Calculus – Soo T. Tan – 1st Edition

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Utilizing a clear, concise style, and use of relevant, real world examples, Tan introduces abstract mathematical concepts with his intuitive approach that brings abstract ideas to life. In keeping with this emphasis on conceptual understanding, each exercise set begins with concept and each end-of-chapter review section includes fill-in-the-blank questions which are useful for mastering the definitions and theorems in each chapter. Additionally, many questions asking for the interpretation of graphical, numerical, and algebraic results are included among both the examples and the exercise sets.

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  • 0: PRELIMINARIES
    Lines
    Functions and Their Graphs
    The Trigonometric Functions
    Combining Functions
    Graphing Calculators and Computers
    Mathematical Models
    Chapter Review

    1: LIMITS
    An Intuitive Introduction to Limits
    Techniques for Finding Limits
    A Precise Definition of a Limit
    Continuous Functions
    Tangent Lines and Rates of Change
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    2: THE DERIVATIVE
    The Derivative
    Basic Rules of Differentiation
    The Product and Quotient Rules
    The Role of the Derivative in the Real World
    Derivatives of Trigonometric Functions
    The Chain Rule
    Implicit Differentiation
    Related Rates
    Differentials and Linear Approximations
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    3: APPLICATIONS OF THE DERIVATIVE
    Extrema of Functions
    The Mean Value Theorem
    Increasing and Decreasing Functions and the First
    Derivative Test
    Concavity and Inflection Points
    Limits Involving Infinity
    Asymptotes
    Curve Sketching
    Optimization Problems
    Newton's Method
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    4: INTEGRATION
    Indefinite Integrals
    Integration by Substitution
    Area
    The Definite Integral
    The Fundamental Theorem of Calculus
    Numerical Integration
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    5: APPLICATIONS OF THE DEFINITE INTEGRAL
    Areas Between Curves
    Volumes: Disks, Washers, and Cross Sections
    Volumes Using Cylindrical Shells
    Arc Length and Areas of Surfaces of Revolution
    Work
    Fluid Pressure and Force
    Moments and Centers of Mass
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    6: THE TRANSCENDENTAL FUNCTIONS
    The Natural Logarithmic Function
    Inverse Functions
    Exponential Functions
    General Exponential and Logarithmic Functions
    Inverse Trigonometric Functions
    Hyperbolic Functions
    Indeterminate Forms and L'Hôpital's Rule
    Chapter Review
    Challenge Problems

    7: TECHNIQUES OF INTEGRATION
    Integration by Parts
    Trigonometric Integrals
    Trigonometric Substitutions
    The Method of Partial Fractions
    Integration Using Tables of Integrals and CAS
    Improper Integrals
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    8: DIFFERENTIAL EQUATIONS
    Differential Equations: Separable Equations
    Direction Fields and Euler's Method
    The Logistic Equation
    First-Order Linear Differential Equations
    Chapter Review
    Challenge Problems

    9: INFINITE SEQUENCES AND SERIES
    Sequences
    Series
    The Integral Test
    The Comparison Tests
    Alternating Series
    Absolute Convergence
    The Ratio and Root Tests
    Power Series
    Taylor and Maclaurin Series
    Approximation by Taylor Polynomials
    Chapter Review
    Problem-Solving Techniques
    Challenge Problems

    10: CONIC SECTIONS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES
    Conic Sections
    Plane Curves and Parametric Equations
    The Calculus of Parametric Equations
    Polar Coordinates
    Areas and Arc Lengths in Polar Coordinates
    Conic Sections in Polar Coordinates
    Chapter Review
    Challenge Problems

    11: VECTORS AND THE GEOMETRY OF SPACE
    Vectors in the Plane
    Coordinate Systems and Vectors in Three-Space
    The Dot Product
    The Cross Product
    Lines and Planes in Space
    Surfaces in Space
    Cylindrical and Spherical Coordinates
    Chapter Review
    Challenge Problems

    12: VECTOR-VALUED FUNCTIONS
    Vector-Valued Functions and Space Curves
    Differentiation and Integration of Vector- Valued
    Functions
    Arc Length and Curvature
    Velocity and Acceleration
    Tangential and Normal Components of Acceleration
    Chapter Review
    Challenge Problems

    13: FUNCTIONS OF SEVERAL VARIABLES
    Functions of Two or More Variables
    Limits and Continuity
    Partial Derivatives
    Differentials
    The Chain Rule
    Directional Derivatives and Gradient Vectors
    Tangent Planes and Normal Lines
    Extrema of Functions of Two Variables
    Lagrange Multipliers
    Chapter Review
    Challenge Problems

    14: MULTIPLE INTEGRAL.S Double Integrals
    Iterated Integrals
    Double Integrals in Polar Coordinates
    Applications of Double Integrals
    Surface Area
    Triple Integrals
    Triple Integrals in Cylindrical and Spherical Coordinates
    Change of Variables in Multiple Integrals
    Chapter Review
    Challenge Problems

    15: VECTOR ANALYSIS
    Vector Fields
    Divergence and Curl
    Line Integrals
    Independence of Path and Conservative Vector Fields
    Green's Theorem
    Parametric Surfaces
    Surface Integrals
    The Divergence Theorem
    Stoke's Theorem
    Chapter Review
    Challenge Problems

    APPENDICES
    A The Real Number Line, Inequalities, and Absolute Value
    B Proofs of Selected Theorems.
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Download now Calculus

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