(PDF) Calculus Late Transcendentals Single Variable - Jon Rogawski - 2nd Edition

Calculus Late Transcendentals Single Variable – Jon Rogawski – 2nd Edition


Este nuevo texto presenta cálculo con precisión matemática sólida pero con una sensibilidad cotidiana que pone los conceptos principales en términos claros. Es riguroso sin ser inaccesible y claro sin ser demasiado informal: tiene el equilibrio perfecto para los instructores y sus estudiantes.

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  • Chapter 1: Precalculus Review
    1.1 Real Numbers, Functions, and Graphs
    1.2 Linear and Quadratic Functions
    1.3 The Basic Classes of Functions
    1.4 Trigonometric Functions
    1.5 Inverse Functions
    1.6 Exponential and Logarithmic Functions
    1.7 Technology: Calculators and Computers
    Chapter Review Exercises

    Chapter 2: Limits
    2.1 Limits, Rates of Change, and Tangent Lines
    2.2 Limits: A Numerical and Graphical Approach
    2.3 Basic Limit Laws
    2.4 Limits and Continuity
    2.5 Evaluating Limits Algebraically
    2.6 Trigonometric Limits
    2.7 Limits at Infinity
    2.8 Intermediate Value Theorem
    2.9 The Formal Definition of a Limit
    Chapter Review Exercises

    Chapter 3: Differentiation
    3.1 Definition of the Derivative
    3.2 The Derivative as a Function
    3.3 Product and Quotient Rules
    3.4 Rates of Change
    3.5 Higher Derivatives
    3.6 Trigonometric Functions
    3.7 The Chain Rule
    3.8 Implicit Differentiation
    3.9 Derivatives of General Exponential and Logarithmic Functions
    3.10 Related Rates
    Chapter Review Exercises

    Chapter 4: Applications of the Derivative
    4.1 Linear Approximation and Applications
    4.2 Extreme Values
    4.3 The Mean Value Theorem and Monotonicity
    4.4 The Shape of a Graph
    4.5 L’Hopital’s Rule
    4.6 Graph Sketching and Asymptotes
    4.7 Applied Optimization
    4.8 Newton’s Method
    Chapter Review Exercises

    Chapter 5: The Integral
    5.1 Approximating and Computing Area
    5.2 The Definite Integral
    5.3 The Indefinite Integral
    5.4 The Fundamental Theorem of Calculus, Part I
    5.5 The Fundamental Theorem of Calculus, Part II
    5.6 Net Change as the Integral of a Rate
    5.7 Substitution Method
    5.8 Further Transcendental Functions
    5.9 Exponential Growth and Decay
    Chapter Review Exercises

    Chapter 6: Applications of the Integral
    6.1 Area Between Two Curves
    6.2 Setting Up Integrals: Volume, Density, Average Value
    6.3 Volumes of Revolution
    6.4 The Method of Cylindrical Shells
    6.5 Work and Energy
    Chapter Review Exercises

    Chapter 7: Techniques of Integration
    7.1 Integration by Parts
    7.2 Trigonometric Integrals
    7.3 Trigonometric Substitution
    7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
    7.5 The Method of Partial Fractions
    7.6 Strategies for Integration
    7.7 Improper Integrals
    7.8 Probability and Integration
    7.9 Numerical Integration
    Chapter Review Exercises

    Chapter 8: Further Applications of the Integral and Taylor Polynomials
    8.1 Arc Length and Surface Area
    8.2 Fluid Pressure and Force
    8.3 Center of Mass
    8.4 Taylor Polynomials
    Chapter Review Exercises

    Chapter 9: Introduction to Differential Equations
    9.1 Solving Differential Equations
    9.2 Models Involving y^´=k(y-b)
    9.3 Graphical and Numerical Methods
    9.4 The Logistic Equation
    9.5 First-Order Linear Equations
    Chapter Review Exercises

    Chapter 10: Infinite Series
    10.1 Sequences
    10.2 Summing an Infinite Series
    10.3 Convergence of Series with Positive Terms
    10.4 Absolute and Conditional Convergence
    10.5 The Ratio and Root Tests
    10.6 Power Series
    10.7 Taylor Series
    Chapter Review Exercises

    Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections
    11.1 Parametric Equations
    11.2 Arc Length and Speed
    11.3 Polar Coordinates
    11.4 Area and Arc Length in Polar Coordinates
    11.5 Conic Sections
    Chapter Review Exercises

    Chapter 12: Vector Geometry
    12.1 Vectors in the Plane
    12.2 Vectors in Three Dimensions
    12.3 Dot Product and the Angle Between Two Vectors
    12.4 The Cross Product
    12.5 Planes in Three-Space
    12.6 A Survey of Quadric Surfaces
    12.7 Cylindrical and Spherical Coordinates
    Chapter Review Exercises

    Chapter 13: Calculus of Vector-Valued Functions
    13.1 Vector-Valued Functions
    13.2 Calculus of Vector-Valued Functions
    13.3 Arc Length and Speed
    13.4 Curvature
    13.5 Motion in Three-Space
    13.6 Planetary Motion According to Kepler and Newton
    Chapter Review Exercises

    Chapter 14: Differentiation in Several Variables
    14.1 Functions of Two or More Variables
    14.2 Limits and Continuity in Several Variables
    14.3 Partial Derivatives
    14.4 Differentiability and Tangent Planes
    14.5 The Gradient and Directional Derivatives
    14.6 The Chain Rule
    14.7 Optimization in Several Variables
    14.8 Lagrange Multipliers: Optimizing with a Constraint
    Chapter Review Exercises

    Chapter 15: Multiple Integration
    15.1 Integration in Two Variables
    15.2 Double Integrals over More General Regions
    15.3 Triple Integrals
    15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
    15.5 Applications of Multiple Integrals
    15.6 Change of Variables
    Chapter Review Exercises

    Chapter 16: Line and Surface Integrals
    16.1 Vector Fields
    16.2 Line Integrals
    16.3 Conservative Vector Fields
    16.4 Parametrized Surfaces and Surface Integrals
    16.5 Surface Integrals of Vector Fields
    Chapter Review Exercises

    Chapter 17: Fundamental Theorems of Vector Analysis
    17.1 Green’s Theorem
    17.2 Stokes’ Theorem
    17.3 Divergence Theorem
    Chapter Review Exercises

    A. The Language of Mathematics
    B. Properties of Real Numbers
    C. Induction and the Binomial Theorem
    D. Additional Proofs

    Answers to Odd-Numbered Exercises
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