Foundations of Differential Calculus: Functions, Limits, and Derivatives

Calculus is the language of change, but mastering its fundamental concepts like limits and functions can be challenging without a clear, systematic guide. This course provides a rigorous, text-based foundation in differential calculus, ensuring you move from basic algebraic concepts to confidently calculating limits and determining continuity and differentiability for complex expressions. What you'll learn: * Understand domain, range, types of functions (inverse, composite), and their graphical representations using formal notation. * Calculate limits using algebraic manipulation, key trigonometric limits, and systematic methods for handling indeterminate forms. * Apply the formal definition of continuity and classify various types of discontinuities across different function types. * Master the definition of the derivative and relate differentiability to continuity and the geometric concept of slope. * Practice solving complex problems involving piecewise functions and advanced limit theorems using structured, written methods. The course begins with foundational concepts, including sets and relations, before systematically exploring the definitions and theorems governing limits, continuity, and differentiability. Practical exercises emphasize applying these formal definitions to solve typical STEM problems. This course is designed for absolute beginners in calculus, high school students, or university students needing a solid conceptual refresher. No prior calculus knowledge is required. Start building your mathematical foundation today and unlock the power of differential calculus.