Free online courseCalculus 1

Course Description

Welcome to "Calculus 1," a comprehensive online course designed to introduce you to the fundamental concepts of calculus. With a total duration of 7 hours and 37 minutes, this course forms an essential part of the Basic Studies category and specifically focuses on the subcategory of Calculus. Although it has no reviews yet, its structured approach makes it ideal for those new to calculus.

Calculus 1 begins with the intriguing subject of the velocity problem, exploring it both numerically and graphically. This foundational topic is pivotal in understanding how calculus can be applied to real-world scenarios. From here, the course transitions into the concept of limits—a cornerstone of calculus. Through a series of lessons, you will explore limits through various lenses, including infinite limits, limit laws, and the limits of oscillating functions, paired with practical examples to solidify your understanding.

Once acquainted with the basic principles of limits, the course delves into the continuity of functions and notable theorems such as the Intermediate Value Theorem. The course offers clear explanations and practical examples, such as piecewise functions, to help you grasp when and how functions are continuous. The journey through limits continues with lessons on computing limits at infinity and distinguishing between infinite limits and limits at infinity of composite functions.

As the course progresses, you'll encounter the definition of the derivative, another fundamental concept in calculus. The course takes you through the process step-by-step, applying the definition to various functions, including rational functions, polynomial functions, and trigonometric functions. You'll also learn valuable derivative rules, such as the power rule, product rule, and chain rule, which are instrumental in solving advanced calculus problems.

The application of these derivative rules is further explored through the derivation of inverse trigonometric functions and logarithmic differentiation. Topics such as implicit differentiation and related rates are also covered, along with practical examples designed to make these complex concepts more intuitive. You’ll gain insights into linear approximations, the Mean Value Theorem, and techniques for finding relative and absolute maximums and minimums.

In addition to foundational topics, Calculus 1 introduces you to optimization problems, L'Hopital's Rule, and exponential indeterminate forms. These lessons are punctuated with engaging example problems, such as optimizing the volume of a box and folding wires into shapes to maximize or minimize dimensions.

No calculus course would be complete without a look at anti-derivatives and integrals. You will learn to solve for the constant in general anti-derivatives and understand the definite integral through various methods, including summation notation, the Fundamental Theorem of Calculus, and substitution methods. The course ensures you are well-prepared with practical exercises and tips on topics ranging from simple substitution to complex back substitution.

The course concludes with a variety of exams and walkthroughs to test your knowledge. Finally, the course shares some final thoughts and tips for success in flipped classrooms, highlighting the importance and wide applications of calculus in various fields. Whether you are a first-time learner or looking to refresh your skills, "Calculus 1" offers a thorough and engaging learning experience.