Schoolhouse.world: peer tutoring, for free.
Schoolhouse.world: peer tutoring, for free.

Math

Algebra 2 Learning Labs
Pre-Calculus Learning Labs
Pre-Algebra
Algebra 1
Algebra 2
Geometry
Pre-Calculus
Calculus
Statistics

Science

Biology
Chemistry
Physics

More

SAT Bootcamp
College Admissions Workshops
SAT Prep
College Prep
Enrichment
Computer Science
Reading and Writing
History
Free SAT® Prep, as part of a research study.
SAT® Bootcamps
Free SAT® Prep, as part of a research study.
A global network of volunteers.
Explore Tutors
A global network of volunteers.
Get free help applying to college.
College Admissions Workshops
Get free help applying to college.
Why get tutored by other students?
Benefits of Peer Tutoring
Why get tutored by other students?
Prove your mastery and get ready to tutor.
About Certifications
Prove your mastery and get ready to tutor.
Learn, grow, and give back through tutoring.
Become a Tutor
Learn, grow, and give back through tutoring.
How we keep virtual tutoring safe.
Session Safety Measures
How we keep virtual tutoring safe.
Have questions? Search our FAQ.
Help Desk
Have questions? Search our FAQ.
Game nights, product updates, and more.
Community Events
Game nights, product updates, and more.
Stay motivated in virtual study rooms.
Study Spaces
Stay motivated in virtual study rooms.
Check out the community's impact.
Leaderboards
Check out the community's impact.
Testimonials from the Schoolhouse community.
Stories
Testimonials from the Schoolhouse community.
Keep up with our volunteer-run blog.
Blog
Keep up with our volunteer-run blog.
Multivariable Calculus and Applied Linear Algebra

SAT Score Range

•

28 sessions

•

+5

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.

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


Tutored by

Jose Roberto Cossich G 🇬🇹

Senior Tutor

Certified in 69 topics

View Profile

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.

Schedule

✋ 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!

SESSION 1

11

Jul

SESSION 1

Other Topics

Other Topics

Thu 10:00 PM - 11:15 PM UTCJul 11, 10:00 PM - 11:15 PM UTC

Topics covered (75m):
(UNIT I)
1. Vector geometry in R^n (magnitude, unit vector, zero vector, dot and cross product)
SESSION 2

12

Jul

SESSION 2

Other Topics

Other Topics

Fri 10:00 PM - 11:15 PM UTCJul 12, 10:00 PM - 11:15 PM UTC

Topics covered (75m):
2. Planes in R^3
3. Span, subspaces, and dimension
SESSION 3

14

Jul

SESSION 3

Other Topics

Other Topics

Sun 10:00 PM - 11:10 PM UTCJul 14, 10:00 PM - 11:10 PM UTC

Topics covered (70m):
4. Basis and orthogonality
SESSION 4

15

Jul

SESSION 4

Other Topics

Other Topics

Mon 10:00 PM - 11:30 PM UTCJul 15, 10:00 PM - 11:30 PM UTC

Topics covered (90m):
5. Projections
6. Applications of projections in R^n: orthogonal bases of planes
SESSION 5

16

Jul

SESSION 5

Other Topics

Other Topics

Tue 10:00 PM - 11:10 PM UTCJul 16, 10:00 PM - 11:10 PM UTC

(Continuing)
Topics covered (90m):
5. Projections
6. Applications of projections in R^n: orthogonal bases of planes
SESSION 6

17

Jul

SESSION 6

Other Topics

Other Topics

Wed 10:00 PM - 11:15 PM UTCJul 17, 10:00 PM - 11:15 PM UTC

Topics covered (90m):
- Homework review (30m)
7. Multivariable functions, level sets, and contour plots
SESSION 7

18

Jul

SESSION 7

Other Topics

Other Topics

Thu 10:00 PM - 11:30 PM UTCJul 18, 10:00 PM - 11:30 PM UTC

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
SESSION 8

19

Jul

SESSION 8

Other Topics

Other Topics

Fri 10:15 PM - 11:30 PM UTCJul 19, 10:15 PM - 11:30 PM UTC

Unit I Test (75m)
SESSION 9

20

Jul

SESSION 9

Other Topics

Other Topics

Sat 10:00 PM - 11:15 PM UTCJul 20, 10:00 PM - 11:15 PM UTC

Topics covered (75m):
10 (part 2). and gradient descent
11. Constrained optimization via Lagrange multipliers
*END OF UNIT 2*
SESSION 10

21

Jul

SESSION 10

Other Topics

Other Topics

Sun 10:00 PM - 11:15 PM UTCJul 21, 10:00 PM - 11:15 PM UTC

(continuing)
Topics covered (75m):
10 (part 2). and gradient descent
11. Constrained optimization via Lagrange multipliers
*END OF UNIT 2*
SESSION 11

22

Jul

SESSION 11

Other Topics

Other Topics

Mon 10:00 PM - 11:15 PM UTCJul 22, 10:00 PM - 11:15 PM UTC

Topics covered (75m):
12. Linear functions, matrices, and the derivative matrix
13. Linear transformations and matrix multiplication
14. Matrix algebra
SESSION 12

23

Jul

SESSION 12

Other Topics

Other Topics

Tue 10:00 PM - 11:30 PM UTCJul 23, 10:00 PM - 11:30 PM UTC

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
SESSION 13

24

Jul

SESSION 13

Other Topics

Other Topics

Wed 10:00 PM - 11:30 PM UTCJul 24, 10:00 PM - 11:30 PM UTC

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
SESSION 14

25

Jul

SESSION 14

Other Topics

Other Topics

Thu 10:00 PM - 11:15 PM UTCJul 25, 10:00 PM - 11:15 PM UTC

(finishing up Unit III)
SESSION 15

26

Jul

SESSION 15

Other Topics

Other Topics

Fri 9:30 PM - 10:45 PM UTCJul 26, 9:30 PM - 10:45 PM UTC

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.
SESSION 16

28

Jul

SESSION 16

Other Topics

Other Topics

Sun 10:00 PM - 11:15 PM UTCJul 28, 10:00 PM - 11:15 PM UTC

- Unit 3 review
We will review and do practice problems.
SESSION 17

29

Jul

SESSION 17

Other Topics

Other Topics

Mon 10:00 PM - 11:30 PM UTCJul 29, 10:00 PM - 11:30 PM UTC

-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.
SESSION 18

31

Jul

SESSION 18

Other Topics

Other Topics

Wed 10:00 PM - 11:30 PM UTCJul 31, 10:00 PM - 11:30 PM UTC

Topic covered (75m):
17. Linear independence and the Gram–Schmidt process
SESSION 19

1

Aug

SESSION 19

Other Topics

Other Topics

Thu 10:00 PM - 11:15 PM UTCAug 1, 10:00 PM - 11:15 PM UTC

Topic covered (75m):
18. Matrix transpose, quadratic forms, and orthogonal matrices
SESSION 20

2

Aug

SESSION 20

Other Topics

Other Topics

Fri 10:00 PM - 11:15 PM UTCAug 2, 10:00 PM - 11:15 PM UTC

Topic covered (75m):
18. Matrix transpose, quadratic forms, and orthogonal matrices
SESSION 21

3

Aug

SESSION 21

Other Topics

Other Topics

Sat 10:00 PM - 11:15 PM UTCAug 3, 10:00 PM - 11:15 PM UTC

Topic covered (75m):
19. Linear systems, column space, and null space
SESSION 22

4

Aug

SESSION 22

Other Topics

Other Topics

Sun 10:00 PM - 11:20 PM UTCAug 4, 10:00 PM - 11:20 PM UTC

Topic covered (80m):
20. Matrix decompositions: QR-decomposition and LU-decomposition
SESSION 23

6

Aug

SESSION 23

Other Topics

Other Topics

Tue 10:00 PM - 11:30 PM UTCAug 6, 10:00 PM - 11:30 PM UTC

Topics covered (90m):
21. Eigenvalues and eigenvectors
22. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers
SESSION 24

7

Aug

SESSION 24

Other Topics

Other Topics

Wed 10:00 PM - 11:15 PM UTCAug 7, 10:00 PM - 11:15 PM UTC

Unit 4 homework review, then I'll hand out the
Unit IV Test (75m)
SESSION 25

8

Aug

SESSION 25

Other Topics

Other Topics

Thu 10:30 PM - Fri, 12:00 AM UTCAug 8, 10:30 PM - Aug 9, 12:00 AM UTC

Topic covered (90m):
23. The Hessian and quadratic approximation
24. Grand finale: application of the Hessian to local extrema, and bon voyage
SESSION 26

9

Aug

SESSION 26

Other Topics

Other Topics

Fri 10:00 PM - 11:15 PM UTCAug 9, 10:00 PM - 11:15 PM UTC

23. The Hessian and quadratic approximation
24. Grand finale: application of the Hessian to local extrema, and bon voyage
SESSION 27

10

Aug

SESSION 27

Other Topics

Other Topics

Sat 10:00 PM - 11:15 PM UTCAug 10, 10:00 PM - 11:15 PM UTC

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 :(
SESSION 28

29

Aug

SESSION 28

Catchup

Catchup

Thu 10:00 PM - 11:00 PM UTCAug 29, 10:00 PM - 11:00 PM UTC

This is a dummy session so I can assign an assessment.

Public Discussion

Please log in to see discussion on this series.

Jul 11 - Aug 29

8 weeks

60 - 90 mins

/ session

SCHEDULE

Thursdays

10:00PM

Fridays

10:00PM

Sundays

10:00PM

Mondays

10:00PM

Tuesdays

10:00PM

Wednesdays

10:00PM

Saturdays

10:00PM