Calculus 2
 |
Description
Book Introduction
For freshmen in science departments
Differential and integral calculus textbooks
Calculus is a basic and essential liberal arts subject.
The third revised edition of Calculus, consisting of two volumes, covers concepts and applications of properties of real numbers, the maximum-minimum theorem, the interval theorem, the mean value theorem, the critical point theorem, convex functions, Taylor expansions, vectors, matrices and determinants, Lagrange multipliers, vector fields and line integrals, and Stokes' theorem.
Also, the most important theorem in calculus, the 'fundamental theorem of calculus' in a broad sense, shows the duality between functions and spaces.
In this sense, understanding Stokes' theorem can be seen as one of the most important goals of this book.
In this revised edition, the amount of learning has been reduced by moving 'Cauchy's Mean Value Theorem', 'Kepler's Laws of Planetary Motion', and 'Curvature of Curves' to the appendix, making it a much easier book than the previous edition.
Differential and integral calculus textbooks
Calculus is a basic and essential liberal arts subject.
The third revised edition of Calculus, consisting of two volumes, covers concepts and applications of properties of real numbers, the maximum-minimum theorem, the interval theorem, the mean value theorem, the critical point theorem, convex functions, Taylor expansions, vectors, matrices and determinants, Lagrange multipliers, vector fields and line integrals, and Stokes' theorem.
Also, the most important theorem in calculus, the 'fundamental theorem of calculus' in a broad sense, shows the duality between functions and spaces.
In this sense, understanding Stokes' theorem can be seen as one of the most important goals of this book.
In this revised edition, the amount of learning has been reduced by moving 'Cauchy's Mean Value Theorem', 'Kepler's Laws of Planetary Motion', and 'Curvature of Curves' to the appendix, making it a much easier book than the previous edition.
- You can preview some of the book's contents.
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index
preface
Part IV: Multivariable Functions and Differentiation
Chapter 10 Multivariable Functions
Section 1 Graphs and isosurfaces
Section 2 Continuous Functions
Section 3 Directional Differentiation and Partial Differentiation
Section 4 Differentiable Functions
Section 5 Chain Law
Section 6 Slope vector and isosurface
Section 7 Appendix: First-class functions, open sets, closed sets, and bounded sets
Chapter 11: Maximum and Minimum Problems and Higher-Order Differentiation
Section 1 Differentiation in integral symbols
Section 2 Second-order differentiation
Section 2 Line Integral
Section 3 Gradient vector field and potential function
Section 4 Total Differentiation and Differential Form
Section 5 Appendix: Poincaré's help theorem, principles of action, and dynamical systems
Part V: Multiple Integrals and Green's Theorem
Chapter 14 Multiple Integrals
Section 1 Area and Volume
Section 2 Multiple Integrals
Section 3: Pubini Theorem
Section 4 Substitution Integration Method
Section 5 Appendix: Proof of Fubini's theorem, Moments of Inertia
Chapter 15: Divergence of Vector Fields and Green's Theorem
Section 1. Vector Fields and Divergence
Section 2 Boundaries and Directions
Section 3 Plane Vector Fields and Divergence Theorem
Section 4 Plane vector fields and degrees of rotation
Section 5 Green Theorem
Section 6 Appendix: Divergent Functions and Volume Changes
Part VI: Surface Integrals, Divergence Theorem, and Stokes' Theorem
Chapter 16 Surfaces and Surface Integrals
Section 1: Surface
Section 2 Area of a curved surface
Section 3 Area integral
Section 4 Vector Fields and Surface Integrity
Chapter 17 Divergence Theorem
Section 1 Divergence Theorem
Section 2 Gauss's Theorem
Section 3 Appendix: Proof of the Divergence Theorem and Newton's Gravitational Formula
Chapter 18 Rotating Fields and Stokes' Theorem
Section 1 Rotating field
Section 2 Stokes' Theorem
Section 3 Appendix: Proof of Stokes' theorem and differentiation of vector fields
supplement
Math Dictionary 2
Practice problem solutions
References
Search
Part IV: Multivariable Functions and Differentiation
Chapter 10 Multivariable Functions
Section 1 Graphs and isosurfaces
Section 2 Continuous Functions
Section 3 Directional Differentiation and Partial Differentiation
Section 4 Differentiable Functions
Section 5 Chain Law
Section 6 Slope vector and isosurface
Section 7 Appendix: First-class functions, open sets, closed sets, and bounded sets
Chapter 11: Maximum and Minimum Problems and Higher-Order Differentiation
Section 1 Differentiation in integral symbols
Section 2 Second-order differentiation
Section 2 Line Integral
Section 3 Gradient vector field and potential function
Section 4 Total Differentiation and Differential Form
Section 5 Appendix: Poincaré's help theorem, principles of action, and dynamical systems
Part V: Multiple Integrals and Green's Theorem
Chapter 14 Multiple Integrals
Section 1 Area and Volume
Section 2 Multiple Integrals
Section 3: Pubini Theorem
Section 4 Substitution Integration Method
Section 5 Appendix: Proof of Fubini's theorem, Moments of Inertia
Chapter 15: Divergence of Vector Fields and Green's Theorem
Section 1. Vector Fields and Divergence
Section 2 Boundaries and Directions
Section 3 Plane Vector Fields and Divergence Theorem
Section 4 Plane vector fields and degrees of rotation
Section 5 Green Theorem
Section 6 Appendix: Divergent Functions and Volume Changes
Part VI: Surface Integrals, Divergence Theorem, and Stokes' Theorem
Chapter 16 Surfaces and Surface Integrals
Section 1: Surface
Section 2 Area of a curved surface
Section 3 Area integral
Section 4 Vector Fields and Surface Integrity
Chapter 17 Divergence Theorem
Section 1 Divergence Theorem
Section 2 Gauss's Theorem
Section 3 Appendix: Proof of the Divergence Theorem and Newton's Gravitational Formula
Chapter 18 Rotating Fields and Stokes' Theorem
Section 1 Rotating field
Section 2 Stokes' Theorem
Section 3 Appendix: Proof of Stokes' theorem and differentiation of vector fields
supplement
Math Dictionary 2
Practice problem solutions
References
Search
GOODS SPECIFICS
- Date of issue: February 10, 2023
- Page count, weight, size: 424 pages | 188*257*30mm
- ISBN13: 9788952131867
- ISBN10: 895213186X
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