Free online courseCalculus 2

Course Description

Calculus 2 is a comprehensive course designed for students who have completed introductory calculus and are ready to delve deeper into the subject. Spanning a total duration of 50 hours and 3 minutes, this course is perfect for those looking to solidify their understanding of advanced calculus concepts or for anyone aspiring to excel in higher-level mathematics.

Rated an impressive 5 stars out of 5, Calculus 2 is highly regarded among students for its clarity, depth, and well-structured content. The course provides a solid foundation in calculus and is part of the Basic Studies category, specifically under the Calculus subcategory. This makes it suitable for a wide range of learners, from undergraduates looking to bolster their math skills to professionals seeking to refresh their knowledge.

The curriculum of this course is meticulously crafted to cover an array of subjects that are crucial for a deep understanding of calculus. It begins with the fundamental properties and usage of the natural logarithm function, extending into the derivatives of inverse functions. This paves the way to an exploration of the derivatives and integrals of exponential functions, both basic and general types.

Students will also encounter the calculus of inverse trigonometric functions, and engage in a rich discussion on hyperbolic functions. Building upon these foundations, the course covers advanced techniques for evaluating the limits of indeterminate forms and explores various integration methods such as integration by parts, trigonometric integrals, trigonometric substitution, and partial fractions.

Further into the course, students will learn about improper integrals and gain hands-on experience in solving first-order differential equations using separation of variables. The journey continues with an in-depth look at the convergence and divergence of sequences and series, including geometric and harmonic series, and various convergence tests such as the integral, comparison, limit comparison, and alternating series tests.

The course also delves into absolute convergence, ratio tests, and root tests for series, and explains the calculus of power series, providing students with the tools to understand and manipulate these series effectively. Additionally, the representation of functions using Taylor and Maclaurin series, as well as the approximation of functions by Taylor polynomials, are thoroughly discussed.

In its final segments, Calculus 2 introduces parametric equations and their calculus, along with a comprehensive study of polar coordinates and equations. The course culminates with numerical integration techniques, specifically the trapezoidal and Simpson's rule, equipping students with practical skills for real-world applications.

Overall, Calculus 2 is an exceptional course that provides a robust education in advanced calculus, all delivered through engaging lectures and practical examples. Students who complete this course will find themselves well-prepared for further studies in mathematics and related fields.