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Language | English |

Pages | 857 |

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Measurement | 46.00 MB |

## Problem Solver Advanced Calculus Contents

POINT SET THEORY

- Units and Sequences
- Closed and Open Units and Norms
- Metric Areas

VECTOR SPACES

- Definitions
- Properties
- Invertibility
- Diagonalization
- Orthogonality

CONTINUITY

- Displaying {that a} Perform is Steady
- Discontinuous Capabilities
- Uniform Continuity and Associated Matters
- Paradoxes of Continuity

ELEMENTS OF PARTIAL DIFFERENTIATION

- Partial Derivatives
- Differentials and the Jacobian
- The Chain Rule
- Gradients and Tangent Planes
- Directional Derivatives
- Potential Capabilities

THEOREMS OF DIFFERENTIATION

- The Imply Worth Theorems
- Taylor’s Theorem
- The Implicit Perform Theorem

MAXIMA AND MINIMA

- Relative Most and Relative Minimal
- Extremes Topic to a Constraint
- Extremes in a Area
- Methodology of Lagrange Multipliers
- Capabilities of Three Variables

THEORYOFINTEGRATION

- Riemann Integrals
- Stieltjes Integrals

LINE INTEGRALS

- Methodology of Parametrization
- Methodology of Discovering Potential Perform (Precise Differential)
- Independence of Path
- Inexperienced’s Theorem

SURFACE INTEGRALS

- Change of Variables System
- Space
- Integral Perform over a Floor
- Integral Vector Area over a Floor
- Divergence Theorem
- Stokes’s Theorem
- Differential Kind

MISCELLANEOUS PROBLEMS AND APPLICATIONS

MISCELLANEOUS PROBLEMS AND APPLICATIONS

IMPROPER INTEGRALS

- Improper Integrals of the first, 2nd, and third Form
- Absolute and Uniform Convergence
- Analysis of Improper Integrals
- Gamma and Beta Capabilities

INFINITE SEQUENCES

- Convergence of Sequences
- Restrict Superior and Restrict Inferior
- Sequence of Capabilities

INFINITE SERIES

- Checks for Convergence and Divergence
- Collection of Capabilities
- Operations on Collection
- Differentiation and Integration of Collection
- Estimates of Error and Sums
- Cesaro Summability
- Infinite Merchandise

POWER SERIES

- Interval of Convergence
- Operations on Energy Collection

FOURIER SERIES

- Definitions and Examples
- Convergence Questions
- Additional Representations
- Purposes

COMPLEX VARIABLES

- Complicated Numbers
- Complicated Capabilities and Differentiation
- Collection
- Integration

LAPLACE TRANSFORMS

- Definitions and Easy Examples
- Fundamental Properties of Laplace Transforms
- Step Capabilities and Periodic Capabilities
- The Inversion Problem
- Purposes

FOURIER TRANSFORMS

- Definition of Fourier Transforms
- Properties of Fourier Transforms
- Purposes of Fourier Transforms

DIFFERENTIAL GEOMETRY

- Curves
- Surfaces

MISCELLANEOUS PROBLEMS AND APPLICATIONS

- Miscellaneous Purposes
- Elliptic Integrals
- Bodily Purposes

INDEX

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