Multivariable/Vector Calculus
SAT Score Range
•
45 sessions
•
HS
JV
NK
+4
•
🔥 3 spots left!
Enrollment for this series has closed.
About
I am back to host another wonderful series: Multivar./VECTOR CALCULUS! I hope you all can join!
This series will cover the content of a semester of college Multivar./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
4. Vector Calculus
Tutored by
✋ 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!
SESSION 1
1
Oct
SESSION 1
Other Topics
Other Topics
Tue 9:00 PM - 10:00 PM UTCOct 1, 9:00 PM - 10:00 PM UTC
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
SESSION 2
4
Oct
SESSION 2
Other Topics
Other Topics
Fri 9:00 PM - 10:00 PM UTCOct 4, 9:00 PM - 10:00 PM UTC
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
4
Oct
SESSION 3
Office Hours
Office Hours
Fri 10:00 PM - 11:00 PM UTCOct 4, 10:00 PM - 11:00 PM UTC
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
4
Oct
SESSION 4
Other Topics
Other Topics
Fri 11:15 PM - Sat, 12:15 AM UTCOct 4, 11:15 PM - Oct 5, 12:15 AM UTC
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
SESSION 5
8
Oct
SESSION 5
Other Topics
Other Topics
Tue 9:00 PM - 10:00 PM UTCOct 8, 9:00 PM - 10:00 PM UTC
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
8
Oct
SESSION 6
Office Hours
Office Hours
Tue 10:00 PM - 11:00 PM UTCOct 8, 10:00 PM - 11:00 PM UTC
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 7
9
Oct
SESSION 7
Other Topics
Other Topics
Wed 9:00 PM - 10:00 PM UTCOct 9, 9:00 PM - 10:00 PM UTC
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;
SESSION 8
11
Oct
SESSION 8
Other Topics
Other Topics
Fri 8:00 PM - 9:30 PM UTCOct 11, 8:00 PM - 9:30 PM UTC
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
SESSION 9
11
Oct
SESSION 9
Office Hours
Office Hours
Fri 9:45 PM - 10:30 PM UTCOct 11, 9:45 PM - 10:30 PM UTC
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 10
15
Oct
SESSION 10
Other Topics
Other Topics
Tue 8:45 PM - 9:45 PM UTCOct 15, 8:45 PM - 9:45 PM UTC
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
SESSION 11
15
Oct
SESSION 11
Office Hours
Office Hours
Tue 10:00 PM - 10:45 PM UTCOct 15, 10:00 PM - 10:45 PM UTC
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 12
16
Oct
SESSION 12
Review
Review
Wed 8:45 PM - 9:30 PM UTCOct 16, 8:45 PM - 9:30 PM UTC
This is intended as a Vector Calc Review Session before our Assessment or in between topics
SESSION 13
18
Oct
SESSION 13
Other Topics
Other Topics
Fri 8:45 PM - 10:15 PM UTCOct 18, 8:45 PM - 10:15 PM UTC
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)
SESSION 14
22
Oct
SESSION 14
Other Topics
Other Topics
Tue 8:45 PM - 9:45 PM UTCOct 22, 8:45 PM - 9:45 PM UTC
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 15
22
Oct
SESSION 15
Office Hours
Office Hours
Tue 10:00 PM - 10:45 PM UTCOct 22, 10:00 PM - 10:45 PM UTC
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 16
23
Oct
SESSION 16
Other Topics
Other Topics
Wed 8:45 PM - 9:45 PM UTCOct 23, 8:45 PM - 9:45 PM UTC
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 17
24
Oct
SESSION 17
Office Hours
Office Hours
Thu 10:00 PM - 10:45 PM UTCOct 24, 10:00 PM - 10:45 PM UTC
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 18
25
Oct
SESSION 18
Other Topics
Other Topics
Fri 8:45 PM - 10:15 PM UTCOct 25, 8:45 PM - 10:15 PM UTC
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)
SESSION 19
30
Oct
SESSION 19
Other Topics
Other Topics
Wed 8:45 PM - 9:45 PM UTCOct 30, 8:45 PM - 9:45 PM UTC
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,
SESSION 20
8
Nov
SESSION 20
Other Topics
Other Topics
Fri 9:45 PM - 10:30 PM UTCNov 8, 9:45 PM - 10:30 PM UTC
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 21
8
Nov
SESSION 21
Review
Review
Fri 10:30 PM - 11:15 PM UTCNov 8, 10:30 PM - 11:15 PM UTC
This is intended as a Vector Calc Review Session before our Assessment or in between topics
SESSION 22
11
Nov
SESSION 22
Other Topics
Other Topics
Mon 9:45 PM - 10:45 PM UTCNov 11, 9:45 PM - 10:45 PM UTC
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
SESSION 23
11
Nov
SESSION 23
Review
Review
Mon 10:45 PM - 11:30 PM UTCNov 11, 10:45 PM - 11:30 PM UTC
This is intended as a Vector Calc Review Session before our Assessment or in between topics
SESSION 24
12
Nov
SESSION 24
Review
Review
Tue 9:30 PM - 10:00 PM UTCNov 12, 9:30 PM - 10:00 PM UTC
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 25
12
Nov
SESSION 25
Other Topics
Other Topics
Tue 10:00 PM - 11:30 PM UTCNov 12, 10:00 PM - 11:30 PM UTC
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)
SESSION 26
13
Nov
SESSION 26
Other Topics
Other Topics
Wed 9:45 PM - 10:45 PM UTCNov 13, 9:45 PM - 10:45 PM UTC
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
SESSION 27
19
Nov
SESSION 27
Other Topics
Other Topics
Tue 9:45 PM - 10:45 PM UTCNov 19, 9:45 PM - 10:45 PM UTC
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)
SESSION 28
22
Nov
SESSION 28
Other Topics
Other Topics
Fri 9:30 PM - 11:00 PM UTCNov 22, 9:30 PM - 11:00 PM UTC
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
SESSION 29
26
Nov
SESSION 29
Other Topics
Other Topics
Tue 9:45 PM - 11:15 PM UTCNov 26, 9:45 PM - 11:15 PM UTC
Vectors/Geometry of Space Part 2 TEST (DUE DEC 1ST)
5. Calculate the tangential and normal components of a vector
6. Describe motion in space
=-=-=-=-=-=-=-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;
SESSION 30
28
Nov
SESSION 30
Review
Review
Thu 9:30 PM - 11:30 PM UTCNov 28, 9:30 PM - 11:30 PM UTC
Review these concepts more in-depth:
5. Calculate the tangential and normal components of a vector
6. Describe motion in space
=-=-=-=-=-=-=-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;
SESSION 31
2
Dec
SESSION 31
Other Topics
Other Topics
Mon 9:45 PM - 11:15 PM UTCDec 2, 9:45 PM - 11:15 PM UTC
Partial Derivatives Day 2
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;
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
SESSION 32
3
Dec
SESSION 32
Review
Review
Tue 11:15 PM - Wed, 12:15 AM UTCDec 3, 11:15 PM - Dec 4, 12:15 AM UTC
Vectors and the Geometry of Space TEST due TODAY—SESSION TIME WAS GIVEN
SESSION 33
6
Dec
SESSION 33
Other Topics
Other Topics
Fri 9:30 PM - 11:00 PM UTCDec 6, 9:30 PM - 11:00 PM UTC
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
SESSION 34
10
Dec
SESSION 34
Other Topics
Other Topics
Tue 9:45 PM - 11:15 PM UTCDec 10, 9:45 PM - 11:15 PM UTC
Partial Derivatives Day 4
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;
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
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 35
13
Dec
SESSION 35
Other Topics
Other Topics
Fri 9:30 PM - 11:00 PM UTCDec 13, 9:30 PM - 11:00 PM UTC
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
SESSION 36
17
Dec
SESSION 36
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCDec 17, 9:30 PM - 10:30 PM UTC
Partial Derivatives Day 5
6. Determine total and partial derivatives using chain rules
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 37
20
Dec
SESSION 37
Other Topics
Other Topics
Fri 9:30 PM - 10:30 PM UTCDec 20, 9:30 PM - 10:30 PM UTC
Multiple Integrals Day 1-2
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.
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
SESSION 38
7
Jan
SESSION 38
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCJan 7, 9:30 PM - 10:30 PM UTC
Multiple Integrals Day 4
5. Define triple integrals, evaluate triple integrals, and know the simplest properties of them. Calculate volumes by triple integrals
6. Evaluate triple integrals in all three coordinate systems (Cartesian, cylindrical, and spherical coordinates); make a change of variables using the Jacobian
SESSION 39
10
Jan
SESSION 39
Other Topics
Other Topics
Fri 9:30 PM - 11:00 PM UTCJan 10, 9:30 PM - 11:00 PM UTC
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
SESSION 40
14
Jan
SESSION 40
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCJan 14, 9:30 PM - 10:30 PM UTC
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
SESSION 41
17
Jan
SESSION 41
Other Topics
Other Topics
Fri 9:30 PM - 10:30 PM UTCJan 17, 9:30 PM - 10:30 PM UTC
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
SESSION 42
20
Jan
SESSION 42
Review
Review
Mon 9:30 PM - 11:30 PM UTCJan 20, 9:30 PM - 11:30 PM UTC
1.) Review Partial Derivatives unit
2.) If time permits, begin Multiple Integrals
SESSION 43
21
Jan
SESSION 43
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCJan 21, 9:30 PM - 10:30 PM UTC
The Last of Vector Calc TEST (DUE JAN 30th)
The Last of Vector Calc Day 4
7. State and use Stokes Theorem
8. State and use the Divergence Theorem
SESSION 44
28
Jan
SESSION 44
Other Topics
Other Topics
Tue 9:30 PM - 10:30 PM UTCJan 28, 9:30 PM - 10:30 PM UTC
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
SESSION 45
31
Jan
SESSION 45
Other Topics
Other Topics
Fri 9:30 PM - 11:30 PM UTCJan 31, 9:30 PM - 11:30 PM UTC
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)