functions As Mathematical Models
  1. Integration
    1. Antiderivatives and the Rules of Integration
    2. Integration by Substitution
    3. Area and the Definite Integral
    4. The Fundamental Theorem of Calculus
    5. Evaluating Definite Integrals
    6. Area Between Two Curves
    7. Applications of the Definite Integral to Business and Economics
    8. Volumes of Solids of Revolution

 

  1. Chapter 1 is intended as a short review of precalculus. (3-4 hours)
  2. Chapter 2 reviews the graphing and algebra of functions, introduces the concepts of limit and continuity, and culminates in the definition of the derivative including motivation and interpretations. (6-9 hours)
  3. Chapter 3 develops the rules of differentiation enabling students to more easily study how fast one quantity is changing with respect to another in many real-world situations. Approximation using differentials and the study of relative error is included. (7-10 hours)
  4. Chapter 4 is organized so that the graphical applications of the first and second derivatives lead smoothly to curve sketching. Then the finding of absolute extrema is covered by two sections - one where the objective function is given and one where it is not given. (5-8 hours)
  5. Chapter 5 introduces exponential and logarithmic functions and proceeds to their differential calculus. (6-8 hours)
  6. Chapter 6 introduces integration and includes applications to solving differential equations, area and volume problems, and business and economic problems. (8-11 hours)
  7. This syllabus covers up to 50 hours of class time. This leaves sufficiently many hours for extra depth, optional topics, and testing.
  8. If you wish to use a graphing calculator in this course, you must notify the chair of the Service Courses Committee one semester in advance so that a note to this effect can be included on the Course Schedule. Optional "Exploring with Technology Questions" appear throughout the main body of the text and serve to enhance the student’s understanding of the concepts and theory presented. Optional "Using Technology Subsections" appear at the end of the section for which their use is appropriate and provide students with an opportunity to interpret results in a real-life setting.