Calculus Unveiled: Mastering Integration, Differential Equations, and Infinite Series.: A Comprehensive Exploration

This course provides a thorough journey into advanced calculus's core concepts and techniques, building upon foundational knowledge of differentiation and basic integration. We expand our integration toolkit with powerful methods such as integration by parts, trigonometric integrals, and trigonometric substitution, enabling us to tackle a wider range of integrals. The course then delves into the applications of integration, exploring how definite integrals can be used to calculate areas between curves and volumes of solids of revolution using the disk, washer, and cylindrical shell methods.
A significant portion of the course is dedicated to differential equations, introducing their fundamental definitions, classifications, and solution techniques for first-order separable and linear equations. Finally, we venture into the realm of infinite sequences and series, establishing concepts of convergence and divergence, exploring key convergence tests, and culminating in the study of power series and their remarkable ability to represent functions. This comprehensive exploration equips learners with essential analytical skills and a deep understanding of these critical areas of calculus.