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

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

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)