Multivariable Functions Course
This course equips you with essential skills in multivariable calculus, focusing on gradients, Hessians, tangent planes, and level curves. You will learn to classify critical points, interpret real-world applications such as temperature distributions, and enhance your analytical and problem-solving abilities for advanced mathematical modelling and practical scenarios.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
Gain expertise in handling multivariable functions via this practical course. You will study quadratic forms, complete the square, understand level curves, and develop geometric intuition for gradients and directional derivatives. Master constructing tangent planes, approximating local changes, classifying critical points using the Hessian, and presenting findings effectively in reports and technical writings.
Elevify advantages
Develop skills
- Classify critical points using Hessian and second derivative tests efficiently.
- Compute and interpret gradients by connecting partial derivatives to actual data.
- Construct linear approximations with tangent planes for rapid multivariable estimates.
- Complete the square in two dimensions to identify extrema, level sets, and surface shapes.
- Analyse level curves to understand contour shapes, steepness, and their 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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