MA 122 Syllabus

Mathematics Department
Indiana University of Pennsylvania
Indiana, PA 15705

Course Number: Math 122

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

Credits: 4 semester hours

Prerequisite: MA 121

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

Brooks/Cole Publishing Company, 1998.

Revised: April 1999

Catalog Description: This second course in a two-course sequence for non-Mathematics majors covers applications of integrals to business, social, and natural sciences, functions of several variables, trigonometric functions, sequences and series, numerical methods, and differential equations.

Course Outline:

Note: It is expected that 3-4 hours will be spent reviewing integration techniques and applications in chapter 6 before proceeding to chapter 7.

  1. Additional Topics in Integration
    1. Integration by Parts
    2. Integration Using Tables of Integrals
    3. Numerical Integration
    4. Improper Integrals
  1. Calculus of Several Variables
    1. Functions of Several Variables
    2. Partial Derivatives
    3. Maxima and Minima of Functions of Several Variables
    4. The Method of Least Squares
    5. Constrained Maxima and Minima and the Method of Lagrange Multipliers
    6. Total Differentials
    7. Double Integrals
    8. Applications of Double Integrals
  1. Differential Equations
    1. Differential Equations
    2. Separation of Variables
    3. Applications of Separable Differential Equations
    4. Approximate Solutions of Differential Equations
  1. Probability and Calculus
    1. Probability Distributions of Random Variables
    2. Expected Value and Standard Deviation
    3. Normal Distributions
  1. Taylor Polynomials and Infinite Sequences
    1. Taylor Polynomials
    2. Infinite Sequences
    3. Infinite Series
    4. Power Series and Taylor Series
    5. More on Taylor Series
    6. The Newton-Raphson Method
  1. Trigonometric Functions
    1. Measurement of Angles
    2. The Trigonometric Functions
    3. Differentiation of Trigonometric Functions
    4. Integration of Trigonometric Functions

 

Notes:

  1. Chapter 7 introduces advanced techniques for doing integration and numerical integration to approximate (difficult) integrals. (4-7 hours)
  2. Chapter 8 generalizes the concept of a one-variable function to a multi-variable function, outlines the calculus of such functions, and inserts many classical applications. (8-12 hours)
  3. Chapter 9 exposes the student to the basic techniques and applications of introductory differential equations in only four sections. (4-6 hours)
  4. Chapter 10 examines the role of calculus in the study of probability. (3-5 hours)
  5. Chapter 11 is a condensed overview of sequences and series with particular attention paid to Taylor polynomials and Taylor series. (6-9 hours)
  6. Chapter 12 extends the study of calculus to the trigonometric functions. (4-6 hours)
  7. This syllabus covers up to 45 hours of class time. This leaves sufficiently many hours for 3-4 hours of reviewing the basic integration techniques and applications in chapter 6, extra depth in certain sections, 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.