Includes appendix and index

Contents : Function and models -- Four ways to represent a function -- Mathematical model: a catalog of essential functions -- New function from old functions -- Graphing calculators and computers -- Review -- Principle of problem solving -- Limits -- The tangent and velocity problems -- The limit of a function -- Calculating limit using the limit laws --The precise defining of a limit -- Continuity -- Review -- Problems plus -- Derivatives -- Derivatives and rates of change -- Writing project -early methods for funding tangents -- The derivatives as a function -- Differentiation formulas -- Applied project-building a better roller coaster -- Derivatives of trigonometric functions -- The chain rule -- Applied project-where should a pilot start decent? -- Implicit differentiation -- Rate of change in the nature and social science -- Related rates -- Linear approximation and differentials -- Laboratory project-Taylor polynomials -- Review -- Problem plus -- Application of differentiation -- Maximum and minimum values -- Applied project-the calculus of rainbows -- The mean value theorem -- How derivatives affect the shape of a graph -- Limits at infinity: horizontal asymptotes -- Summary of curve sketching -- Graphing with calculus and calculators -- Optimization problems -- Applied project- the shape of a can -- Newton's method -- Anti derivatives -- Review -- Problem plus -- Integrals -- areas and distances -- The definite integral -- Discovery project - area functions -- The function theorem of calculus -- Indefinite integrals and the net change theorem -- Writing project- Newton,Leibniz,and the invention of calculus -- The substitution rule -- Review -- Problem plus -- Application of integration -- Area between curves -- Volumes -- Volumes by cylindrical shells -- Work -- Average value of a function -- Review -- problem plus -- Inverse functions : exponential,logarithmic,and inverse trigonometric functions -- Inverse functions -- Exponential growth and decay -- Inverse trigonometric functions -- Applied project- where to sit at the movies -- Hyperbolic functions -- Indeterminate forms and L 'hospital 'S rules -- Writing project- the origin of L 'hospital 's rules -- review -- technique of integration -- integration by parts -- Trigonometric integrals -- Trigonometric substitution -- Integration of rational functions by partial fractions -- Strategy for integration -- Integration using table and computer algebra systems -- Discovery project- patterns in integrals -- Approximate integration -- Improper integrals -- Review -- Problems plus -- Further applications of integration -- Arc length -- Discovery contest -- Area of a surface of revolution -- Discovery project - rotation on a slant -- Application to physics and engineering -- Discovery project- complementary coffee cups -- Applications to economics and biology -- probability -- Review -- Problem plus -- Differential equations -- modeling with differential equations -- Direction field and euler's method -- Separable equations -- Applied project- how fast does a tank drain? -- Applied project- which is faster going up or coming down? -- Model for population growth -- Applied project- calculus and baseball -- Linear equations -- Predator- prey systems -- Review -- Problems plus -- Parametric equations and polar coordinates -- Curve defined by parametric equations -- Laboratory project - running circles around circles -- Calculus with parametric curves -- Laboratory project- Bezier curves -- Polar coordinates -- Area and length in polar coordinates -- Conic sections -- Conic section in polar coordinates -- Review -- problem plus -- Infinite sequences and series -- Sequences -- Laboratory project - logistic sequences -- Series -- The integral test and estimates of sums -- The comparison tests -- Alternating series -- Absolute convergence and the ratio and root tests -- Strategy for testing series -- Power series -- Representation of functions as power series -- Taylor and maclaurin series -- Laboratory project- an elusive limit -- Writing project- how Newton discovered the binomial series -- Application of Taylor polynomials -- Applied Project - radiation from the stars -- Review -- Problems plus -- Vectors and the geometry of space -- Three-dimensional coordinate systems -- Vectors -- The dot product -- The cross product -- Discovery project- the geometry of a tetrahedron -- Equations of lines and planes -- Laboratory project- putting 3D in perspective -- Cylinders and quadric surfaces -- Review -- Problem plus -- Vector functions -- Vector functions and space curves -- Derivatives and integrals of vector functions -- Arc length and curvature -- Motion in space: velocity and acceleration -- Applied in space: velocity and acceleration -- Applied project- Kepler's laws -- Review -- Problem -- Partial derivatives -- Function of several variables -- Limits and continuity -- Partial derivatives -- Tangent planes and linear approximations -- The chain rule -- Directional derivatives and the gradient vector -- Maximum and minimum values -- Applied project- designing a dumpster -- Discovery project- approximations and critical points -- Lagrange multipliers -- Applied project- rocket science -- Applied project- hydro-turbine optimization -- Review -- Problem plus -- Multiple integrals -- Double integrals over rectangles -- Iterated integrals -- Double integrals over general regions -- Double integrals in polar coordinates -- Applications of double integrals -- Triple integrals -- Discovery project- volumes of hypersphere -- Triple integrals in cylindrical coordinates -- Discovery project- the intersection of three cylinders -- Triple integrals in spherical coordinates -- Applied project-roller derby -- Change of variables in multiple integrals -- Review -- Problems plus -- Vector calculus -- Vector fields -- Line integrals -- The fundamental theorem for line integrals -- Green's theorem -- Curl and divergence -- Parametric surface and their areas -- Surface integrals -- Stokes' theorem -- Writing project- three men and two theorems -- The divergence theorem -- Summary -- Review -- Problems plus -- Second-order differentials equations -- Second-order linear equations -- Non homogeneous linear equations -- Application of second-order differential equations -- Series solutions -- Review -- Appendixes -- A numbers,inequalities,and absolute values -- B Coordinate Geometry and lines -- C Graphs of second-degree equations -- D Trigonometry -- E Sigma notation -- F Proofs of theorems -- G Complex numbers -- H Answer to odd-numbered exercises.