Multivariable Calculus and Applied Linear Algebra

Jose Roberto Cossich G

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This series ended on August 29, 2024. All 1:1 and group chats related to this series are disabled 7 days after the last session.

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About

Hey everyone, it's finally here! Calculus 3 
(the equivalent of the first semester of a full-year course).
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NOTE: REQUIRED READING OF APPROXIMATELY 25 PAGES A WEEK + WEEKLY HOMEWORK (with feedback) + 1 TEST PER UNIT (in-class and graded with feedback)
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Prerequisites:
- Calculus 1 and 2 (the equivalent of Calc BC)
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CONTENT COVERED:
(UNIT I)  Basic Vector Operation
1. Vector geometry in R^n 
2. Planes in R^3
3. Span, subspaces, and dimension
4. Basis and orthogonality
5. Cross Products
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(UNIT II) Partial Derivatives and Applications
6. Multivariable functions, level sets, and contour plots
7. Partial derivatives and contour plots
8. Maxima, minima, and critical points
9. Gradients, local approximations, and gradient descent
10. Constrained optimization via Lagrange multipliers
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(UNIT III) Basic Matrix Operations
11. Linear functions, matrices, and the derivative matrix
12. Linear transformations and matrix multiplication
13. Matrix algebra
14. Multivariable Chain Rule
15. Matrix inverses and multivariable Newton’s method for zeros
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(UNIT IV) Further Matrix Properties
16. Linear independence and the Gram–Schmidt process
17. Matrix transpose, quadratic forms, and orthogonal matrices
18. Linear systems, column space, and null space
19. Matrix decompositions: QR-decomposition and LU-decomposition
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(UNIT V) Motivating the Second Derivative Test
20. Eigenvalues and eigenvectors
21. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers
22. The Hessian and quadratic approximation
23. Application of the Hessian to local extrema
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✋ ATTENDANCE POLICY

I try to make the session times as accommodating as possible, however make-up sessions are always available. Please feel free to ask for one if needed!

Dates

July 11 - August 29

Learners

8 / 10

Total Sessions

About the Tutor

A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.

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