دانلود کتاب An Illustrative Guide to Multivariable and Vector Calculus

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Cover
S Title
Title: An Illustrative Guide to Multivariable and Vector Calculus
Copyright © Springer Nature Switzerland AG 2020
Dedication
Preface
Acknowledgements
Contents
Important Formulæ
Multivariable calculus
Vector calculus
Chapter 1 Vectors and functions
1.A Some vector algebra essentials
1.B Introduction to sets
1.C Real-valued functions
1.D Coordinate systems
1.E Drawing or visualizing surfaces in $mathbbR3$
1.F Level sets
1.G Supplementary problems
Chapter 2 Differentiation of multivariable functions
2.A The derivative
2.B Limits and continuity
2.C Partial derivatives
2.D Differentiability of f:mathbbRn-3murightarrow mathbbR
2.E Directional derivatives and the gradient
2.F Higher-order derivatives
2.G Composite functions and the chain rule
2.H Implicit functions
2.I Taylor\'s formula and Taylor series
2.J Supplementary problems
Chapter 3 Applications of the differential calculus
3.A Extreme values of f:mathbbRn-3murightarrowmathbbR
3.B Extreme points: The complete story
3.C Differentials and error analysis
3.D Method of least squares
3.E Partial derivatives in equations: Partial differential equations
3.F Supplementary problems
Chapter 4 Integration of multivariable functions
4.A Multiple integrals
4.B Iterated integration in $mathbbR2$
4.C Integration over complex domains
4.D Generalized (improper) integrals in $mathbbR2$
4.E Change of variables in $mathbbR2$
4.F Triple integrals
4.G Iterated integration in $mathbbR3$
4.H Change of variables in $mathbbR3$
4.I $n$-tuple integrals
4.J Epilogue: Some practical tips for evaluating integrals
4.K Supplementary problems
Chapter 5 Vector calculus
5.A Vector-valued functions
5.B Vector fields
5.C Line integrals
5.D Surface integrals
5.E Gauss\'s theorem
5.F Green\'s and Stokes\'s theorems
5.G Supplementary problems
Glossary of symbols
Bibliography
Index