Set, Measure and Probability Theory by Alencar, Marcelo S.

Table of Contents: “…1.10: Problems -- Chapter 2: Relations and Functions -- 2.1: Definition of a Relation -- 2.1.1: Relation Representation -- 2.1.2: Types of Relations -- 2.2: Definition of Function -- 2.2.1: Types of Functions -- 2.3: Mathematical Functions -- 2.3.1: Indicator Function -- 2.3.2: Fuzzy Sets -- 2.3.3: Properties of Set Functions -- 2.4: The Count of Arts and Mathematics -- 2.5: Problems -- Chapter 3: Fundamentals of Measure Theory -- 3.1: Measuring His -- 3.2: Measure in an Algebra of Sets -- 3.3: The Riemann Integral -- 3.4: The Lebesgue Integral -- 3.4.1: The Lebesgue Measure…”
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A math primer for engineers / Colin Walker Cryer. by Cryer, Colin W.

Table of Contents: “…7.2 Differentiation in Rn7.3 Applications of Differentiation -- 7.3.1 Taylor Series -- 7.3.2 Calculation of Extrema -- 7.3.3 Newton's Method -- 7.3.4 Spline Functions -- 7.4 Integral Calculus -- 7.4.1 Riemann Integrals in One Dimension -- 7.4.1.1 Indefinite Integrals -- 7.4.1.2 Definite Integrals -- 7.4.1.3 The Connection between Definite and Indefinite Integrals -- 7.4.1.4 Integration by Parts -- 7.4.1.5 The Differentiation of Integrals with Parameters -- 7.4.1.6 Improper Riemann Integrals -- 7.4.1.6.0.1 One Endpoint Equal to…”
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Variational methods for engineers with Matlab / Eduardo Souza de Cursi. by Cursi, Eduardo Souza de

Table of Contents: “…""Table of Contents""; ""Title""; ""Copyright""; ""Introduction""; ""1: Integrals""; ""1.1 Riemann integrals""; ""1.2 Lebesgue integrals""; ""1.3 Matlab® classes for a Riemann integral by trapezoidal integration""; ""1.4 Matlab® classes for Lebesgue's integral""; ""1.5 Matlab® classes for evaluation of the integrals when/is defined by a subprogram""; ""1.6 Matlab® classes for partitions including the evaluation of the integrals""; ""2: Variational Methods for Algebraic Equations""; ""2.1 Linear systems""; ""2.2 Algebraic equations depending upon a parameter""; ""2.3 Exercises""…”
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Variational methods for engineers with Matlab / Eduardo Souza de Cursi. by Cursi, Eduardo Souza de

Table of Contents: “…""Table of Contents""; ""Title""; ""Copyright""; ""Introduction""; ""1: Integrals""; ""1.1 Riemann integrals""; ""1.2 Lebesgue integrals""; ""1.3 Matlab® classes for a Riemann integral by trapezoidal integration""; ""1.4 Matlab® classes for Lebesgue's integral""; ""1.5 Matlab® classes for evaluation of the integrals when/is defined by a subprogram""; ""1.6 Matlab® classes for partitions including the evaluation of the integrals""; ""2: Variational Methods for Algebraic Equations""; ""2.1 Linear systems""; ""2.2 Algebraic equations depending upon a parameter""; ""2.3 Exercises""…”
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Variational methods for engineers with Matlab / Eduardo Souza de Cursi. by Cursi, Eduardo Souza de

Table of Contents: “…""Table of Contents""; ""Title""; ""Copyright""; ""Introduction""; ""1: Integrals""; ""1.1 Riemann integrals""; ""1.2 Lebesgue integrals""; ""1.3 Matlab® classes for a Riemann integral by trapezoidal integration""; ""1.4 Matlab® classes for Lebesgue's integral""; ""1.5 Matlab® classes for evaluation of the integrals when/is defined by a subprogram""; ""1.6 Matlab® classes for partitions including the evaluation of the integrals""; ""2: Variational Methods for Algebraic Equations""; ""2.1 Linear systems""; ""2.2 Algebraic equations depending upon a parameter""; ""2.3 Exercises""…”
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Mathematical methods for finance : tools for asset and risk management / Sergio M. Focardi, Frank J. Fabozzi, Turan G. Bali. by Focardi, Sergio M.

Table of Contents: “…Application of the Chain RuleTAYLOR SERIES EXPANSION; Application to Bond Analysis; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 3 Integral Calculus; INTRODUCTION; RIEMANN INTEGRALS; Properties of Riemann Integrals; LEBESGUE-STIELTJES INTEGRALS; INDEFINITE AND IMPROPER INTEGRALS; THE FUNDAMENTAL THEOREM OF CALCULUS; INTEGRAL TRANSFORMS; Laplace Transforms; Fourier Transforms; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 4 Matrix Algebra; INTRODUCTION; VECTORS AND MATRICES DEFINED; Vectors; Matrices; SQUARE MATRICES; Diagonals and Antidiagonals; Identity Matrix.…”
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Mathematical methods for finance : tools for asset and risk management / Sergio M. Focardi, Frank J. Fabozzi, Turan G. Bali. by Focardi, Sergio M.

Table of Contents: “…Application of the Chain RuleTAYLOR SERIES EXPANSION; Application to Bond Analysis; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 3 Integral Calculus; INTRODUCTION; RIEMANN INTEGRALS; Properties of Riemann Integrals; LEBESGUE-STIELTJES INTEGRALS; INDEFINITE AND IMPROPER INTEGRALS; THE FUNDAMENTAL THEOREM OF CALCULUS; INTEGRAL TRANSFORMS; Laplace Transforms; Fourier Transforms; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 4 Matrix Algebra; INTRODUCTION; VECTORS AND MATRICES DEFINED; Vectors; Matrices; SQUARE MATRICES; Diagonals and Antidiagonals; Identity Matrix.…”
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Mathematical methods for finance : tools for asset and risk management / Sergio M. Focardi, Frank J. Fabozzi, Turan G. Bali. by Focardi, Sergio M.

Table of Contents: “…Application of the Chain RuleTAYLOR SERIES EXPANSION; Application to Bond Analysis; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 3 Integral Calculus; INTRODUCTION; RIEMANN INTEGRALS; Properties of Riemann Integrals; LEBESGUE-STIELTJES INTEGRALS; INDEFINITE AND IMPROPER INTEGRALS; THE FUNDAMENTAL THEOREM OF CALCULUS; INTEGRAL TRANSFORMS; Laplace Transforms; Fourier Transforms; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 4 Matrix Algebra; INTRODUCTION; VECTORS AND MATRICES DEFINED; Vectors; Matrices; SQUARE MATRICES; Diagonals and Antidiagonals; Identity Matrix.…”
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Basic analysis I : functions of a real variable / James K. Peterson. by Peterson, James K. (James Kent)

Table of Contents: “…Series of Functions and Power Series. 26.Riemann Integration: Discontinuities and Compositions. 27. …”
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Learning and teaching mathematics using simulations : plus 2000 examples from physics / Dieter Röss. by Röss, Dieter, 1932-

Table of Contents: “…Interactive visualization of Taylor expansionsGraphical presentation of functions; Functions of one to three variables; Functions of four variables: World line in the theory of relativity; General properties of functions y=f(x); Exotic functions; The limiting process for obtaining the differential quotient; Derivatives and differential equations; Phase space diagrams; Antiderivatives; Definition of the antiderivative via its differential equation; Definite integral and initial value; Integral as limit of a sum; The definition of the Riemann integral; Lebesgue integral.…”
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A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration / Patrick Muldowney. by Muldowney, P. (Patrick), 1946-

Table of Contents: “…; 2.6 Riemann Sums and Random Variability; 2.7 How to Integrate a Function; 2.8 Extension of the Lebesgue Integral; 2.9 Riemann Sums in Basic Probability; 2.10 Variation and Outer Measure; 2.11 Outer Measure and Variation in [0,1]; 2.12 The Henstock Lemma; 2.13 Unbounded Sample Spaces; 2.14 Cauchy Extension of the Riemann Integral; 2.15 Integrability on]0, (infinity)[; 2.16 ""Negative Probability""…”
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Probability theory / Marcelo Sampaio de Alencar and Raphael Tavares de Alencar. by Alencar, Marcelo Sampaio de, Alencar, Raphael Tavares de

Table of Contents: “…Fundamentals of measure theory -- 2.1 A short history of measure -- 2.2 Measure in an algebra of sets -- 2.3 The Riemann integral -- 2.4 The Lebesgue integral --…”
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A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration / Patrick Muldowney. by Muldowney, P. (Patrick), 1946-

Table of Contents: “…; 2.6 Riemann Sums and Random Variability; 2.7 How to Integrate a Function; 2.8 Extension of the Lebesgue Integral; 2.9 Riemann Sums in Basic Probability; 2.10 Variation and Outer Measure; 2.11 Outer Measure and Variation in [0,1]; 2.12 The Henstock Lemma; 2.13 Unbounded Sample Spaces; 2.14 Cauchy Extension of the Riemann Integral; 2.15 Integrability on]0, (infinity)[; 2.16 ""Negative Probability""…”
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Examples and Problems in Mathematical Statistics by Zacks, Shelemyahu

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A modern theory of random variation : with applications in stochastic calculus, financial mathematics, and Feynman integration / Patrick Muldowney. by Muldowney, P. (Patrick), 1946-

Table of Contents: “…; 2.6 Riemann Sums and Random Variability; 2.7 How to Integrate a Function; 2.8 Extension of the Lebesgue Integral; 2.9 Riemann Sums in Basic Probability; 2.10 Variation and Outer Measure; 2.11 Outer Measure and Variation in [0,1]; 2.12 The Henstock Lemma; 2.13 Unbounded Sample Spaces; 2.14 Cauchy Extension of the Riemann Integral; 2.15 Integrability on]0, (infinity)[; 2.16 ""Negative Probability""…”
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From Calculus to Analysis by Rinaldo B. Schinazi. by Schinazi, Rinaldo B. (Rinaldo Bruno)

Table of Contents: “….-4.3 Convergence of infinite products -- 4.4 The number pi is irrational -- Ch. 5 Continuity, Limits, and Differentiation -- 5.1 Continuity -- 5.2 Limits of functions and derivatives -- 5.3 Algebra of derivatives and mean value theorems -- 5.4 Intervals, continuity, and inverse functions -- Ch. 6 Riemann Integration -- 6.1 Construction of the integral -- 6.2 Properties of the integral -- 6.3 Uniform continuity -- Ch 7 Decimal Represenation of Numbers -- Ch 8 Countable and Uncountable Sets -- Further Readings -- Index.…”
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Nonlinear integrals and their applications in data mining / Zhenyuan Wang, Rong Yang, Kwong-Sak Leung. by Wang, Zhenyuan

Table of Contents: “…Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. …”
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Time series analysis : nonstationary and noninvertible distribution theory / Katsuto Tanaka, professor of statistics and econometrics, Gakushuin University, Tokyo. by Tanaka, Katsuto, 1950-

Table of Contents: “…1.6 Panel Unit Root TestsChapter 2 Brownian Motion and Functional Central Limit Theorems; 2.1 The Space L2 of Stochastic Processes; 2.2 The Brownian Motion; 2.3 Mean Square Integration; 2.3.1 The Mean Square Riemann Integral; 2.3.2 The Mean Square Riemann-Stieltjes Integral; 2.3.3 The Mean Square Ito Integral; 2.4 The Ito Calculus; 2.5 Weak Convergence of Stochastic Processes; 2.6 The Functional Central Limit Theorem; 2.7 FCLT for Linear Processes; 2.8 FCLT for Martingale Differences; 2.9 Weak Convergence to the Integrated Brownian Motion.…”
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Time series analysis : nonstationary and noninvertible distribution theory / Katsuto Tanaka, professor of statistics and econometrics, Gakushuin University, Tokyo. by Tanaka, Katsuto, 1950-

Table of Contents: “…1.6 Panel Unit Root TestsChapter 2 Brownian Motion and Functional Central Limit Theorems; 2.1 The Space L2 of Stochastic Processes; 2.2 The Brownian Motion; 2.3 Mean Square Integration; 2.3.1 The Mean Square Riemann Integral; 2.3.2 The Mean Square Riemann-Stieltjes Integral; 2.3.3 The Mean Square Ito Integral; 2.4 The Ito Calculus; 2.5 Weak Convergence of Stochastic Processes; 2.6 The Functional Central Limit Theorem; 2.7 FCLT for Linear Processes; 2.8 FCLT for Martingale Differences; 2.9 Weak Convergence to the Integrated Brownian Motion.…”
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Mathematical Modelling, Optimization, Analytic and Numerical Solutions edited by Pammy Manchanda, René Pierre Lozi, Abul Hasan Siddiqi.

Table of Contents: “…Distribution Theory by Riemann Integrals -- Chapter 19. Wavelet Galerkin Methods for Higher Order Partial Differential Equations -- Chapter 20. …”
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