Change and Motion: Calculus Made Clear, 2nd Edition

1
    Two Ideas, Vast Implications
    2
    Stop Sign Crime—The First Idea of Calculus—The Derivative
    3
    Another Car, Another Crime—The Second Idea of Calculus—The Integral
    4
    The Fundamental Theorem of Calculus
    5
    Visualizing the Derivative—Slopes
    6
    Derivatives the Easy Way—Symbol Pushing
    7
    Abstracting the Derivative—Circles and Belts
    8
    Circles, Pyramids, Cones, and Spheres
    9
    Archimedes and the Tractrix
    10
    The Integral and the Fundamental Theorem
    11
    Abstracting the Integral—Pyramids and Dams
    12
    Buffon’s Needle or π from Breadsticks

    13
    Achilles, Tortoises, Limits, and Continuity
    14
    Calculators and Approximations
    15
    The Best of All Possible Worlds—Optimization
    16
    Economics and Architecture
    17
    Galileo, Newton, and Baseball
    18
    Getting off the Line—Motion in Space
    19
    Mountain Slopes and Tangent Planes
    20
    Several Variables—Volumes Galore
    21
    The Fundamental Theorem Extended
    22
    Fields of Arrows—Differential Equations
    23
    Owls, Rats, Waves, and Guitars
    24
    Calculus Everywhere