Every skill mapped
Multivariable Calculus on Aristotle is 131 skills across 5 units, each linked to the skills it builds on.
Multivariable Calculus
Your child's own
Multivariable Calculus tutor
Pioneered by Stanford AI researchers and learning scientists, Aristotle is the world's first voice-based AI tutor. A full Multivariable Calculus course, mapped skill by skill.
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Fits your child's Multivariable Calculus class
Mapped skill by skill
Your class or your curiosity
Share a syllabus, textbook, or reading list and sessions follow it, or let Aristotle lead the way through the course.
Your child's pace
Aristotle moves on when a skill is mastered and slows down when it isn't, so no time goes to what your child already knows.
Features
All the tools of a great tutor.
Talk things through, work side by side, and come back next time to a tutor who remembers where you left off.
Learn out loud
Ask questions out loud, hear explanations in Aristotle’s voice, and interrupt whenever you need to.
An interactive whiteboard
Aristotle draws steps, diagrams, and images to help you learn visually.
Practice built for you
Get practice problems tailored to the exact topics you’re struggling with.
65 subjects and counting
From middle-school math to AP exams to SAT/ACT prep. We also build custom plans matched to state standards and specific courses.
Review with ease
Revisit session summaries, session whiteboards, and uploads in one place.
Upload your own materials
Aristotle can read and navigate any PDFs and images with the learner. That includes textbooks with hundreds of pages!
Personalized tracking
We break all subjects down into granular skills, then track mistakes and mastery on each one. Parents can see the whole picture at a glance.
A tutor that knows you
Aristotle remembers every session: what you’ve covered, where you got stuck, how you like things explained. It picks up right where you left off.
The curriculum
131 Multivariable Calculus skills, personalized to your child
Aristotle is designed to always know what to teach at exactly the right time.
Sample curriculum
Not startedIn progressMastered* Click a topic to see the skills inside
* Click a topic to see the skills inside
Vectors and the Geometry of Space
Vector Functions and Space Curves
Partial Derivatives
Multiple Integrals
Vector Calculus
Multivariable Calculus tutoring curriculum131 skills across 5 units
Vectors and the Geometry of Space
This unit builds the language of three-dimensional space. Topics: Three-Dimensional Coordinate Systems, Vectors, The Dot Product, The Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces.
Vector Functions and Space Curves
This unit studies functions whose input is a single parameter and whose output is a vector, so that one moving vector traces a curve through space. Topics: Vector Functions and Space Curves, Derivatives and Integrals of Vector Functions, Arc Length and Reparametrization, Curvature and the TNB Frame, Motion in Space.
Partial Derivatives
This unit extends differential calculus to functions of several variables. Topics: Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations, The Chain Rule, Directional Derivatives and the Gradient Vector, Maximum and Minimum Values, Lagrange Multipliers.
Multiple Integrals
Multiple integrals extend integration from a single variable to functions defined over two- and three-dimensional regions, accumulating infinitely many infinitesimal pieces into volumes, masses, and averages. Topics: Double Integrals over Rectangles, Double Integrals over General Regions, Double Integrals in Polar Coordinates, Applications of Double Integrals, Surface Area, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables in Multiple Integrals.
Vector Calculus
Vector calculus is the capstone of multivariable calculus: it develops the calculus of vector fields (functions that attach a vector to every point of the plane or of space) and the integrals that measure how such a field acts along a curve or across a surface. Topics: Vector Fields, Line Integrals, The Fundamental Theorem for Line Integrals, Green's Theorem, Curl and Divergence, Parametric Surfaces and Their Areas, Surface Integrals, Stokes' Theorem, The Divergence Theorem.
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Common questions about online Multivariable Calculus tutoring
A few things you might wonder before getting started.
What does Aristotle's Multivariable Calculus course cover?
Aristotle's Multivariable Calculus course tracks 131 skills across 5 units, including Vectors and the Geometry of Space, Vector Functions and Space Curves, and Partial Derivatives. Every skill is linked to the skills it builds on, so the tutor always knows which parts of Multivariable Calculus your child has mastered and what to teach next.
Who is Aristotle's Multivariable Calculus course for?
What does a Multivariable Calculus tutoring session look like?
Does Aristotle follow my child's Multivariable Calculus class?
Can Aristotle help if my child is struggling with Multivariable Calculus?
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