Multivariable Functions Course
This course builds expertise in multivariable functions using gradients, Hessians, tangent planes, and level curves. Students learn to classify critical points and interpret real-world models such as temperature fields, enhancing mathematical analysis and problem-solving abilities for practical applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain essential skills for multivariable functions in this practical course. Analyze quadratic forms, complete the square, interpret level curves, and develop geometric understanding of gradients and directional derivatives. Construct tangent planes, estimate local changes, classify critical points using the Hessian, and communicate findings effectively in reports and technical writings.
Elevify advantages
Develop skills
- Classify critical points quickly with Hessian and second derivative tests.
- Compute gradients and connect partial derivatives to real-world data.
- Create linear approximations using tangent planes for multivariable estimates.
- Complete the square in two dimensions to identify extrema, level sets, and surface shapes.
- Interpret level curves for 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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