Calculus I

Calculus I Course Notes Overview

These notes are provided by Lamar University as a self-contained resource for students learning Calculus I or seeking a refresher on foundational topics.

Important Student Warnings

• Not a substitute for class: These notes do not cover every insight or topic discussed in lectures.
• Content variance: The notes include extra material not always covered in class and may omit specific examples or paths explored during live instruction.
• Collaboration: Students are advised to compare these notes with classmates to capture missed information or unique classroom discussions.

Course Content Sections

• Review (Algebra & Trig):
  • Inverse functions, trigonometric functions, and the unit circle.
  • Solving trigonometric, exponential, and logarithmic equations.
  • Review of common function graphs.
• Limits:
  • Conceptual introduction, one-sided limits, and limit properties.
  • Computing limits (piecewise functions, Squeeze Theorem).
  • Infinite limits and limits at infinity (vertical/horizontal asymptotes).
  • Continuity and the Intermediate Value Theorem.
  • Precise definition of a limit.
• Derivatives:
  • Interpretations: Rate of change, velocity, and slope of tangent lines.
  • Differentiation formulas: Product rule, quotient rule, and chain rule.
  • Derivatives of specific functions: Polynomials, roots, trigonometric, inverse trigonometric, hyperbolic, exponential, and logarithmic functions.
  • Advanced techniques: Implicit differentiation, related rates, higher-order derivatives, and logarithmic differentiation.