Welcome to this repository, a comprehensive study guide designed to help you ace Calculus III at the University of São Paulo's School of Engineering! As a fellow Electrical Engineering student who not only survived but thrived in this course, I've compiled the resources and strategies that proved most effective for me
Calculus III is a fundamental course in the Electrical Engineering curriculum at USP. It extends the concepts of single-variable calculus to functions of multiple variables, vector calculus, and multivariable integration. Mastering this subject is crucial for understanding advanced topics in electromagnetism, signal processing, and other core areas of our field.
Here's a curated list of videos and websites that I found particularly helpful for understanding the concepts of Calculus III:
| Website | Preview |
|---|---|
| Paul's Online Notes |  |
| Math Insight |  |
| Video/Playlist Tittle | Preview |
|---|---|
| Double Integrals |  |
| What are double integrals? What are they for? |  |
| Introduction to Iterated Integrals |  |
| a double integral, 3 ways |  |
| Polar Coordinates |  |
| Video/Playlist Tittle | Preview |
|---|---|
| CALCULUS 3 CH 5 TRIPLE INTEGRALS |  |
| Video/Playlist Tittle | Preview |
|---|---|
| Integrais de Linha sobre Curvas |  |
| Line Integrals Practice Problems |  |
| Line Integral Example |  |
| Video/Playlist Tittle | Preview |
|---|---|
| Campos Vetoriais |  |
| Integrais de linha de Campos Vetoriais |  |
| Line Integrals of Vector Fields Practice Problems |  |
| Line integral of a vector field |  |
| Video/Playlist Tittle | Preview |
|---|---|
| Campos Conservativos - Parte 1 |  |
| Campos Conservativos - Parte 2 |  |
| Campos Conservativos - Parte 3 |  |
| Campos Conservativos - Parte 4 |  |
| Conservative Vector Fields Practice Problems |  |
| Video/Playlist Tittle | Preview |
|---|---|
| CALCULUS 3 CH 7 GREEN'S THEOREM |  |
| Green's Theorem Examples |  |
| Green's Theorem Example - Vector Calculus |  |
| Video/Playlist Tittle | Preview |
|---|---|
| Divergente e Rotacional |  |
| Divergence and curl: The language of Maxwell's equations, fluid flow, and more |  |
The video lectures listed here introduce several key concepts, such as flux, Gauss's Theorem, and others.
The content was pretty tough, and I had to watch many videos to get a good grasp on it.
If you're still struggling (which I doubt after all those theory videos and exercises), here are some more videos and playlists you can check out. I'd recommend going through the content list first, but feel free to skip ahead if you're feeling confident.
This folder contains exercise lists for Calculus III, including those from USP and other sources.
- USP: Exercise lists provided by the University of São Paulo.
- Other Universities: Subfolders for exercise lists from other universities (contributions are welcome!).
This folder contains past Calculus III exams, primarily from USP.
- USP: Past exams from the University of São Paulo.
- Other Universities: Subfolders for past exams from other universities (contributions are welcome!).
This folder contains additional resources that may be helpful for understanding the material, such as PDFs, links, and other study aids.
- Start Early: Don't wait until the last minute to start studying. Calculus III requires consistent effort throughout the semester.
- Active Learning: Engage actively with the material. Don't just passively read the textbook or notes. Try to solve exercises on your own, and don't be afraid to ask for help when you need it.
- Practice, Practice, Practice: The more you practice solving problems, the better you'll become at it. Use the exercise lists and past exams to your advantage.
- Form Study Groups: Studying with friends can be a great way to learn from each other and stay motivated.
- Don't Give Up: Calculus III can be challenging, but don't get discouraged. With hard work and perseverance, you can succeed!
This repository was initially created after I completed Calculus III, as a way to share my study materials with a friend. Today, its growth and improvement depend on contributions from other students like you! Feel free to add subfolders to the "Exercise Lists" and "Exams" directories with materials from your institution. Any contribution is welcome, whether it's past exams, exercise lists, or other helpful resources. Please ensure that any materials you contribute are properly attributed and do not infringe on any copyright laws.
I'd like to thank my professors, classmates, and anyone else who contributed to my understanding of Calculus III.
If you have any questions, suggestions, or feedback, please feel free to reach out to me.
Remember: This guide is a collaborative effort, and your contributions are essential to make it even better!
