高等数学微积分课件 多元变量的函数

1、Chapter 13Functions of Several VariablesCopyright Houghton Mifflin Company. All rights reserved. 13-2Definition of a Function of Two VariablesCopyright Houghton Mifflin Company. All rights reserved. 13-3Figure 13.2Copyright Houghton Mifflin Company. All rights reserved. 13-4Figure 13.5 and Figure 13

2、.6 Copyright Houghton Mifflin Company. All rights reserved. 13-5Figure 13.7 and Figure 13.8Alfred B. Thomas/Earth ScenesUSGSCopyright Houghton Mifflin Company. All rights reserved. 13-6Figure 13.14Copyright Houghton Mifflin Company. All rights reserved. 13-7Figure 13.15Reprinted with permission. 199

3、7 Automotive Engineering Magazine. Society of Automotive Engineers, Inc.Copyright Houghton Mifflin Company. All rights reserved. 13-8Figure 13.17Copyright Houghton Mifflin Company. All rights reserved. 13-9Rotatable Graphs ICopyright Houghton Mifflin Company. All rights reserved. 13-10Rotatable Grap

4、hs IICopyright Houghton Mifflin Company. All rights reserved. 13-11Rotatable Graphs IIICopyright Houghton Mifflin Company. All rights reserved. 13-12Figure 13.18Copyright Houghton Mifflin Company. All rights reserved. 13-13Figure 13.19Copyright Houghton Mifflin Company. All rights reserved. 13-14Def

5、inition of the Limit of a Function of Two Variables and Figure 13.20Copyright Houghton Mifflin Company. All rights reserved. 13-15Definition of Continuity of a Function of Two VariablesCopyright Houghton Mifflin Company. All rights reserved. 13-16Theorem 13.1 Continuous Functions of Two VariablesCop

6、yright Houghton Mifflin Company. All rights reserved. 13-17Figure 13.24 and Figure 13.25Copyright Houghton Mifflin Company. All rights reserved. 13-18Theorem 13.2 Continuity of a Composite FunctionCopyright Houghton Mifflin Company. All rights reserved. 13-19Figure 13.28Copyright Houghton Mifflin Co

7、mpany. All rights reserved. 13-20Definition of Continuity of a Function of Three VariablesCopyright Houghton Mifflin Company. All rights reserved. 13-21Definition of Partial Derivatives of a Function of Two VariablesCopyright Houghton Mifflin Company. All rights reserved. 13-22Notation for First Par

8、tial DerivativesCopyright Houghton Mifflin Company. All rights reserved. 13-23Figure 13.29 and Figure 13.30Copyright Houghton Mifflin Company. All rights reserved. 13-24Theorem 13.3 Equality of Mixed Partial DerivativesCopyright Houghton Mifflin Company. All rights reserved. 13-25Definition of Total

9、 DifferentialCopyright Houghton Mifflin Company. All rights reserved. 13-26Definition of DifferentiabilityCopyright Houghton Mifflin Company. All rights reserved. 13-27Theorem 13.4 Sufficient Condition for DifferentiabilityCopyright Houghton Mifflin Company. All rights reserved. 13-28Figure 13.35Cop

10、yright Houghton Mifflin Company. All rights reserved. 13-29Theorem 13.5 Differentiability Implies ContinuityCopyright Houghton Mifflin Company. All rights reserved. 13-30Theorem 13.6 Chain Rule: One Independent Variable and Figure 13.39Copyright Houghton Mifflin Company. All rights reserved. 13-31Th

11、eorem 13.7 Chain Rule: Two Independent Variables and Figure 13.41Copyright Houghton Mifflin Company. All rights reserved. 13-32Theorem 13.8 Chain Rule: Implicit DifferentiationCopyright Houghton Mifflin Company. All rights reserved. 13-33Figure 13.42, Figure 13.43, and Figure 13.44Copyright Houghton

12、 Mifflin Company. All rights reserved. 13-34Definition of Directional DerivativeCopyright Houghton Mifflin Company. All rights reserved. 13-35Theorem 13.9 Directional DerivativeCopyright Houghton Mifflin Company. All rights reserved. 13-36Figure 13.45Copyright Houghton Mifflin Company. All rights re

13、served. 13-37Definition of Gradient of a Function of Two Variables and Figure 13.48Copyright Houghton Mifflin Company. All rights reserved. 13-38Theorem 13.10 Alternative Form of the Directional DerivativeCopyright Houghton Mifflin Company. All rights reserved. 13-39Theorem 13.11 Properties of the G

14、radientCopyright Houghton Mifflin Company. All rights reserved. 13-40Figure 13.50Copyright Houghton Mifflin Company. All rights reserved. 13-41Theorem 13.12 Gradient Is Normal to Level CurvesCopyright Houghton Mifflin Company. All rights reserved. 13-42Directional Derivative and Gradient for Three V

15、ariablesCopyright Houghton Mifflin Company. All rights reserved. 13-43Figure 13.56Copyright Houghton Mifflin Company. All rights reserved. 13-44Definition of Tangent Plane and Normal LineCopyright Houghton Mifflin Company. All rights reserved. 13-45Theorem 13.13 Equation of Tangent PlaneCopyright Ho

16、ughton Mifflin Company. All rights reserved. 13-46Figure 13.61Copyright Houghton Mifflin Company. All rights reserved. 13-47Theorem 13.14 Gradient Is Normal to Level SurfacesCopyright Houghton Mifflin Company. All rights reserved. 13-48Figure 13.63 and Theorem 13.15 Extreme Value TheoremCopyright Ho

17、ughton Mifflin Company. All rights reserved. 13-49Definition of Relative Extrema and Figure 13.64Copyright Houghton Mifflin Company. All rights reserved. 13-50Definition of Critical PointCopyright Houghton Mifflin Company. All rights reserved. 13-51Figure 13.65Copyright Houghton Mifflin Company. All

18、 rights reserved. 13-52Theorem 13.16 Relative Extrema Occur Only at Critical PointsCopyright Houghton Mifflin Company. All rights reserved. 13-53Figure 13.68Copyright Houghton Mifflin Company. All rights reserved. 13-54Theorem 13.17 Second Partials TestCopyright Houghton Mifflin Company. All rights reserved. 13-55Figure 13.73 and Figure 13.74Copyright Houghton Mifflin Company. All rights reserved. 13-56Figure 13.75Copyright Houghton Mifflin Company. All rights reserved. 13-57Theorem 13.18 Least Squar