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Multi-Variable Calculus

SAT Score Range

16 sessions

+5

🔥 2 spots left!

About

Dive into the world of higher dimensions with our comprehensive Multi-Variable Calculus Series. This course is auxiliary in nature where, unlike any standardized models like AP or IB, no "standardized" course framework exists; however, specific topics (linked below) generally associated with Multi-Variable Calculus will be covered. Nonetheless, this course is designed to broaden your mathematical horizon and provide a solid foundation for handling more problems with... well... multiple variables.

Whether you're preparing for advanced studies in college or exploring mathematical concepts out of sheer curiosity, we highly recommend you join our series and learn with us. Note that we recommend that you have taken or currently are taking AP Calculus AB/BC or an equivalent course and are comfortable with general knowledge of Calculus I/II. This includes, but of course not limited to, general integration/differentiation proficiency.
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Regarding sessions, this series plans to host around two sessions per week. Each session will be hosted on Friday and Sunday at 5:00 p.m. PST. Each session will be hosted for an hour, depending strictly; however, extra time past may be permitted, not obligated, and dependent on learners' and hosts' preferences.

On Sunday, there will be a 'learning' session where the hosts will teach learners topics relevant to our week's points (such points are again listed in the doc linked below). We highly recommend you take notes (handwritten ones), as they will help you immensely with practice problems hosted on Friday.

On Friday, there will be a 'practice' session where we will focus on practice problems concerning topics covered on Sunday. This will serve as an opportunity to clarify and sink in topics, aided by your own notes and collaborative guidance with other learners and hosts.

We will discuss how these will look in our first introductory session on Friday. I wanted to write down a rough idea of our series format in case any learners join the series late.
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Through a mix of engaging lectures, collaborative problem-solving, and independent exploration, you’ll build the skills to master Multi-variable Calculus at your own pace. While we may not cover all topics within the time limit, our focus remains on delivering a thorough and enjoyable learning experience.
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This course plans to cover the topics listed in the doc linked:
https://docs.google.com/document/d/1FIrmlTk6XKyfHpTJPYpS2BbkvaCQNLbex6Xo68QfMt0/edit?usp=sharing


Our reference material (tests, assignments, etc.) can be found [or later implemented] in:


Tutored by

Isahi S 🇺🇸

Certified in 8 topics

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I am a senior enrolled in a public high school, open to assisting others in analytical subjects related to math or physics. I enjoy helping others understand challenging concepts and am always open to answering questions or providing guidance in problem-solving. I engage in activities like ATV riding or small projects related to computer science. Feel free to contact me with any inquiries or questions!

Sam F 🇺🇸

Certified in 12 topics

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I'm a highschool student from Arizona. My hobbies are playing the piano, working out, and Brazilian jiu jitsu. I am joining Schoolhouse because I love helping others out, especially in fields I love.

✋ ATTENDANCE POLICY

Given the relatively short amount of time per session in every accompanying unit, each session is quite comprehensive, and it is highly recommended that you attend every session as they build upon one another.

However, we understand that there are circumstances where you must miss a session, which is why, in our drive, resources and materials are made public for you to catch up independently. Nonetheless, if this case applies to you, please get in touch with a host (and co-host) informing us of your absence. Failure to do so will result in an unexcused absence and could result in a withdrawal if you accumulate at least two of these absences.

Again, communication is key, and registering for this series is taking the first step in trying to learn Multi-Variable Calculus. You must put in the effort, and attending these classes is just one of many steps to ensure a greater understanding.

So yeah, attend, please :).

SESSION 7

25

Jan

SESSION 7

Review

Review

Sat 1:00 AM - 2:00 AM UTCJan 25, 1:00 AM - 2:00 AM UTC

Unit 1.2 | Determinants and Planes Worksheet Review
Unit 1.3 | Matrices and Systems of Equations Worksheet Review
SESSION 8

27

Jan

SESSION 8

Other Topics

Other Topics

Mon 1:00 AM - 2:00 AM UTCJan 27, 1:00 AM - 2:00 AM UTC

Parametric Equations for Lines & Curves

Key Topics:
Deriving parametric equations for lines using points and direction vectors.
Tangent lines: finding equations for lines tangent to curves at specified points.
Intersections: solving for where lines meet planes or each other.
Sketching and analyzing cycloids and other parameterized curves.
Exploring vector-valued functions and their geometric properties.

SESSION 9

1

Feb

SESSION 9

Other Topics

Other Topics

Sat 1:00 AM - 2:00 AM UTCFeb 1, 1:00 AM - 2:00 AM UTC

Quadric Surfaces & the 3D-Plane

Key Topics:
Recognizing and sketching basic quadric surfaces: spheres, ellipsoids, paraboloids, and hyperboloids.
Transforming equations into standard forms for visualization and analysis.
The intersection of planes and quadric surfaces, emphasizing geometric relationships.
Applications of 3D parametric equations to describe curves on surfaces.

SESSION 10

3

Feb

SESSION 10

Other Topics

Other Topics

Mon 1:00 AM - 2:00 AM UTCFeb 3, 1:00 AM - 2:00 AM UTC

Position, Velocity, & Acceleration
Focus: Describing motion in 3D space through vector functions and exploring the relationships between position, velocity, and acceleration.

Key Topics:
Velocity and acceleration: deriving and interpreting vectors from position functions.
Speed as a scalar measure of motion.
Applications of position and velocity to problems involving initial conditions.
Tangential and normal components of acceleration.

Unit 1.4 | Parametric Equations for Curves & 3D Space Worksheet due by Friday.

SESSION 11

8

Feb

SESSION 11

Review

Review

Sat 1:00 AM - 2:00 AM UTCFeb 8, 1:00 AM - 2:00 AM UTC

Unit 1.4 | Parametric Equations for Curves & 3D Space Worksheet Review
SESSION 12

10

Feb

SESSION 12

Other Topics

Other Topics

Mon 1:00 AM - 2:00 AM UTCFeb 10, 1:00 AM - 2:00 AM UTC

Arc Length & Tangent, Normal, & Binormal Vectors

Key Topics:
Integral formulations for arc length.
Tangent vectors: derivation and unitization for directional properties.
Normal and binormal vectors: understanding their geometric significance.
Application to problems involving curvature and path-following.

Curvature

Key Topics:
Curvature definitions: formulas involving derivatives and cross-products.
Relationships between curvature and motion parameters.
Special cases: circles, ellipses, and orbits.

Unit 1.5 | Motion, Arc-Length, & Kepler Worksheet due by Friday

SESSION 13

15

Feb

SESSION 13

Review

Review

Sat 1:00 AM - 2:00 AM UTCFeb 15, 1:00 AM - 2:00 AM UTC

Unit 1.5 | Motion, Arc-Length, & Kepler Worksheet Review

Unit 1 Survey

Unit 1 Test due by Monday
SESSION 14

17

Feb

SESSION 14

Other Topics

Other Topics

Mon 1:00 AM - 2:00 AM UTCFeb 17, 1:00 AM - 2:00 AM UTC

Level Curves; Partial Derivatives; Tangent Plane Approximation

Key Topics:
Level curves: definition, sketching, and analysis for functions of two variables.
Traces and their role in visualizing 3D functions.
Partial derivatives: calculating first-order derivatives and their geometric interpretations.
Tangent planes: equations and applications in local linearization

Unit 2.1 | Graphs, Limits, and Derivatives of Multi-Variable Functions Worksheet due by Friday
SESSION 15

22

Feb

SESSION 15

Review

Review

Sat 1:00 AM - 2:00 AM UTCFeb 22, 1:00 AM - 2:00 AM UTC

Unit 1 Test Review
Unit 2.1 | Graphs, Limits, and Derivatives of Multi-Variable Functions Worksheet Review
SESSION 16

24

Feb

SESSION 16

Orientation

Orientation

Mon 1:00 AM - 2:00 AM UTCFeb 24, 1:00 AM - 2:00 AM UTC

TBD (more sessions to be added later, same pattern).

Public Discussion

Please log in to see discussion on this series.

Jan 4 - Feb 24

8 weeks

60 mins

/ session

Next session on January 25, 2025

SCHEDULE

Saturdays

1:00AM

Mondays

1:00AM