Calculus IV completes the introductory calculus sequence by extending the theory of integration to higher dimensions. The course starts with multiple integrals (double and triple), covering Fubini’s theorem, the change of variables formula (including polar, cylindrical, and spherical coordinates), and applications to volume and mass.
We then transition to vector calculus, introducing line and surface integrals for both scalar functions and vector fields. Key concepts such as work, conservative fields, potential functions, and flux across surfaces are developed in detail to prepare for the fundamental theorems of the subject.
The course culminates with the three major integral theorems: Green’s Theorem, Stokes’ Theorem, and the Divergence (Gauss) Theorem. These results relate integrals over a region to integrals over its boundary, providing a powerful generalization of the Fundamental Theorem of Calculus to multidimensional space.
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.
