Mathematics Department Indiana University of Pennsylvania Indiana, PA 15705 Course Number: MA 127 Course Title: Calculus I Credits: 4 semester hours Prerequisites: Permission of the mathematics department Textbook: Calculus (6th ed) by Swokowski PWS-Kent Revised: 9/94 Catalog Description:The first in a three-course series of courses which stresses the theory of the calculus as well as the application in problem solving. Topics to be included are: real numbers, an introduction to analytic geometry, functions, limits and continuity, derivatives and applications, the differential and antidifferentiation.
Course Outline/Time Schedule: I. Precalculus Review A. Algebra B. Functions and Their Graphs C. Trigonometry D. Exponentials and Logarithms E. Conic Sections II. Limits of Functions A. Introduction to Limits B. Definition of Limit C. Techniques for Finding Limits D. Limits Involving Infinity E. Continuous Functions III. The Derivative A. Tangent Lines and Rates of Change B. Definition of Derivative C. Techniques of Differentiation D. Derivatives of Trigonometric Functions E. The Chain Rule F. Implicit Differentiation G. Related Rates H. Linear Approximations and Differentials I. Newton's Method IV. Applications of the Derivative A. Extrema of Functions B. The Mean Value Theorem C. The First Derivative Test D. Concavity and the Second Derivative Test E. Summary of Graphical Methods F. Optimization Problems G. Velocity And Acceleration H. Applications to Economics, Social Sciences, and Life Sciences V. Integrals A. Antiderivatives, Indefinite Integrals, and Simple Differential Equations B. Change of Variables in Indefinite Integrals C. Summation Notation and Area D. The Definite Integral E. Properties of the Definite Integral F. The Fundamental Theorem of Calculus G. Numerical Integration References: 1. The Calculus with Analytic Geometry, by Louis Leithold. 2. Calculus with Analytic Geometry, by Robert Ellis and Denny Gulick. 3. Calculus and Analytic Geometry, by Abe Mizrahi and Michael Sullivan. 4. Calculus with Analytic Geometry, by Harley Flanders and Justin Price. 5. Calculus, by M.A. Munem and D.J. Foulis. 6. Theory and Problems of Differential and Integral Calculus (Schaum's Outline Series), by Frank Ayres.
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