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Calculus: Single Variable

🔢 Calculus: Single Variable

Welcome to the Single Variable Calculus module. This module covers the fundamental concepts of limits, derivatives, integrals, and series, which are essential for understanding more advanced topics in mathematics, physics, and computer science.

📚 Module Overview

  • 01: Limits & Continuity: Understanding behavior at a point and the concept of “nearness.”
  • 02: Derivatives & Rules: Measuring rates of change and optimization.
  • 03: Integrals & Fundamental Theorem: Accumulation of change and the area under a curve.
  • 04: Sequences & Series: Infinite sums and function approximations.

🎯 Learning Objectives

By the end of this module, you should be able to:

  • Compute limits using various techniques.
  • Apply differentiation rules to complex functions.
  • Solve optimization problems using derivatives.
  • Understand the relationship between differentiation and integration through the Fundamental Theorem of Calculus.
  • Test for convergence of infinite series and build Taylor polynomials.