Multivariable Calculus using Applied Linear Algebra

Jose Roberto Cossich G

Series Details

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This series was cancelled on June 19, 2024. We're very sorry–you can explore more Calculus series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

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 45 PAGES A WEEK + WEEKLY HOMEWORK (graded 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) Geometry of vectors and projections
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1. Vector geometry in R^n and correlation coefficients
2. Planes in R^3
3. Span, subspaces, and dimension
4. Basis and orthogonality
5. Projections
6. Applications of projections in R^n: orthogonal bases of planes
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(UNIT II) Multivariable functions and optimization
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7. Multivariable functions, level sets, and contour plots
8. Partial derivatives and contour plots
9. Maxima, minima, and critical points
10. Gradients, local approximations, and gradient descent
11. Constrained optimization via Lagrange multipliers
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(UNIT III) Geometry and algebra of matrices
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12. Linear functions, matrices, and the derivative matrix
13. Linear transformations and matrix multiplication
14. Matrix algebra
15. Multivariable Chain Rule
16. Matrix inverses and multivariable Newton’s method for zeros
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(UNIT IV) Further matrix algebra and linear systems
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17. Linear independence and the Gram–Schmidt process
18. Matrix transpose, quadratic forms, and orthogonal matrices
19. Linear systems, column space, and null space
20. Matrix decompositions: QR-decomposition and LU-decomposition
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(UNIT V) Eigenvalues and second partial derivatives
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21. Eigenvalues and eigenvectors
22. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers
23. The Hessian and quadratic approximation
24. Grand finale: application of the Hessian to local extrema, and bon voyage

✋ 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

June 18 - June 19

Learners

10 / 12

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.

View Jose Roberto Cossich G's Profile

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