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Multivariable Calculus - Integration and Vector Analysis

SAT Score Range

•

16 sessions

•

+12

This series was cancelled by the tutor on September 4, 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.

About

Are you interested in learning Calculus 3?
Well, this course is the equivalent of a second-semester course, a continuation of my last series. Don't worry though if you weren't there. This series can be taken by anyone who has completed

the only prerequisite: Calculus 1 (with integration)
and the rest of the necessary background information will be covered or reviewed in the initial sessions.

NOTE: Required reading of about 35 pages a week (for units 2 and 3 only)+ weekly homework (with feedback) + 1 test per unit (inside or outside of class depending on time but always graded with feedback within 2 days)

Sessions are between 1h15m to 1h30m.

Content Covered:
(UNIT I) Single-Variable Integration and Vector Analysis
1. Physical interpretations of the integral and the average value of a function over an interval
2. Finding the area between curves expressed as functions of y
3. Finding the area between curves that intersect at more than two points
4. Volumes with cross sections: squares, rectangles, triangles, and semicircles
5. Volume with the disc and washer method: revolving around x-, y-, and different axes
6. Arc length, distance traveled, and unit calculator practice
7. Defining and differentiating parametric vector-valued functions
8. Finding arc lengths of curves given by parametric equations and solving motion problems
9. Defining polar coordinates and differentiating in polar form
10. Finding the area of a polar region bounded by one and multiple polar curves, and unit calculator practice.
11. Finding the surface area of surfaces or revolution, including in polar coordinates.

(UNIT II) Multivariable Integration and Applications
11. Formulating Riemann sums
12. The Double Integral and Iterated Integral
13. Applications of The Double Integral
14. Triple Integrals
15. The Jacobian and uv-substitution
16. Integration in Polar, Cylindrical, and Spherical Coordinates
17. Applications of Triple Integrals

(Unit III) Multivariable Vector Analysis
18. Scalar-valued Line Integrals
19. Vector-valued line integrals
20. Path Independence
21. Exact Differentials
22. Divergence and Green's Theorem
23 Curl, Stokes' Theorem, and parameterizing surfaces.
24. Flux and Divergence Theorem

25+ (applications to Electrodynamics and other special topics?)

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

Aug

SESSION 1

Applications of integration

Applications of integration

Sun 9:45 PM - 11:00 PM UTCAug 11, 9:45 PM - 11:00 PM UTC

1. Physical interpretations of the integral and the average value of a function over an interval
2. Finding the area between curves expressed as functions of y
3. Finding the area between curves that intersect at more than two points
SESSION 2

13

Aug

SESSION 2

Other Topics

Other Topics

Tue 9:45 PM - 11:00 PM UTCAug 13, 9:45 PM - 11:00 PM UTC

5. Volume with the disc and washer method: revolving around x-, y-, and different axes (part 2)
6. Arc length, distance traveled, and unit calculator practice
7. Defining and differentiating parametric vector-valued functions
8. Finding arc lengths of curves given by parametric equations and solving motion problems
9. Defining polar coordinates and differentiating in polar form

SESSION 3

14

Aug

SESSION 3

Other Topics

Other Topics

Wed 10:00 PM - 11:15 PM UTCAug 14, 10:00 PM - 11:15 PM UTC

10. Finding the area of a polar region bounded by one and multiple polar curves, and unit calculator practice.
11. Finding the surface area of surfaces or revolution, including in polar coordinates.
SESSION 4

16

Aug

SESSION 4

Other Topics

Other Topics

Fri 9:45 PM - 11:15 PM UTCAug 16, 9:45 PM - 11:15 PM UTC

Unit 1 Test (90m)
SESSION 5

17

Aug

SESSION 5

Other Topics

Other Topics

Sat 9:45 PM - 11:00 PM UTCAug 17, 9:45 PM - 11:00 PM UTC

11. Formulating Riemann sums
12. The Double Integral and Iterated Integral (part 1)
SESSION 6

18

Aug

SESSION 6

Other Topics

Other Topics

Sun 9:45 PM - 11:00 PM UTCAug 18, 9:45 PM - 11:00 PM UTC

12. The Double Integral and Iterated Integral (part 2)
SESSION 7

19

Aug

SESSION 7

Other Topics

Other Topics

Mon 10:00 PM - 11:15 PM UTCAug 19, 10:00 PM - 11:15 PM UTC

12. The Double Integral and Iterated Integral (part 2)
SESSION 8

20

Aug

SESSION 8

Other Topics

Other Topics

Tue 9:45 PM - 11:00 PM UTCAug 20, 9:45 PM - 11:00 PM UTC

13. Applications of The Double Integral
SESSION 9

21

Aug

SESSION 9

Other Topics

Other Topics

Wed 9:45 PM - 11:00 PM UTCAug 21, 9:45 PM - 11:00 PM UTC

13. Applications of The Double Integral
SESSION 10

23

Aug

SESSION 10

Other Topics

Other Topics

Fri 9:45 PM - 11:00 PM UTCAug 23, 9:45 PM - 11:00 PM UTC

14. Triple Integrals
SESSION 11

26

Aug

SESSION 11

Other Topics

Other Topics

Mon 9:45 PM - 11:00 PM UTCAug 26, 9:45 PM - 11:00 PM UTC

14. Triple Integrals
15. The Jacobian and uv-substitution
16. Integration in Polar, Cylindrical, and Spherical Coordinates
SESSION 12

27

Aug

SESSION 12

Other Topics

Other Topics

Tue 9:45 PM - 11:00 PM UTCAug 27, 9:45 PM - 11:00 PM UTC

17. Applications of Triple Integrals
SESSION 13

29

Aug

SESSION 13

Other Topics

Other Topics

Thu 11:15 PM - Fri, 12:30 AM UTCAug 29, 11:15 PM - Aug 30, 12:30 AM UTC

15. The Jacobian and uv-substitution
16. Integration in Polar, Cylindrical, and Spherical Coordinates
SESSION 14

30

Aug

SESSION 14

Other Topics

Other Topics

Fri 11:15 PM - Sat, 12:30 AM UTCAug 30, 11:15 PM - Aug 31, 12:30 AM UTC

17. Applications of Triple Integrals
SESSION 15

2

Sep

SESSION 15

Other Topics

Other Topics

Mon 11:15 PM - Tue, 12:30 AM UTCSep 2, 11:15 PM - Sep 3, 12:30 AM UTC

17. Applications of Triple Integrals
18. Scalar-valued Line Integrals
19. Vector-valued line integrals
20. Path Independence
SESSION 16

3

Sep

SESSION 16

Other Topics

Other Topics

Tue 11:15 PM - Wed, 12:30 AM UTCSep 3, 11:15 PM - Sep 4, 12:30 AM UTC

21. Exact Differentials

Public Discussion

Please log in to see discussion on this series.

Aug 11 - Sep 4

4 weeks

75 - 90 mins

/ session

SCHEDULE

Tuesdays

9:45PM