Free online courseCalculus 1

Course Description

Are you ready to dive deep into the fascinating world of calculus? "Calculus 1" offers a comprehensive introduction to calculus over an engaging 44 hours and 56 minutes of instruction. Highly rated with an average score of 5 out of 5, this course is perfect for those embarking on their basic studies journey, particularly in the subcategory of calculus.

The course starts by laying a strong foundation, exploring fundamental concepts related to lines, angles of inclination, and the distance formula. It then proceeds to the essential topic of functions and provides a thorough review of trigonometry, ensuring that students are well-prepared for the more advanced subjects that follow.

Students will encounter a variety of intriguing topics as they navigate through the curriculum. Combining and composing functions, understanding limits, and grasping the crucial concept of continuity form the building blocks for more complex ideas. The course delves deeply into the principles of differentiation, from basic techniques to the application of product and quotient rules, ensuring that learners can find derivatives with ease.

Further exploration into the world of derivatives involves practical applications. Students will understand how to use derivatives to analyze the behavior of functions, including discussions on related rates and implicit differentiation. By examining increasing and decreasing functions, concavity, and essential theorems like Rolle's Theorem and the Mean-Value Theorem, students gain a robust understanding of these fundamental concepts.

To make the learning process even more engaging, the course dives into graphing functions, finding optimization solutions, and addressing limits of functions at infinity. Each concept is intricately connected, providing students with a holistic view of calculus.

The course doesn't stop at differentiation; it also offers a detailed introduction to integral calculus. Starting with indefinite integrals and advancing through techniques like integration by substitution, students are guided step-by-step through the intricacies of finding areas under curves using Riemann Sums and evaluating definite integrals.

The program culminates with a comprehensive exploration of the fundamental theorem of calculus, bridging the gap between differentiation and integration. Practical applications extend to finding areas between curves and calculating volumes of solids using various methods, including disks, washers, and cylindrical shells. Finally, students learn how to find the length of a curve on a plane, rounding out their understanding.

With a detailed curriculum designed to take learners from foundational principles to advanced applications, "Calculus 1" is an exceptional choice for anyone seeking to master the fundamentals of calculus. Whether preparing for advanced studies or looking to strengthen mathematical skills, this course ensures a well-rounded, in-depth understanding of calculus.