GL
RN
Rodrigo N
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
GL
RN
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
OT
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
OH
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
OT
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
OT
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
OH
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
OT
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
OT
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
OT
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.
OH
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
OT
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
OT
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
OH
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
OT
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
OT
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
OT
Session 16
Other Topics
The Last of Vector Calc Day 3
7. State and use Stokes Theorem
8. State and use the Divergence Theorem
OH
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
OT
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)