Tabla de Contenidos: “…7.2 Integration by Parts -- 7.3 Trigonometric integrals -- 7.4 Trigonometric substitutions -- 7.5 Partial Fractions -- 7.6 Other integration strategies -- 7.7 Numerical integration -- 7.8 Improper integrals -- 7.9 Introduction to differential Equations -- Review Exercises -- 8 Sequences and infinite series -- 8.1 An overview -- 8.2 Sequences -- 8.3 Infinite series -- 8.4 The divergence and integral Tests -- 8.5 The ratio, root, and comparison Tests -- 8.6 Alternating series -- Review Exercises -- 9 Power series -- 9.1 Approximating Functions with Polynomials -- 9.2 Properties of Power series -- 9.3 Taylor series -- 9.4 Working with Taylor series -- Review Exercises -- 10 Parametric and Polar curves -- 10.1 Parametric Equations -- 10.2 Polar coordinates -- 10.3 Calculus in Polar coordinates -- 10.4 Conic sections -- Review Exercises -- 11 Vectors and Vector-Valued Functions -- 11.1 Vectors in the Plane -- 11.2 Vectors in Three dimensions -- 11.3 Dot Products -- 11.4 Cross Products -- 11.5 Lines and curves in space -- 11.6 Calculus of Vector-Valued Functions -- 11.7 Motion in space -- 11.8 Length of curves -- 11.9 Curvature and normal Vectors -- Review Exercises -- 12 Functions of several Variables -- 12.1 Planes and surfaces -- 12.2 Graphs and level curves -- 12.3 Limits and continuity -- 12.4 Partial derivatives -- 12.5 The chain rule -- 12.6 Directional derivatives and the Gradient -- 12.7 Tangent Planes and linear approximation -- 12.8 Maximum/minimum Problems -- 12.9 Lagrange multipliers -- Review Exercises -- 13 Multiple integration -- 13.1 Double integrals over rectangular regions -- 13.2 Double integrals over General regions -- 13.3 Double integrals in Polar coordinates -- 13.4 Triple integrals -- 13.5 Triple integrals in cylindrical and spherical coordinates -- 13.6 Integrals for mass calculations…”

Tabla de Contenidos: “…8.1 Basic Approaches -- 8.2 Integration by Parts -- 8.3 Trigonometric Integrals -- 8.4 Trigonometric Substitutions -- 8.5 Partial Fractions -- 8.6 Other Integration Strategies -- 8.7 Numerical Integration -- 8.8 Improper Integrals -- 8.9 Introduction to Differential Equations -- Review Exercises -- 9 Sequences and Infinite Series -- 9.1 An Overview -- 9.2 Sequences -- 9.3 Infinite Series -- 9.4 The Divergence and Integral Tests -- 9.5 The Ratio, Root, and Comparison Tests -- 9.6 Alternating Series -- Review Exercises -- 10 Power Series -- 10.1 Approximating Functions with Polynomials -- 10.2 Properties of Power Series -- 10.3 Taylor Series -- 10.4 Working with Taylor Series -- Review Exercises -- 11 Parametric and Polar Curves -- 11.1 Parametric Equations -- 11.2 Polar Coordinates -- 11.3 Calculus in Polar Coordinates -- 11.4 Conic Sections -- Review Exercises -- 12 Vectors and Vector-Valued Functions -- 12.1 Vectors in the Plane -- 12.2 Vectors in Three Dimensions -- 12.3 Dot Products -- 12.4 Cross Products -- 12.5 Lines and Curves in Space -- 12.6 Calculus of Vector-Valued Functions -- 12.7 Motion in Space -- 12.8 Length of Curves -- 12.9 Curvature and Normal Vectors -- Review Exercises -- 13 Functions of Several Variables -- 13.1 Planes and Surfaces -- 13.2 Graphs and Level Curves -- 13.3 Limits and Continuity -- 13.4 Partial Derivatives -- 13.5 The Chain Rule -- 13.6 Directional Derivatives and the Gradient -- 13.7 Tangent Planes and Linear Approximation -- 13.8 Maximum/Minimum Problems -- 13.9 Lagrange Multipliers -- Review Exercises -- 14 Multiple Integration -- 14.1 Double Integrals over Rectangular Regions -- 14.2 Double Integrals over General Regions -- 14.3 Double Integrals in Polar Coordinates -- 14.4 Triple Integrals -- 14.5 Triple Integrals in Cylindrical and Spherical Coordinates -- 14.6 Integrals for Mass Calculations…”

Tabla de Contenidos: “…7.2.1 Discrete and Integral Forms of the Jensen Inequality -- 7.2.2 Generalizations of the Jensen Inequality -- 7.3 The Hermite-Hadamard Inequality -- 7.3.1 The Classic Form of the Hermite-Hadamard Inequality -- 7.3.2 Generalizations of the Hermite-Hadamard Inequality -- 7.4 The Rogers-Hölder Inequality -- 7.4.1 Integral and Discrete Forms of the Rogers-Hölder Inequality -- 7.4.2 Generalizations of the Rogers-Hölder Inequality -- 7.5 The Minkowski Inequality -- 7.5.1 Integral and Discrete Forms of the Minkowski Inequality -- 7.5.2 Generalizations of the Minkowski Inequality -- Bibliography -- Chapter 8 Refinements of Young's Integral Inequality via Fundamental Inequalities and Mean Value Theorems for Derivatives -- 8.1 Young's Integral Inequality and Several Refinements -- 8.1.1 Young's Integral Inequality -- 8.1.2 Refinements of Young's Integral Inequality via Lagrange's Mean Value Theorem -- 8.1.3 Refinements of Young's Integral Inequality via Hermite-Hadamard's and Čebyšev's Integral Inequalities -- 8.1.4 Refinements of Young's Integral Inequality via Jensen's Discrete and Integral Inequalities -- 8.1.5 Refinements of Young's Integral Inequality via H ̈older's Integral Inequality -- 8.1.6 Refinements of Young's Integral Inequality via Taylor's Mean Value Theorem of Lagrange's Type Remainder -- 8.1.7 Refinements of Young's Integral Inequality via Taylor's Mean Value Theorem of Cauchy's Type Remainder and H ̈older's Integral Inequality -- 8.1.8 Refinements of Young's Integral Inequality via Taylor's Mean Value Theorem of Cauchy's Type Remainder and Čebyšev's Integral Inequality -- 8.1.9 Refinements of Young's Integral Inequality via Taylor's Mean Value Theorem of Cauchy's Type Remainder and Jensen's Inequalities…”