PENN STATE UNIVERSITY ABINGTON COLLEGE MATHEMATICS DEPARTMENT MATH 110 Catalog Description:TECHNIQUES OF CALCULUS I (4: 4: 0). Functions, graphs, derivatives, integrals, techniques of differentiation and integration, exponentials, improper integrals, applications. (Students may take only one course for credit from Math 110, 140 and 140A.) Prerequisite:Math 22 or a satisfactory performance on the mathematics algebra proficiency examination. Text: Calculus, 6th ed., S.T. Tan, Brooks/Cole 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 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 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 6.5 Evaluating Definite Integrals 6.6 Area between Two Curves CHAPTER 7 ADDITIONAL TOPICS IN INTEGRATION 7.1 Integration by Parts 7.4 Improper Integrals The Mathematics Department requires that the instructor must adhere to the syllabus. (8/26/04)