My Strategy for Learning Calc 3/ A Guide to Self-Learning Calculus 3 [calculus 3 problem set 📘]

I got a few comments a while ago asking me to go through my strategy for learning calc 3. With the move and trying to figure out how to film in the new apartment I thought it would be a great time to present my guide to self-learning calculus 3 that I used way back right before I started undergrad in order to get out of taking calculus 3 in college.

The video can be broken up into the following sections:

00:00 Intro
00:50 Where is the Outline and the Problem Set?
01:43 What research should I do before getting started?
03:34 What concepts are in Calc III?
04:29 Importance of Problems for Learning Calculus 3
10:26 Structuring your time while Self-Learning Calc 3
12:37 You wrote yourself a calc 3 exam?!?!
13:19 Outro, Bloopers, End Screen

Here is the my outline/ guide for self-learning calc 3 I found in my old calc 3 self-learning materials. It also contains the calculus 3 problem set 📘that I used while self-learning.
===========================
Summary of Topics: Calculus III
Book: Calculus Early Transcendentals Second Edition by Jon Rogawski
1. Quadratic Surfaces
1. Just a summary for identification in later problems
2. Hyperbolic Functions!
1. Derivatives and Integrals of and derivation (without the book)
2. Derivatives of arc-hyperbolic functions and derivation (without the book)
3. Spherical Parameters
1. Sphere parameterization: Khan Academy and Book Derivations
2. Parameterization of a Torus Derivation (without book)
4. Vectors in 3 dimensions Review
1. Line Parameterizations (12.2 #29-42 )
2. Tangent Planes, Linear Approximations (without book)
5. Curvature
1. Formula Derivation for Parameterized Curves
1. Formula for the Curvature of a Circle Derivation
2. Problems (13.4 #1-27 odd, The answer given in the book for 21 appears to be incorrect.)
6. Limits and Continuity in Several Variables
1. Squeeze Theorem
2. Differentiability
3. Problems (14.2 #17-31 odd)
7. Partial Derivatives
1. Clairaut’s Theorem
2. Problems (14.3 #3-9 odd,13-31odd, 57-63odd, 74, 79)
8. Gradient and Directional Derivatives
1. Interpretation of the Gradient: Khan Academy, and Book Explanations
2. Chain Rule For Paths
3. The Laplace Operator
4. Problems (14.5 #1-3, 5-29 odd, 31-33, 35, 37-39, 41-55 odd ,61)
9. The Chain Rule
1. Multivariable Implicit differentiation
2. The Cyclic relation
3. Problems (14.6 #1, 3-5, 7, 11-15odd, 16-17,19, 22-23, 25-31odd, 38, 40[not sure on 31])
10. Optimization in Several Variables
1. Fermat's Theorem
2. Second Derivative Test and Conclusions of
3. Multivariable Discriminant
4. Problems (14.7 #7, 9, 12, 13-23odd, 24, 25, 29-45odd, 46-50even, 51)
11. Lagrange Multipliers
1. The Lagrange Condition
2. The Lagrange Condition for Multiple Constraints
3. Problems (14.8 #1, 3-9, 11-12, 15-21odd, 22, 27, 43, 46)
12. Integration in Two and Three Variables
1. Fubini’s Theorem
2. Problems (15.1 #1,8-9,15-45 odd, 48-50)
3. Double Integrals over More General Regions (15.2 #5-37odd, 38-39, 41-57odd, 58-61)
4. Triple Integrals (15.3 1-5,7,9-11,15,17,21-25odd, 29-33odd, 39)
5. Integration in Polar, Cylindrical, and Spherical Coordinates (15.4, 1-55odd, 56)
6. Applications of Multiple Integration (15.5, 1-7odd, 11, 13, 17, 19, 23-27odd, 60-63)
13. Change of Variables
1. Jacobian Relationships
2. Problems (15.6 #1-41odd, 45, 49)
14. Vector Fields
1. Problems (16.1 #1-15odd,16-20, 21-23odd, 35)
2. Conservative Vector Fields (16.3 #1-27odd)
15. Line Integrals
1. Interpretation of : Khan Academy and Book Explanations
2. Reverse Parameterizations: Khan Academy
3. Problems (16.2 #1-13odd, 15-17,19-29odd, 30, 31, 35-55, 56, 57, 59, 63-67odd, 68-71)
16. Parametrized Surfaces and Surface Integrals
1. Problems (16.4 #1-9 odd, 13-27odd, 35)
2. Surface Integrals of Vector Fields (16.5 #1-17odd, 23-27odd)
17. Fundamental Theorems of Vector Analysis
1. Divergence and Curl, Interpretation of and Calculation: Khan Academy and Book.
2. Green’s Theorem
1. Derivation: Khan Academy and Book
2. Problems (17.1 #1-15odd)
3. Stokes’ Theorem
1. Derivation
2. Problems (17.2 #1-9odd)
4. Divergence Theorem
1. 2D Divergence Theorem Derivation: Khan Academy
2. 3D Divergence Theorem Derivation
3. Problems (17.3 1-9odd, 11-13)
5. Review (17.3 Review #1,3,9,11,13,17 also Section 17.1 #17)
18. Overall Review
================================

_____________________
_____________________

Subscriber Count as of release: 1,529 (Hello to the new 246 of y'all since I last posted!)

#CHALK #Calculus3 #Self-Learning

Full ✅!

[CHALKND]

Ran out of room in the description box, but I wanted to say thanks to Freddy Yano and Leon Masuda for suggesting the topic for this video! If you have any math things that you would like me to cover in a future video feel free to respond to this comment here or leave a comment on any of my other videos (newer or older doesn't matter) here on my channel. Thanks for watching!!

[osiel_ac]

I'm a math student from Mexico, and I had the fortune to find this channel. I really love to see your videos, the effort on these are amazing, audio, image, content, really high quality. Keep going like this!!
The next semester I will study multivariable calculus and I think this will help a lot

[LucasDimoveo]

I'm a super slow learner, so I write everything down from the textbook verbatim, and I have a spreadsheet with tge dates I need to repeat topics by

[suprecam]

Hey man! I wasn’t sure what to expect from your video, but your honest and candid perspective was refreshing. I’ve heard a lot of the same advice from my professors in office hours, and I think it’s great that you are putting that same guidance out there for others to understand who may not have the same opportunities as myself or another student at an institution. This really is quality advice. I subscribed, have a great day :)

[speedcuber]

Just fell upon this channel and subbed instantly, looks like a lovely little gem

[millamulisha]

Taught myself calculus one summer while working around the country, got to university and tested out of calculus I and into II, III and Differential Equations (taken concurrently). Whew... Was quite a steep learning curve for me. Love mathematics though! :D

[isaacmandell-seaver]

Have you seen the multi variable calc course on MIT Opencourseware?

[noarogoszinski]

would you recommend using graph paper/blank paper rather than typical lined paper for calc 3 notes since it's multivariable? or does it not really matter?

[stanleygomes]

Can I like implement this format to self-study calculus myself?

[rithikkhanna]

Did you go to Carleton College? If so, do you know Eric Egge?

[TheDrguru]

Hi. can you cover the math topics that have application in machine learning? I know there are many resources out there on this topic, but I need it from a mathematician's perspective. Your videos are quite inspiring btw. I have a 'pure" non-math background but have been trying to self study real analysis(from abott). Also useful for me would be if you could cover what functional analysis entails.

[pureroseangemuse]

the problem is that the professor don't really teach us in a way how to solve a specific problem