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Calculus • Series

Vector Calculus

Next session on Oct 4, 2024

Rodrigo N

Series Details

Sessions

Public Discussion

Series Details

About

I am back to host another wonderful series: VECTOR CALCULUS! I hope you all can join!

This series will cover the content of a semester of college Vector Calculus

PREREQ:
Calculus 1 and Calculus 2
OR Successful Completion of AP® Calculus BC

why Prereq?
It is expected that you know how to take derivatives and integrals of single variable functions!

STRUCTURE:
1. Lecture (45-60 min)
2. Homework
*repeat above until unit is complete*
3. Problem Set for the Unit
4. Unit TEST


Here is the syllabus for the series:
Main Topics:
1. Vectors and the Geometry of Space
2. Partial Derivatives
3. Multiple Integrals
Subtopics in Vector Calculus:
4. Vector fields
5. Line integrals
6. Green's theorem
7. Curl, gradient, and the divergence of a vector field
8. Flux of a vector field
9. Stokes Theorem
10. The Divergence Theorem


✋ ATTENDANCE POLICY

You are free to attend/skip whichever sessions you want but remember that the MORE practice/help you get, the MORE you will improve! NOTE: USE THE TUTOR CHAT to message me if you won't be here before the session starts!

Dates

October 1 - November 1

Learners

8 / 10

Total Sessions

18

About the Tutor

I am a high school student with a passion for STEM. I enjoy learning from my mistakes and hope to encourage that same idea with students from around the globe.

View Rodrigo N's Profile

Upcoming Sessions

17
4
Oct

Session 2

Other Topics

  • Live now!
Vectors and the Geometry of Space Part 2 Day 1
1. Sketch vector valued functions
2. Determine the relation between these functions and the parametric
representations of space curves
3. Compute the limit, derivative, and integral of a vector valued function

Session 3

Office Hours

If you have a question about anything Calc. related, please stop by and I will do my best to help! :D
This place, for Vector Calc students, will serve as a place for review before our test next class

Session 4

Other Topics

Vectors and the Geometry of Space Part 1 Day 2
4. Calculate the dot product and cross product of vectors, use the products to
calculate the angle between two vectors, and to determine whether vectors are
perpendicular or parallel
5. Determine the scalar and vector projections
Write the equations of lines and planes in space
6. Draw various quadric surfaces and cylinders using the concepts of trace and
cross-section
8
Oct

Session 5

Other Topics

Vectors and the Geometry of Space Part 2 Day 2
4. Calculate the arc length of a curve and its curvature; identify the unit tangent, unit
normal and binormal vectors
5. Calculate the tangential and normal components of a vector
6. Describe motion in space

Session 6

Office Hours

If you have a question about anything Calc. related, please stop by and I will do my best to help! :D
This place, for Vector Calc students, will serve as a place for review before our test next class
9
Oct

Session 7

Other Topics

Partial Derivatives Day 1
1. Define functions of several variables and know the concepts of dependent
variable, independent variables, domain and range.
2. Calculate limits of functions in two variables or prove that a limit does not exist;
3. Test the continuity of functions of several variables;
11
Oct

Session 8

Other Topics

Partial Derivatives Day 2
4. Calculate partial derivatives and interpret them geometrically, calculate higher
partial derivatives
5. Determine the equation of a tangent plane to a surface; calculate the change in a
function by linearization and by differentials,
6. Determine total and partial derivatives using chain rules,
15
Oct

Session 9

Other Topics

Partial Derivatives Day 3
7. Calculate directional derivatives and interpret the results
8. Identify the gradient, interpret the gradient, and use it to find directional derivative
9. Apply intuitive knowledge of concepts of extrema for functions of several
variables, and apply them to mathematical and applied problems. Lagrange
multipliers.

Session 10

Office Hours

If you have a question about anything Calc. related, please stop by and I will do my best to help! :D
This place, for Vector Calc students, will serve as a place for review before our test next class
16
Oct

Session 11

Other Topics

Multiple Integrals Day 1
1. Define double integral, evaluate a double integral by the definition and the
midpoint rule and describe the simplest properties of them.
2. Calculate iterated integrals by Fubini's Theorem
3. Calculate double integrals over general regions and use geometric interpretation
of double integral as a volume to calculate such volumes. Some applications of
double integrals may include computing mass, electric charge, center of mass
and moment of inertia
18
Oct

Session 12

Other Topics

Multiple Integrals Day 2
4. Evaluate double integrals in polar coordinates to calculate polar areas, evaluate
Cartesian double integrals of a particular form by transforming to polar double
integrals
5. Define triple integrals, evaluate triple integrals, and know the simplest properties
of them. Calculate volumes by triple integrals
6. Transform between Cartesian, cylindrical, and spherical coordinate systems;
evaluate triple integrals in all three coordinate systems; make a change of
variables using the Jacobian

Session 13

Office Hours

If you have a question about anything Calc. related, please stop by and I will do my best to help! :D
This place, for Vector Calc students, will serve as a place for review before our test next class
22
Oct

Session 14

Other Topics

The Last of Vector Calc Day 1
1. Describe vector fields in two and three dimensions graphically; determine if
vector fields are conservative, directly and using theorems
2. Identify the meaning and set-up of line integrals and evaluate line integrals
3. Apply the connection between the concepts of conservative force field,
independence of path, the existence of potentials, and the fundamental theorem
for line integrals. Calculate the work done by a force as a line integral
25
Oct

Session 15

Other Topics

The Last of Vector Calc Day 2
4. Apply Green's theorem to evaluate line integrals as double integrals and
conversely
5. Calculate and interpret the curl, gradient, and the divergence of a vector field
6. Evaluate a surface integral. Understand the concept of flux of a vector field
29
Oct

Session 16

Other Topics

The Last of Vector Calc Day 3
7. State and use Stokes Theorem
8. State and use the Divergence Theorem

Session 17

Office Hours

If you have a question about anything Calc. related, please stop by and I will do my best to help! :D
This place, for Vector Calc students, will serve as a place for review before our test next class
1
Nov

Session 18

Other Topics

FINAL EXAM
~2 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)

Public Discussion

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