query: why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem?
positive_passages.docid: 19279
positive_passages.text: dropping injectivity from multivariable change of variables
negative_passages.docid: 71260
negative_passages.text: Check differentiability of multivariable functions
negative_passages.docid: 47838
negative_passages.text: Lemma 3.3-7 and Theorem 3.6-2 in Kreyszig's "Introductory Functional Analysis With Applications": What if completeness is lost?
negative_passages.docid: 50850
negative_passages.text: Multivariable Calculus Book Reference
negative_passages.docid: 94165
negative_passages.text: Why is a map to a smaller dimensional space not injective?
negative_passages.docid: 149470
negative_passages.text: Intuitive Understanding About the Implicit Function Theorem
negative_passages.docid: 8502
negative_passages.text: Why aren't integration and differentiation inverses of each other?
negative_passages.docid: 95774
negative_passages.text: $\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$
negative_passages.docid: 27812
negative_passages.text: Understanding the differential $dx$ when doing $u$-substitution
negative_passages.docid: 25898
negative_passages.text: (Theoretical) Multivariable Calculus Textbooks
negative_passages.docid: 78572
negative_passages.text: Why do we restrict the definition of Lebesgue Integrability?
negative_passages.docid: 146188
negative_passages.text: Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
negative_passages.docid: 48920
negative_passages.text: Mean value theorem for integrals: how does the sign matter?
negative_passages.docid: 32642
negative_passages.text: The formalism behind integration by substitution
negative_passages.docid: 17440
negative_passages.text: Differentiation using first principles with rational powers
negative_passages.docid: 20801
negative_passages.text: Application of inverse function theorem for several variable functions
negative_passages.docid: 32722
negative_passages.text: Necessity of Brackets for Integration