Foundational Calculus: Limits, Derivatives, and Integration

Calculus is the essential mathematical framework for understanding change, motion, and accumulation across engineering, physics, and advanced data analysis. Start building the powerful mathematical tools necessary to model complex real-world dynamics. By the end of this course, you will have a robust understanding of limits, continuity, differentiation, and integration. You will be able to apply these techniques to solve practical problems involving optimization, curve sketching, and calculating volumes or areas. What you'll learn: * Understand the rigorous definition of limits and continuity for single-variable functions. * Master differentiation techniques, including the chain rule and implicit differentiation, to find instantaneous rates of change. * Apply derivatives to practical problems like optimization, related rates, and sketching curve behavior. * Learn the Fundamental Theorem of Calculus, linking differentiation and integration. * Practice essential integration methods, including substitution and integration by parts, for finding areas and volumes. * Configure and solve basic differential equations using separation of variables. The course begins with foundational concepts of limits and functions before moving systematically through differential calculus and its applications. The final sections focus on mastering definite and indefinite integration techniques and their real-world uses. This course is designed for absolute beginners with basic algebra skills who require a comprehensive introduction to calculus. No prior experience with advanced mathematics is necessary. Start developing the mathematical expertise required for advanced technical study today.