Free online courseCalculus 1 lectures

Course Description

The "Calculus 1 Lectures" is an extensive online course that delves into the foundational aspects of calculus, perfect for anyone embarking on their journey in this critical field of mathematics. With a duration of 22 hours and 27 minutes, this course provides a comprehensive overview of Calculus 1, tailored for students in the Basic Studies category and specifically categorized under Calculus.

Throughout the course, you will explore various crucial concepts, beginning with the intuitive idea of finding limits. The lectures cover how to find limits graphically and numerically, setting the stage for understanding more complex topics later on. The subsequent lectures delve deeper into Continuity and One-Sided Limits, presenting the foundational blocks necessary for mastering calculus.

Infinite Limits are tackled with a thorough and engaging approach, followed by an introduction to The Derivative and the Tangent Line Problem. These concepts are pivotal as they serve as the gateway to understanding how to differentiate functions. The course continues with comprehensive sessions on Differentiation, Rates of Change, and the crucial Product, Quotient, and Chain Rules which are essential tools in any calculus toolkit.

Implicit Differentiation and Related Rates are presented in a clear and concise manner, emphasizing real-world applications and problem-solving techniques. Further into the course, you will delve into Extrema on an Interval, and explore significant theorems such as Rolle's Theorem and the Mean Value Theorem, which are essential in understanding the behavior of functions.

The lectures on Increasing and Decreasing Functions and the First Derivative Test, along with Concavity and The Second Derivative Test, provide a robust framework for analyzing and interpreting function graphs. These skills are essential for anyone looking to master Calculus. A succinct review lecture helps reinforce these concepts, preparing you for forthcoming topics.

Limits at Infinity are skillfully explained, followed by a lecture that summarizes Curve Sketching, providing a practical and visual approach to understanding calculus. Optimization Problems and Newton's Method are also covered, ensuring you are well-equipped to tackle a variety of calculus challenges.

The course takes a deeper dive into exponential and logarithmic functions, presenting differentiation and integration of The Natural Logarithmic Function, and Exponential Functions with clarity and precision. Growth and Decay via Separable Differential Equations offer a peek into applications commonly encountered in various scientific fields.

Towards the end of the course, comprehensive exam reviews prepare you for assessments, ensuring you're well-versed in all the topics covered. This course is meticulously structured to provide a thorough understanding of Calculus 1, making it an invaluable resource for beginners.

Although no reviews are available yet, the detailed structure and breadth of topics ensure that you are receiving high-quality, in-depth education delivered by a reputed figure in the field of mathematics education.