6: Vector-Valued Functions of Several Variables
- Page ID
- 33462
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IN THIS CHAPTER we study the differential calculus of vector-valued functions of several variables.
- SECTION 6.1 reviews matrices, determinants, and linear transformations, which are integral parts of the differential calculus as presented here.
- SECTION 6.2 defines continuity and differentiability of vector-valued functions of several variables. The differential of a vector-valued function \(\mathbf{F}\) is defined as a certain linear transformation. The matrix of this linear transformation is called the differential matrix of \(\mathbf{F}\), denoted by \(\mathbf{F}'\). The chain rule is extended to compositions of differentiable vector-valued functions.
- SECTION 6.3 presents a complete proof of the inverse function theorem.
- SECTION 6.4. uses the inverse function theorem to prove the implicit function theorem.