Integrals of Multivariable Functions | FOSSEE
Before joining M.Sc., I worked as a FOSSEE summer fellow for two months under IIT Bombay. During this period I worked on creating illustrative notes to aid students with Integrals of Multivariable Functions.
Location: Indian Institute of Technology Bombay, India
Multivariable calculus is the calculus of more than one variable as the name indicates. For most of the real-life application functions of several variables are dealt more frequently than the functions of a single variable. Integration and differentiation are the two important operations of Calculus. In this project I dealt mostly with the Integration part. Multiple integral and line integral are the topics under integrals of multivariable functions. Double and triple integrals may be used to calculate areas and volumes of regions in the plane and in space. For evaluating multiple integrals as repeated single integrals we need Fubini’s Theorem. Line integral is used to integrate along a curve in a field, and to calculate the length of a wire curved in space or work done along a path in a field. Two types of functions are are discussed here - scalar functions and vector functions. Vector functions are used to describe physical fields as vector fields
- Created lucid notes on Integrals of Multivariable Functions.
- Illustrations with animations generated with python MANIM library.
- Work report is available at https://fossee.in/fellowship/2020.
- Codes used to generate animation available at FOSSEE_github
Topics
- Double Integrals
- Fubini’s Theorem
- Line Integrals
- The Fundamental Theorem of Line Integrals
- Vector Fields
Tools used
- Python
- Manim
- Git
