GL
RN
Rodrigo N
Enrollment for this series has closed.
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 - January 31
Learners
5 / 5
Total Sessions
42
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
14
26
Nov
OT
Session 29
Other Topics
Vectors/Geometry of Space Part 2 TEST (DUE DEC 1ST)
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;
3
Dec
OT
Session 30
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,
6A. Determine total and partial derivatives using chain rules
6
Dec
OT
Session 31
Other Topics
Partial Derivatives Day 3
6B. Determine total and partial derivatives using chain rules (if need be)
7. Calculate directional derivatives and interpret the results
8. Identify the gradient, interpret the gradient, and use it to find directional derivative
10
Dec
OT
Session 32
Other Topics
Partial Derivatives Day 4
9. Apply intuitive knowledge of concepts of extrema for functions of several
variables, and apply them to mathematical and applied problems. Lagrange
multipliers.
13
Dec
OT
Session 33
Other Topics
Partial Derivatives TEST (DUE DEC 15th)
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
3A. Calculate double integrals over general regions (RECTANGLE REGIONS) and use geometric interpretation of double integral as a volume to calculate such volumes.
For extra credit: Some applications of double integrals may include computing mass, electric charge, center of mass and moment of inertia
17
Dec
OT
Session 34
Other Topics
Multiple Integrals Day 2
3B. Calculate double integrals over other regions (Type1/Type2 REGIONS)
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
20
Dec
OT
Session 35
Other Topics
Multiple Integrals Day 3
5. Define triple integrals, evaluate triple integrals, and know the simplest properties of them. Calculate volumes by triple integrals
7
Jan
OT
Session 36
Other Topics
Multiple Integrals Day 4
6. Evaluate triple integrals in all three coordinate systems (Cartesian, cylindrical, and spherical coordinates); make a change of variables using the Jacobian
10
Jan
OT
Session 37
Other Topics
Multiple Integrals TEST (DUE JAN 12th)
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
14
Jan
OT
Session 38
Other Topics
The Last of Vector Calc Day 2
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
4. Apply Green's theorem to evaluate line integrals as double integrals and
conversely
17
Jan
OT
Session 39
Other Topics
The Last of Vector Calc Day 3
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
21
Jan
OT
Session 40
Other Topics
The Last of Vector Calc Day 4
7. State and use Stokes Theorem
8. State and use the Divergence Theorem
28
Jan
OT
Session 41
Other Topics
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 FINAL EXAM next session
31
Jan
OT
Session 42
Other Topics
FINAL EXAM (01/30)
~2 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
Past Sessions
28
1
Oct
OT
Session 1
Other Topics
Vectors and the Geometry of Space Part 1 Day 1
1. Identify and apply the parts of the 3D coordinate system, distance
formula and the equation of the sphere
2. Compute the magnitude, scalar multiple of a vector, and find a unit vector in the
direction of a given vector
3. Calculate the sum, difference, and linear combination of vectors
4
Oct
OT
Session 2
Other Topics
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
Vectors and the Geometry of Space Part 1 Day 2
2. Compute the scalar multiple of a vector, and find a unit vector in the
direction of a given vector
3. Calculate the sum, difference, and linear combination of vectors
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
OH
Session 9
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
15
Oct
OT
Session 10
Other Topics
Vectors and the Geometry of Space Part 1 Day 3
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
OH
Session 11
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
R
Session 12
Review
This is intended as a Vector Calc Review Session before our Assessment or in between topics
18
Oct
OT
Session 13
Other Topics
MORE REVIEW ->> Then take home test ANNOUNCEMENT
Vectors/Geometry of Space Part 1 TEST (10/18)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
22
Oct
OT
Session 14
Other Topics
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 15
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
23
Oct
OT
Session 16
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
24
Oct
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
25
Oct
OT
Session 18
Other Topics
Vectors/Geometry of Space Part 2 TEST (10/25)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
30
Oct
OT
Session 19
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,
8
Nov
OT
Session 20
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.
R
Session 21
Review
This is intended as a Vector Calc Review Session before our Assessment or in between topics
11
Nov
OT
Session 22
Other Topics
7. FInish Spherical and Cylindrical Coordinates
Begin 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
R
Session 23
Review
This is intended as a Vector Calc Review Session before our Assessment or in between topics
12
Nov
R
Session 24
Review
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 25
Other Topics
Vectors/Geometry of Space Part 1 TEST (10/25)
~1.5 hours
-feedback
-will be curved if need be (if I do that, I will send you your raw scores and curved scores)
13
Nov
OT
Session 26
Other Topics
Begin 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
19
Nov
OT
Session 27
Other Topics
Vectors and the Geometry of Space Part 2 Day 2
3. Compute the limit, derivative, and integral of a vector-valued function
4. Calculate the arc length of a curve and its curvature; identify the unit tangent, unit normal, and binormal vectors (TNB Frame)
22
Nov
OT
Session 28
Other Topics
Vectors and the Geometry of Space Part 2 Day 3
4. Calculate the arc length of a curve and its curvature; identify the unit tangent, unit normal, and binormal vectors (TNB Frame)
5. Calculate the tangential and normal components of a vector
6. Describe motion in space