College Credit Calculus

Angel Website:  http://pcps.myelearning.org/frameIndex.htm
Angela Schmit's Website:  http://manila.esu4.org/angelaschmit/

Peru State College
Calculus I
Math 225--Spring 2006

Course Syllabus

Description of Course

Prerequisites

The Objectives of the Course

• To understand the fundamentals of limits, differentiation, and integration and their applications.
• To appreciate the value of calculus.

Texts

Explanation of Instruction

• Lecture and discussion every day.
• Quizzes every two or three lessons.
• Tests after every unit.
• Spelling/Writing assignments as needed.
• Angel Website--On-Line Learning
  

Visual Aids, Utilized Films, Film Strips, Etc.

• Marker board
• Calculators (Texas Instruments--TI 83, TI 85, and TI 92) provided by the school district
• Computer Software/Technology
• Supplementary Workbooks

Units and Contents

Prerequisites:  The Cartesian Plane and Functions

• Real Numbers and the Real Line
• The Cartesian Plane
• Graphs of Equations
• Lines in the Plane
• Functions
• Review of Trigonometric Functions

Chapter 1:  Limits and Their Properties

• An Introduction to Limits
• Properties of Limits
• Techniques for Evaluating Limits
• Continuity and One-sided Limits
• Infinite Limits

Chapter 2:  Differentiation

• The Derivative and the Tangent Line Problem
• Basic Differentiation Rules and Rates of Change
• The Product and Quotient Rules and Higher-Order Derivatives
• The Chain Rule
• Implicit Differentiation
• Related Rates

Chapter 3:  Applications of Derivatives

• Extrema on an Interval
• Rolle's Theorem and the Mean Value Theorem
• Increasing and Decreasing Functions and the First Derivative Test
• Concavity and the Second Derivative Test
• Limits at Infinity
• A Summary of Curve Sketching
• Optimization Problems
• Newton's Method
• Differentials
• Business and Economics Applications

Chapter 4:  Integration

• Antiderivatives and Indefinite Integration
• Area
• Riemann Sums and Definite Integrals
• The Fundamental Theorem of Calculus
• Integration by Substitution
• Numerical Integration

Chapter 5:  Logarithmic, Exponential, and Other Transcendental Functions

• The Natural Logarithmic Function and Differentiation
• The Natural Logarithmic Function and Integration
• Inverse Functions
• Exponential Functions:  Differentiation and Integration
• Bases Other Than e and Applications
• Differential Equations:  Growth and Decay
• Inverse Trigonometric Functions and Differentiation
• Inverse Trigonometric Functions:  Integration and Completing the Square
• Hyperbolic Functions

This Page was last update: Wednesday, May 31, 2006 at 5:33:18 PM
This page was originally posted: 3/22/2004; 1:04:33 PM.
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