Multivariable Functions Course
Master multivariable functions through gradients, Hessians, tangent planes, and level curves. Learn to classify critical points and interpret real-world models like temperature fields for sharper mathematical analysis and problem-solving.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
Master core tools for working with multivariable functions in this focused, application-driven course. You will analyze quadratic forms, complete the square, interpret level curves, and build geometric insight into gradients and directional derivatives. Learn to construct tangent planes, estimate local change, classify critical points with the Hessian, and clearly communicate results in reports and technical documents.
Elevify advantages
Develop skills
- Classify critical points: apply Hessian and second derivative tests fast.
- Compute and interpret gradients: link partial derivatives to real data.
- Build linear approximations: use tangent planes for quick multivariable estimates.
- Complete the square in 2D: reveal extrema, level sets, and surface geometry.
- Analyze level curves: read contour shape, steepness, and physical meaning.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workloadWhat our students say
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