Free online courseCalculus

Course Description

The course "Calculus" is a comprehensive and well-structured program designed to introduce learners to the fundamental concepts of calculus. With a duration of 34 hours, this course empowers students to build a solid foundation in calculus, enhancing their mathematical proficiency through an array of engaging lessons and examples.

Designed for beginners, this course falls under the "Basic studies" category and is specifically tailored to those interested in the subcategory of Calculus. The course content unfolds with an intriguing combination of theoretical explanations and practical applications, making complex topics accessible and comprehensible.

The journey into calculus begins with the historical context and significance of calculus with "Newton, Leibniz, and Usain Bolt," setting the stage for an immersive exploration into the subject. Students are then introduced to the concept of derivatives through a series of lessons that elucidate the nature and applications of slopes and tangent lines.

As learners progress, they encounter the intriguing topic of limits, beginning with an introduction and advancing through multiple examples. Here, the squeeze theorem and epsilon-delta definitions are unveiled, providing a rigorous understanding of limits and their practical implications.

The course proceeds to deepen the understanding of derivatives, covering fundamental rules like the power rule, chain rule, product rule, and quotient rule. The intricacies of differentiation are enhanced through proofs and intuitive problem-solving sessions, allowing students to appreciate the elegance of calculus.

Applications of derivatives are explored in varied contexts such as optimization, rate-of-change problems, and graphing functions. The course also delves into advanced techniques like L'Hôpital's rule and implicit differentiation, showcasing their power in solving complex problems.

Integral calculus is introduced next, where students learn both indefinite and definite integrals. The process is thoroughly explained with numerous examples, including the use of substitution and integration by parts. Practical applications, such as finding the area under curves and solving differential equations, highlight the relevance of integrals in real-world problems.

The final segments focus on multivariable calculus, introducing concepts such as partial derivatives, gradient, divergence, curl, and multiple integrals. These lessons expand the understanding of calculus to functions of several variables, integrating them with vector fields and surface integrals.

Additionally, the course includes a series of AP Calculus AB and BC exam reviews, providing invaluable practice for students preparing for these standardized tests. The comprehensive coverage ensures that learners are well-prepared for academic success in advanced calculus.

Overall, "Calculus" is a meticulously crafted course that empowers students with the essential tools and insights needed to master the complex world of calculus. With clear explanations, a variety of examples, and practical applications, this course ensures a thorough and engaging learning experience. While no reviews are available yet, the depth and breadth of the content promise a rewarding journey into the realm of calculus.