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Geometric Transformations
Geometric TransformationsI.M. YaglomI. Displacements
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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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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Ordinary Differential Equations
Ordinary Differential EquationsE.L. IncePart I. Differential Equations in the Real Domain
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
Theory of Ordinary Differential EquationsEarl A. Coddington, Norman Levinson1. Existence and Uniqueness of Solutions
2. Existence and Uniqueness of Solutions (continued)
3. Linear Differential Equations
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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Operations Research - An Introduction
Operations Research - An IntroductionHamdy A. TahaI. Linear, Dynamic, and Integer Programming
II. Probabilistic Models
III. Nonlinear Programming
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Homology Theory
Homology TheoryP.J. Hilton, S. WyliePart I. Homology Theory of Polyhedra
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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An Introduction to Plane Projective Geometry
An Introduction to Plane Projective GeometryE.J. Hopkins, J.S. HailsI. Fundamental Elements and Axioms of Incidence
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
Elementary Geometry from an Advanced StandpointEdwin E. MoiseOne of the purposes of this book is to reexamine geometry, to clean up behind introductory courses, furnishing valid definitions and valid proofs for concepts and theorems which were already known, at least in some sense and some form.
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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Principles of Operations Research
Principles of Operations ResearchHarvey M. Wagner1. The Art and Science of Executive Decisions
2. Formulation of Linear Optimization Models
3. Algebraic and Geometric Representations of Linear Optimization Models
4. Simplex Method of Solution
5. Sensitivity Testing and Duality
6. Transportation Problem
7. Shortest-Route and other Network Models
8. Introduction to Dynamic Optimization Models
9. Dynamic Optimization of Inventory Scheduling
10. Other Examples of Dynamic Programming
11. Decision-Mak...
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Infinite Sequences and Series
Infinite Sequences and SeriesKonrad KnoppTranslated by Frederick Bagemihl
1. Introduction and Prerequisites
2. Sequences and Series
3. The Main Tests for Infinite Series. Operating with Convergent Series
4. Power Series
5. Development of the Theory of Convergence
6. Expansion of the Elementary Functions
7. Numerical and Closed Evaluation of Series
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Functions of Several Variables
Functions of Several VariablesWendell H. Fleming1. Euclidean Spaces, Convexity
2. Differentiation of Real-Valued Functions
3. Vector-Valued Functions of One Variable
4. Vector-Valued Functions of Several Variables
5. Integration
6. Exterior Algebra and Differential Calculus
7. Integration on Manifolds
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Vector and Tensor Analysis
Vector and Tensor AnalysisLouis BrandI. Vector Algebra
II. Motor Algebra
III. Vector Functions of One Variable
IV. Linear Vector Functions
V. Differential Invariants
VI. Integral Transformations
VII. Hydrodynamics
VIII. Geometry of a Surface
IX. Tensor Analysis
X. Quaternions
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The Art and Theory of Dynamic Programming
The Art and Theory of Dynamic ProgrammingStuart E. Dreyfus, Averill M. Law1. Elementary Path Problems
2. Equipment Replacement
3. Resource Allocation
4. The General Shortest-Path Problem
5. The Traveling-Salesman Problemx
6. Problems with Linear Dynamics and Quadratic Criteria
7. Discrete-Time Optimal-Control Problems
8. The Cargo-Loading Problem
9. Stochastic Path Problems
10. Stochastic Equipment Inspection and Replacement Models
11. Dynamic Inventory Systems
12. Inventory Models with Special ...
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Mathematical Methods for Physicists
Mathematical Methods for PhysicistsGeorge Arfken1. Vector Analysis
2. Coordinate Systems
3. Tensor Analysis
4. Determinants, Matrices, and Group Theory
5. Infinite Series
6. Functions of a Complex Variable I
7. Functions of a Complex Variable II: Calculus of Residues
8. Differential Equations
9. Sturm-Liouville Theory - Orthogonal Functions
10. The Gamma Function (Factorial Function)
11. Bessel Functions
12. Legendre Functions
13. Special Functions
14. Fourier Series
15. Integral Trnasforms
16. ...
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Differential and Integral Calculus volume I
Differential and Integral Calculus volume IR. CourantTranslated from the German by E.J. McShane
I. Introduction
II. The fundamental ideas of the integral and differential calculus
III. Differentiation and integration of the elementary functions
IV. Further development of the integral calculus
V. Applications
VI. Taylor's theorem and the approximate expression of functions by polynomials
VII. Numerical methods
VIII. Infinite series and other limiting processes
IX. Fourier series
X. A sketch of ...
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Differential and Integral Calculus volume II
Differential and Integral Calculus volume IIR. CourantTranslated from the German by E.J. McShane
I. Preliminary remarks on analytical geometry and vector analysis
II. Functions of several variables and their derivatives
III. Developments and applications of the differential calculus
IV. Multiple integrals
V. Integration over regions in several dimensions
VI. Differential equations
VII. Calculus of variations
VIII. Functions of a complex variable
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Finite-Dimensional Vector Spaces
Finite-Dimensional Vector SpacesPaul R. HalmosI. Spaces
II. Transformations
III. Orthogonality
IV. Analysis
Appendix. Hilbert Space
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Introduction to Hilbert Space and the Theory of Spectral Multiplicity
Introduction to Hilbert Space and the Theory of Spectral MultiplicityPaul R. HalmosI. The Geometry of Hilbert Space
II. The Algebra of Operators
III. The Analysis of Spectral Measures
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Measure Theory
Measure TheoryPaul R. HalmosI. Sets and Classes
II. Measures and Outer Measures
III. Extension of Measures
IV. Measurable Functions
V. Integration
VI. General Set Functions
VII. Product Spaces
VIII. Transformations and Functions
IX. Probability
X. Locally Compact Spaces
XI. Haar Measure
XII. Measure and Topology in Groups
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Functional analysis in historical perspective
Functional analysis in historical perspectiveDr. A.F. MonnaI. The development of functional analysis
II. The development of the notion of a linear space
III. General analysis
IV. Some characteristic topics
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