Calculus Foundations: Limits, Continuity, and Differentiability

Calculus forms the backbone of advanced mathematics and engineering, yet mastering its foundational concepts can often feel daunting. This written course simplifies complex mathematical behaviors by breaking down functions, limits, and continuity into logical, step-by-step explanations. You will transition from memorizing formulas to deeply understanding how functions behave, establishing a rock-solid mathematical foundation. What you'll learn: - Understand the fundamental concepts of limits, including one-sided limits and indeterminate forms. - Analyze the continuity of algebraic, exponential, logarithmic, and trigonometric functions. - Evaluate special functions such as modulus, greatest integer, signum, and fractional part functions. - Apply differentiability tests to determine where a function can be differentiated. - Explore graphical behaviors of complex functions through detailed written descriptions and analytical methods. - Solve structured calculus problems designed to build confidence for rigorous exams. The course begins with essential terminology and foundational definitions of functions before moving systematically through limits, continuity, differentiability, and practical mathematical applications. Designed for beginners in calculus, high school students preparing for competitive exams, and college students seeking a clear refresher, this course requires no prior calculus experience. Start reading today to build a precise, analytical understanding of calculus.