Mastering Partial Derivatives

Overview

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Learn to master partial derivatives through this comprehensive 40-hour course covering functions of several variables. Identify domains and ranges of multivariable functions while analyzing their continuity properties. Compute first-order partial derivatives and progress to calculating higher-order and mixed partial derivatives for complex multivariable functions. Apply the chain rule specifically in the context of partial differentiation and master the computation of directional derivatives. Develop skills in using partial derivatives to find tangent planes and normal lines to surfaces, then advance to determining extremum points of multivariable functions. Practice solving real-world application problems involving rates of change and optimization using partial derivative techniques, building a solid foundation in multivariable calculus essential for advanced mathematics, physics, and engineering applications.

Syllabus

At the end of this session, the learners/participants should be able to identify the domain and range of functions of several variables.
At the end of this session, the learners/participants should be able to discuss the continuity of functions of several variables.
At the end of this session, the learners/participants should be able to perform partial derivatives.
At the end of this session, the learners/participants should be able to apply the chain rule in partial derivatives
At the end of this session, the learners/participants should be able to perform directional derivatives
At the end of this session, the learners/participants should be able to apply concept of partial derivatives into finding tangent planes and normal lines
At the end of this session, the learners/participants should be able to apply concept of partial derivatives into finding extrema
Identify the domain, range and analyse the continuity of a function of several variables.
Compute partial derivatives of functions with multiple variables.
Calculate higher-order and mixed partial derivatives for functions with multiple variables.
Apply the concept of partial derivatives to solve practical application questions, such as calculating rates of change and determining extremum points.
Determine extremum points of functions of several variables using partial derivatives.