MAT 234: Calculus I

Eastern Kentucky University

Course Description

MAT 234 is the first course in the calculus sequence at Eastern Kentucky University. This course is designed to provide students with a fundamental understanding of differential calculus and its applications. It serves as a foundation for subsequent mathematics courses and is essential for students pursuing degrees in mathematics, science, engineering, economics, and various other fields that require quantitative reasoning.

Students will explore the concept of limits, derivatives, and their applications. The course emphasizes conceptual understanding, computational techniques, and real-world applications of calculus.

Prerequisites

Prior to enrolling in MAT 234, students should have completed:

• MAT 112 (Precalculus Mathematics) or equivalent with a minimum grade of C-, or
• A satisfactory score on the mathematics placement examination
• Strong background in algebra and trigonometry

Course Objectives

Upon successful completion of MAT 234, students will be able to:

• Understand and evaluate limits, including one-sided limits and limits at infinity
• Define and calculate derivatives using various techniques including the definition, basic rules, product and quotient rules, and chain rule
• Apply derivatives to solve related rates problems and optimization problems
• Use derivatives to analyze functions, determine extrema, and sketch curves
• Understand the concept of continuity and its relation to limits and derivatives
• Apply L'Hpital's rule for evaluating indeterminate forms
• Solve applied problems involving derivatives in areas such as physics, engineering, and economics

Course Content

The following topics are covered in MAT 234:

• Limits and Continuity:
  • Limits (intuitive approach, rigorous definition)
  • One-sided and two-sided limits
  • Limits at infinity
  • Continuity and intermediate value theorem
• Derivatives:
  • Definition of derivative as a limit
  • Geometric interpretation
  • Differentiation rules (power rule, constant multiple rule, sum/difference rule)
  • Product rule and quotient rule
  • Chain rule and implicit differentiation
  • Derivatives of trigonometric, exponential, and logarithmic functions
  • Higher-order derivatives
• Applications of Derivatives:
  • Rates of change and related rates
  • Extrema of functions (maximum and minimum values)
  • Mean Value Theorem
  • First and second derivative tests
  • Curve sketching using derivative analysis
  • Optimization problems
  • L'Hpital's rule
  • Indeterminate forms
  • Newton's method (if time permits)