6: Differentiation on Eⁿ and Other Normed Linear Spaces Last updated Save as PDF Page ID 19203 Elias Zakon University of Windsor via The Trilla Group (support by Saylor Foundation) 6.1: Directional and Partial Derivatives 6.1.E: Problems on Directional and Partial Derivatives 6.2: Linear Maps and Functionals. Matrices 6.2.E: Problems on Linear Maps and Matrices 6.3: Differentiable Functions 6.3.E: Problems on Differentiable Functions 6.4: The Chain Rule. The Cauchy Invariant Rule 6.4.E: Further Problems on Differentiable Functions 6.5: Repeated Differentiation. Taylor’s Theorem 6.5.E: Problems on Repeated Differentiation and Taylor Expansions 6.6: Determinants. Jacobians. Bijective Linear Operators 6.6.E: Problems on Bijective Linear Maps and Jacobians 6.7: Inverse and Implicit Functions. Open and Closed Maps 6.7.E: Problems on Inverse and Implicit Functions, Open and Closed Maps 6.8: Baire Categories. More on Linear Maps 6.8.E: Problems on Baire Categories and Linear Maps 6.9: Local Extrema. Maxima and Minima 6.9.E: Problems on Maxima and Minima 6.10: More on Implicit Differentiation. Conditional Extrema 6.10.E: Further Problems on Maxima and Minima