Calculus 1
 |
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 intermediate value 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 intermediate value 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 I Series and Taylor Expansion
Chapter 1: Water Supply
Section 1 Sequences and Series
Section 2 Geometric series
Section 3 Comparative Judgment Method
Section 4: Square root test
Section 5 Ratio Determination Method
Section 6 Integral Test
Section 7 Alternating series and absolutely convergent series
Appendix 8: A Story of Mistakes
Chapter 2 Power Series
Section 1 Power Series
Section 2 Power series and radius of convergence
Section 3 Exponential functions and power series
Section 4 Trigonometric Functions and Power Series
Section 5 Hyperbolic Functions
Section 6: Inverse function theorem, inverse trigonometric functions, and power series
Section 7 Appendix: Differential equations, mean value theorem, etc.
Chapter 3 Taylor Expansion
Section 1 L'Hôpital's Rule
Section 2 Infinitesimals and Approximate Polynomials
Section 3 Lagrange's theorem for the remaining terms
Section 4 Taylor expansion around an arbitrary point
Section 5 Appendix: Proof of L'Hôpital's Rule and Uninterpretable Functions
Part II Vectors and Matrices
Chapter 4 Coordinate Space and Coordinate Systems
Section 1 Coordinate Space
Section 2 Polar Coordinates
Section 3 Cylindrical and Spherical Coordinate Systems
Section 4 Appendix: Euclidean Space
Chapter 5 Vectors
Section 1 Parallel Movement
Section 2: Directional Lines and Vectors
Section 3 Dot Product of Vectors
Section 4 Equations of planes and lines, center of gravity
Section 5 Primary Independence and Primary Dependence
Section 6 Appendix: Basis and Dimension of Coordinate Space
Chapter 6 Matrices and Linear Mapping
Section 1: Matrix
Section 2 Linear mapping
Section 3 Appendix: Transformations and Matrix Limits
Chapter 7 Square Matrices and Determinants
Section 1 Inverse Matrix
Section 2 Substitution
Section 3 Determinant
Section 4 Appendix: Signs of substitution and properties of determinants
Chapter 8 Three-Dimensional Space and Vector Cross Product
Section 1 Vector Product
Section 2 Appendix: Vector Product and Rotational Motion
Part III Curves
Chapter 9 Curves
Section 1 Parameterized Curves
Section 2 Acceleration
Section 3 Plane Curves and Polar Coordinates
Section 4 Reparameterization
Section 5 Length of the curve
Section 6: Length and reparameterization of the arc
Section 7 Line Integral
Section 8 Appendix: Kepler's Laws, Curvature, Catenary Lines, and Isochrones
supplement
1.
Collection of symbols
2.
integral table
3.
Hyperbolic and trigonometric functions
4.
square root table
5.
log table
6.
Math Dictionary 1
7.
Practice problem solutions
References
Search
Part I Series and Taylor Expansion
Chapter 1: Water Supply
Section 1 Sequences and Series
Section 2 Geometric series
Section 3 Comparative Judgment Method
Section 4: Square root test
Section 5 Ratio Determination Method
Section 6 Integral Test
Section 7 Alternating series and absolutely convergent series
Appendix 8: A Story of Mistakes
Chapter 2 Power Series
Section 1 Power Series
Section 2 Power series and radius of convergence
Section 3 Exponential functions and power series
Section 4 Trigonometric Functions and Power Series
Section 5 Hyperbolic Functions
Section 6: Inverse function theorem, inverse trigonometric functions, and power series
Section 7 Appendix: Differential equations, mean value theorem, etc.
Chapter 3 Taylor Expansion
Section 1 L'Hôpital's Rule
Section 2 Infinitesimals and Approximate Polynomials
Section 3 Lagrange's theorem for the remaining terms
Section 4 Taylor expansion around an arbitrary point
Section 5 Appendix: Proof of L'Hôpital's Rule and Uninterpretable Functions
Part II Vectors and Matrices
Chapter 4 Coordinate Space and Coordinate Systems
Section 1 Coordinate Space
Section 2 Polar Coordinates
Section 3 Cylindrical and Spherical Coordinate Systems
Section 4 Appendix: Euclidean Space
Chapter 5 Vectors
Section 1 Parallel Movement
Section 2: Directional Lines and Vectors
Section 3 Dot Product of Vectors
Section 4 Equations of planes and lines, center of gravity
Section 5 Primary Independence and Primary Dependence
Section 6 Appendix: Basis and Dimension of Coordinate Space
Chapter 6 Matrices and Linear Mapping
Section 1: Matrix
Section 2 Linear mapping
Section 3 Appendix: Transformations and Matrix Limits
Chapter 7 Square Matrices and Determinants
Section 1 Inverse Matrix
Section 2 Substitution
Section 3 Determinant
Section 4 Appendix: Signs of substitution and properties of determinants
Chapter 8 Three-Dimensional Space and Vector Cross Product
Section 1 Vector Product
Section 2 Appendix: Vector Product and Rotational Motion
Part III Curves
Chapter 9 Curves
Section 1 Parameterized Curves
Section 2 Acceleration
Section 3 Plane Curves and Polar Coordinates
Section 4 Reparameterization
Section 5 Length of the curve
Section 6: Length and reparameterization of the arc
Section 7 Line Integral
Section 8 Appendix: Kepler's Laws, Curvature, Catenary Lines, and Isochrones
supplement
1.
Collection of symbols
2.
integral table
3.
Hyperbolic and trigonometric functions
4.
square root table
5.
log table
6.
Math Dictionary 1
7.
Practice problem solutions
References
Search
GOODS SPECIFICS
- Date of issue: February 10, 2023
- Page count, weight, size: 484 pages | 188*257*30mm
- ISBN13: 9788952131850
- ISBN10: 8952131851
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