Foundations of Differential Calculus: Limits, Continuity, and Derivatives

Understanding the mathematics of change is essential for careers in physics, engineering, data science, and advanced mathematics. This text-based course guides you through the fundamental concepts of differential calculus, breaking down complex theories into intuitive, readable explanations. By working through this structured guide, you will transition from basic algebra to thinking dynamically about rates of change, establishing a powerful mathematical toolkit. You will learn to analyze functions, evaluate limits, and apply derivatives to real-world optimization scenarios. What you'll learn: - Understand the core concepts of limits and how they define mathematical infinity and convergence. - Analyze the continuity of functions and identify different types of mathematical discontinuities. - Calculate derivatives using fundamental rules, including the product, quotient, and chain rules. - Apply differentiation to solve practical optimization and rate-of-change problems. - Explore how calculus concepts underpin modern algorithms and computational modeling. - Practice solving algebraic and trigonometric calculus problems through step-by-step written exercises. The course starts with essential terminology and the geometric intuition of limits before progressing to formal continuity and the mechanics of the derivative. Each section features detailed, written walkthroughs and practice problems to solidify your analytical skills. This course is designed for high school students, aspiring engineering majors, and self-taught learners looking for a clear, rigorous introduction to calculus, with no prior calculus experience required. Start reading today to master the foundational mathematics of change and optimization.