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Vector Calculus
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2. Differentiation in Several Variables
3. Vector-Valued Functions
4. Maxima and Minima in Several Variables
5. Multiple Integration
6. Line Integrals
7. Surface Integrals and Vector Analysis
8. Vector Analysis iin Higher Dimensions
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1 bod
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Advanced Calculus of Several Variables
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II. Multivariable Differential Calculus
III. Successive Approximations and Implicit Functions
IV. Multiple Integrals
V. Line and Surface Integrals; Differential Forms and Stokes' Theorem
VI. The Calculus of Variations
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Worked Problems in Applied Mathematics
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2. Some Special Methods for Solving Hyperbolic and Elliptic Equations
3. Steady-state Harmonic Oscillations
4. The Fourier Method
5. The Eigenfunction Method for Solving Inhomogeneous Problems
6. Integral Transforms
7. Curvilinear Coordinates
8. Integral Equations
Solutions
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Real and Complex Analysis
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1. Abstract Integration
2. Positive Borel Measures
3. L p -Spaces
4. Elementary Hilbert Space Theory
5. Examples of Banach Space Techniques
6. Complex Measures
7. Integration on Product Spaces
8. Differentiation
9. Fourier Transforms
10. Elementary Properties of Holomorphic Functions
11. Harmonic Functions
12. The Maximum Modulus Principle
13. Approximation by Rational Functions
14. Conformal Mapping
15. Zeros of Ho...
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6 biedingen
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Complex Analysis
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II. Complex Functions
III. Complex Integration
IV. Infinite Sequences
V. The Dirichlet Problem
VI. Multiple-Valued Functions
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Linear Algebra
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2. Vector Spaces
3. Matrices
4. Linear Mappings
5. Linear Maps and Matrices
6. Scalar Products and Orthogonality
7. Determinants
8. Bilinear Forms and the Standard Operators
9. Polynomials and Matrices
10. Triangulation of Matrices and Linear Maps
11. Spectral Theorem
12. Polynomials and Primary Decomposition
13. Multilinear Products
14. Groups
15. Rings
Appendix 1. Convex Sets
Appendix 2. Odds and Ends
Appendix 3. Angles
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A First Course in Wavelets with Fourier Analysis
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1. Fourier Series
2. The Fourier Transform
3. Discrete Fourier Analysis
4. Haar Wavelet Analysis
5. Multiresolution Analysis
6. The Daubechies Wavelets
7. Other Wavelet Topics
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Ordinary Differential Equations
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I. Introductory
II. Elementary methods of integration
III. The existence and nature of solutions of ordinary differential equations
IV. Continuous transformation-groups
V. The general theory of linear differential equations
VI. Linear equations with constant coefficients
VII. The solution of linear differential equations in an infinite form
VIII. The solution of linear differential equations by definite int...
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Theory of Ordinary Differential Equations
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2. Existence and Uniqueness of Solutions (continued)
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4. Linear Systems with Isolated Singularities: Singularities of the First Kind
5. Linear Systems with Isolated Singularities: Singularities of the Second Kind
6. Asymptotic Behavior of Linear Systems Containing a Large Parameter
7. Self-adjoint Eigenvalue Problems on a Finite Interval
8. Oscillat...
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Homology Theory
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1. The Topology of Polyhedra
2. Homology Theory of a Simplicial Complex
3. Chain Complexes
4. The Contrahomology Ring for Polyhedra
5. Abian Groups and Homological Algebra
6. The Fundamental Group and Covering Spaces
Part II. General Homology Theory
7. Contrahomology and Maps
8. Singular Homology Theory
9. The Singular Contrahomology Ring
10. Spectral Homology Theory and Homology Theory of Groups
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Geometric Transformations
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1. Translations
2. Half Turn and Rotation
II. Symmetry
1. Refection and Glide Reflection
2. Directly Congruent and Oppositely Congruent Figures. Classification of Isometries of the Plane
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An Introduction to Plane Projective Geometry
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II. Orthogonal Projection
III. General or Conical Projection
IV. Homogeneous Coordinates and the Straight Line
V. Perspectivity and Projectivity
VI. Projective Transformations
VII. Cross-ratio
VIII. The Generation of the Conic
IX. The Conic: General Properties
X. Special Forms of the Equations of the Conic
XI. Quadrilaterals and Quadrangles
XII. Pencils and Ranges of Conics
XIII. P...
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Elementary Geometry from an Advanced Standpoint
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Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry fr...
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Finite Mathematics
Finite MathematicsRobert F. Brown, Brenda W. Brown1. Matrices and Systems of Linear Equations
2. Linear Programming
3. Probability
4. More Probability
5. Markov Chains
6. Game Theory
7. Graphs and Networks
8. Mathematics of Finance
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Univalent Functions - Selected Topics
Univalent Functions - Selected TopicsGlenn Schober1. Functions with positive real part
2. Special classes: convex, starlike, real, typically real, close-to-convex, bounded boundary rotation
3. The Pólya-Schoenberg conjecture
4. Representation of continuous linear functionals
5. Faber polynomials
6. Extremal length and equicontinuity
7. Compact families ℱ(D,ℓ1,ℓ2,P,Q) of univalent functions normalized by two linear functionals
8. Properties of extreme points for some compact families ℱ(D...
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Theta Functions on Riemann Surfaces
Theta Functions on Riemann SurfacesJohn D. FayI. Riemann's theta function
II. The prime-form
III. Degenerate Riemann surfaces
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V. Ramified double coverings
VI. Bordered Riemann surfaces
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Analytic Capacity and Measure
Analytic Capacity and MeasureJohn GarnettI. Analytic capacity
II. The Cauchy transform
III. Hausdorff measure
IV. Some examples
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Extremum Problems for Bounded Univalent Functions
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1. Introduction
2. Löwner-functions
3. Generalized Löwner-functions
4. A generalization of the class S(b)
5. Functions with bounded boundary rotation
II. Variation of the extremum function
1. Variation of Green's function
2. The Schiffer-condition for S(b)-functions
3. The coefficient a3
III. The area principle
1. The power inequality
2. Application to the coefficient a3 and a4
3. Optimization of parameters for...
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Classification Theory of Riemannian Manifolds
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O. Laplace-Beltrami operator
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II. Quasiharmonic functions
III. Bounded biharmonic functions
IV. Dirichlet finite biharmonic functions
V. Bounded Dirichlet finite biharmonic functions
VI. Harmonic, quasiharmonic, and biharmonic degeneracies
VII. Riesz representation of biharmonic functions
VIII. Biharmonic Green’s function γ
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Topics in Nevanlinna Theory
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II. Equidimensional higher dimensional theory
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