Multivariable Functions Course
This course equips learners with key techniques for multivariable functions, including gradients, Hessians, tangent planes, and level curves. Participants will classify critical points, interpret models such as temperature fields, and enhance mathematical analysis and problem-solving for real-world applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain essential skills for multivariable functions via practical applications. Explore quadratic forms, completing the square, level curves, gradients, directional derivatives, tangent planes, local change estimation, critical point classification using the Hessian, and effective reporting in technical documents.
Elevify advantages
Develop skills
- Classify critical points using Hessian and second derivative tests efficiently.
- Compute gradients and connect partial derivatives to practical data interpretation.
- Construct linear approximations with tangent planes for accurate multivariable estimates.
- Complete the square in two dimensions to identify extrema, level sets, and surface geometry.
- Analyze level curves to understand contour shapes, steepness, and physical significance.
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 workload.What our students say
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