Single Variable Calculus – Jon Rogawski – 2nd Edition

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engages while reinforcing the relevance of to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.

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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 2: Limits2.1 Limits, Rates of Change, and Tangent Lines
    2.2 Limits: A Numerical and Graphical Approach2.3 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 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 Derivatives of Inverse Functions
    3.9 Derivatives of General Exponential and Logarithmic Functions
    3.10 Implicit Differentiation
    3.11 Related Rates

    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
    4.9 Antiderivatives

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

    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 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 Improper Integrals
    7.7 Probability and Integration
    7.8 Numerical Integration

    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 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 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 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 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
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