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Tom M. Apostol Livres

    Cálculo con funciones de una variable, con una introducción al álgebra lineal
    Cálculo con funciones de varias variables y álgebra lineal, con aplicaciones a las ecuaciones diferenciales y a las probabilidades
    Modular Functions and Dirichlet Series in Number Theory
    Calculus II
    Calculus, Volume I
    Introduction to Analytic Number Theory

    • Introduction to Analytic Number Theory

      • 356pages
      • 13 heures de lecture
      4,0(1)Évaluer

      Focusing on the fundamental concepts and techniques of number theory, this textbook emphasizes analytic number theory. It is structured for undergraduate students, featuring clear explanations and a variety of exercises at the end of each chapter. The initial ten chapters cater to those familiar with elementary calculus, while the final four chapters delve into more advanced topics, necessitating an understanding of complex function theory, including complex integration and residue calculus.

      Introduction to Analytic Number Theory

    • Calculus, Volume I

      One-variable Calculus, with an Introduction to Linear Algebra

      4,3(11)Évaluer

      · Some Basic Concepts Of The Theory Of Sets · A Set Of Axioms For The Real Number System · Mathematical Induction, Summation Notation, And Related Topics · The Concepts Of The Integral Calculus · Some Applications Of Differentiation · Continuous Functions · Differential Calculus · The Relation Between Integration And Differentiation · The Logarithm, The Exponential, And The Inverse Trigonometric Functions · Polynomial Approximations To Functions · Introduction To Differential Equations · Complex Numbers · Sequences, Infinite Series, Improper Integrals · Sequences And Series Of Functions · Vector Algebra · Applications Of Vector Algebra To Analytic Geometry · Calculus Of Vector-Valued Functions · Linear Spaces · Linear Transformations And Matrices

      Calculus, Volume I

    • Calculus II

      Multi-variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability

      4,0(8)Évaluer

      Linear analysis · linear spaces · linear transformations and matrices · determinants · eigenvalues and eigenvectors · eigenvalues of operators acting on euclidean spaces · linear differential equations · systems of differential equations · nonlinear analysis · differential calculus of scalar and vector fields · applications of the differential calculus · line integrals · special topics · set functions and elementary probability · calculus of probabilities · introduction to numerical analysis

      Calculus II

    • Modular Functions and Dirichlet Series in Number Theory

      • 220pages
      • 8 heures de lecture

      Focusing on elliptic and modular functions, this textbook builds on foundational concepts from number theory and complex analysis. Key topics include Rademacher's series for the partition function, Lehner's congruences for Fourier coefficients, and Hecke's theory of entire forms. The final chapter explores Bohr's theory of Dirichlet series equivalence. Aimed at both nonspecialists and specialists, the volume highlights classical mathematics while acknowledging modern developments, honoring students who contributed to the field.

      Modular Functions and Dirichlet Series in Number Theory