Foundational Calculus: Understanding Derivatives and Integrals

Many technical and scientific fields require a solid understanding of fundamental mathematical concepts. Calculus is the essential language for modeling change, motion, and accumulation in the real world. This course introduces you to the core principles of calculus, focusing on single-variable differentiation and integration. You will move from abstract mathematical concepts to practical methods for solving optimization problems and analyzing accumulated quantities. ### What you'll learn * Understand the concept of limits and continuity as the basis for all calculus operations. * Master the rules of differentiation (power, product, quotient, chain rules) for finding instantaneous rates of change. * Apply derivatives to solve practical optimization problems and sketch the behavior of functions. * Learn the Fundamental Theorem of Calculus, linking differentiation and integration. * Practice basic techniques of integration (indefinite and definite integrals) to calculate areas and total accumulation. * Analyze how derivatives are used in foundational algorithms, such as gradient descent, for data modeling. The material begins with foundational definitions and notation, progressing through step-by-step written explanations of differentiation techniques, followed by the introduction of integration and its applications. Practice exercises reinforce each concept. This course is designed for absolute beginners who need a strong mathematical foundation for future studies in engineering, physics, economics, or data science. No prior calculus experience is required. Start building your essential mathematical toolkit today.