Calculus • Series
Multivariable Calculus and Applied Linear Algebra
PL
JG
Jose Roberto Cossich G
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.
Series Details
About
Hey everyone, it's finally here! Calculus 3
(the equivalent of the first semester of a full-year course).
NOTE: REQUIRED READING OF APPROXIMATELY 25 PAGES A WEEK + WEEKLY HOMEWORK (with feedback) + 1 TEST PER UNIT (in-class and graded with feedback)
Prerequisites:
- Calculus 1 and 2 (the equivalent of Calc BC)
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
(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
(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
(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
(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
✋ 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
28
About the Tutor
PL
JG
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
Upcoming Sessions
0
Past Sessions
28
11
Jul
OT
Session 1
Other Topics
Topics covered (75m):
(UNIT I)
1. Vector geometry in R^n (magnitude, unit vector, zero vector, dot and cross product)
12
Jul
OT
Session 2
Other Topics
Topics covered (75m):
2. Planes in R^3
3. Span, subspaces, and dimension
14
Jul
OT
Session 3
Other Topics
Topics covered (70m):
4. Basis and orthogonality
15
Jul
OT
Session 4
Other Topics
Topics covered (90m):
5. Projections
6. Applications of projections in R^n: orthogonal bases of planes
16
Jul
OT
Session 5
Other Topics
(Continuing)
Topics covered (90m):
5. Projections
6. Applications of projections in R^n: orthogonal bases of planes
17
Jul
OT
Session 6
Other Topics
Topics covered (90m):
- Homework review (30m)
7. Multivariable functions, level sets, and contour plots
18
Jul
OT
Session 7
Other Topics
Please have the two homeworks posted done before class.
8. Partial derivatives and contour plots
Topics covered (75m):
9. Maxima, minima, and critical points
10 (part 1). Gradients and local approximations
19
Jul
OT
Session 8
Other Topics
Unit I Test (75m)
20
Jul
OT
Session 9
Other Topics
Topics covered (75m):
10 (part 2). and gradient descent
11. Constrained optimization via Lagrange multipliers
*END OF UNIT 2*
21
Jul
OT
Session 10
Other Topics
(continuing)
Topics covered (75m):
10 (part 2). and gradient descent
11. Constrained optimization via Lagrange multipliers
*END OF UNIT 2*
22
Jul
OT
Session 11
Other Topics
Topics covered (75m):
12. Linear functions, matrices, and the derivative matrix
13. Linear transformations and matrix multiplication
14. Matrix algebra
23
Jul
OT
Session 12
Other Topics
Please have the homework (for Unit II) posted done before class.
Topics covered (90m):
12. Linear functions, matrices, and the derivative matrix
13. Linear transformations and matrix multiplication
14. Matrix algebra
15. Multivariable Chain Rule
24
Jul
OT
Session 13
Other Topics
Please have the homework (for Unit II) posted done before class.
15. Multivariable Chain Rule
16. Matrix inverses and multivariable Newton’s method for zeros
Afterwards, I'll hand out the Unit II Test
25
Jul
OT
Session 14
Other Topics
(finishing up Unit III)
26
Jul
OT
Session 15
Other Topics
BREAK! This will be an hour and a half dedicated to doing the unit 3 homework due tomorrow, to give you guys some time to digest previous concepts and work during session time.
28
Jul
OT
Session 16
Other Topics
- Unit 3 review
We will review and do practice problems.
29
Jul
OT
Session 17
Other Topics
-Unit III Test (75m)
-Midterm Review (40m)
A mock midterm, which you should complete on your own and then check with the posted solutions before tomorrow.
31
Jul
OT
Session 18
Other Topics
Topic covered (75m):
17. Linear independence and the Gram–Schmidt process
1
Aug
OT
Session 19
Other Topics
Topic covered (75m):
18. Matrix transpose, quadratic forms, and orthogonal matrices
2
Aug
OT
Session 20
Other Topics
Topic covered (75m):
18. Matrix transpose, quadratic forms, and orthogonal matrices
3
Aug
OT
Session 21
Other Topics
Topic covered (75m):
19. Linear systems, column space, and null space
4
Aug
OT
Session 22
Other Topics
Topic covered (80m):
20. Matrix decompositions: QR-decomposition and LU-decomposition
6
Aug
OT
Session 23
Other Topics
Topics covered (90m):
21. Eigenvalues and eigenvectors
22. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers
7
Aug
OT
Session 24
Other Topics
Unit 4 homework review, then I'll hand out the
Unit IV Test (75m)
8
Aug
OT
Session 25
Other Topics
Topic covered (90m):
23. The Hessian and quadratic approximation
24. Grand finale: application of the Hessian to local extrema, and bon voyage
9
Aug
OT
Session 26
Other Topics
23. The Hessian and quadratic approximation
24. Grand finale: application of the Hessian to local extrema, and bon voyage
10
Aug
OT
Session 27
Other Topics
Unit V Test (75m)
We'll go through the Unit V homework and any last questions you guys have on any of the 5 units as Final Exam review.
I will post the Unit V test and will grade them as soon as I receive them. I will post the final exam tomorrow Sunday. Turning in your exam will be you last assignment :(
29
Aug
C
Session 28
Catchup
This is a dummy session so I can assign an assessment.