Principles of Mathematical AnalysisWalter Rudin1. The Real and Complex Number Systems 2. Elements of Set Theory 3. Numerical Sequences and Series 4. Continuity 5. Differentiation 6. The Riemann-Stieltjes Integral 7. Sequences and Series of Functions 8. Further Topics in the Theory of Series 9. Functions of Several Variables 10. The Lebesgue Theory

A Survey of Modern AlgebraGarrett Birkhoff, Saunders Mac LaneI. The Integers II. Rational Numbers and Fields III. Polynomials IV. Real Numbers V. Complex Numbers VI. Group Theory VII. Vectors and Vector Spaces VIII. The Algebra of Matrices IX. Linear Groups X. Determinants and Canonical Forms XI. Algebra of Classes XII. Transfinite Arithmetic XIII. Rings and Ideals XIV. Algebraic Number Fields XV. Galois Theory

Introduction to Modern AlgebraJohn L. Kelley1. Axioms for Numbers 2. Sets and Numbers 3. Vectors and Lines 4. Inner Products 5. The Complex Plane 6. Vector Geometry 7. Matrix Algebra

Vector CalculusSusan Jane Colley1. Vectors 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

Advanced Calculus of Several VariablesC.H. Edwards, Jr.I. Euclidean Space and Linear Mappings 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

Worked Problems in Applied MathematicsN.N. Lebedev, I.P. Skalskaya, Y.S. Uflyand1. Derivation of Equations and Formulation of Problems 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

Real and Complex AnalysisWalter RudinPreface Prologue: The Exponential Function 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...

Complex AnalysisLars V. AhlforsI. Complex Numbers II. Complex Functions III. Complex Integration IV. Infinite Sequences V. The Dirichlet Problem VI. Multiple-Valued Functions

Linear AlgebraSerge Lang1. Vectors 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

A First Course in Wavelets with Fourier AnalysisAlbert Boggess, Francis J. Narcowich0. Inner Product Spaces 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

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...

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...

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

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

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...

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...

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

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...

Theta Functions on Riemann SurfacesJohn D. FayI. Riemann's theta function II. The prime-form III. Degenerate Riemann surfaces IV. Cyclic unramified coverings V. Ramified double coverings VI. Bordered Riemann surfaces

Analytic Capacity and MeasureJohn GarnettI. Analytic capacity II. The Cauchy transform III. Hausdorff measure IV. Some examples V. Applications to approximation