Calculus II builds upon the foundations laid in the first course to develop the theory of integration. The course begins with the rigorous construction of the definite integral via Riemann sums and the Fundamental Theorem of Calculus, establishing the deep connection between differentiation and integration.
A key feature of this course is the formal definition of transcendental functions (logarithmic, exponential, and trigonometric) through integration. We also cover essential methods of integration and apply these tools to solve geometric and physical problems, such as computing areas of planar regions, volumes of solids of revolution, arc lengths, and work.
The final part of the course introduces the study of infinite sequences and series. We examine convergence criteria, power series, and Taylor polynomials, concluding with an introduction to Fourier series as a powerful tool for function approximation.
This document compiles selected notes and examples developed during the course. While not intended as a comprehensive textbook, these materials provide detailed explanations of key topics and are designed to serve as a robust supplementary resource for students.
As with the notes, this section contains a compilation of various homework assignments and problem sets. Although they do not follow a unified structure, they may serve as valuable practice material for anyone who wishes to reinforce their understanding of the topics covered in the course.
