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5. Integrals. Areas and Distances / The Definite Integral / Discovery Project: Area Functions / The Fundamental Theorem of Calculus / Indefinite Integrals and the Net Change Theorem / Writing Project: Newton, Leibniz, and the Invention of Calculus / The Substitution Rule 6. Applications of Integration. Areas between Curves / Volume / Volumes by Cylindrical Shells / Work / Average Value of a Function. 7. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions Inverse Functions / (Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*) / Exponential Functions and Their Derivatives / Logarithmic Functions / Derivatives of Logarithmic Functions / *The Natural Logarithmic Function / *The Natural Exponential Function / *General Logarithmic and Exponential Functions / Exponential Growth and Decay / Inverse Trigonometric Functions / Applied Project: Where to Sit at the Movies / Hyperbolic Functions / Indeterminate Forms and L'Hospital's Rule / Writing Project: The Origins of L'Hospital's Rule. 8. Techniques of Integration. Integration by Parts / Trigonometric Integrals / Trigonometric Substitution / Integration of Rational Functions by Partial Fractions / Strategy for Integration / Integration Using Tables and Computer Algebra Systems / Discovery Project: Patterns in Integrals /Approximate. Integration / Improper Integrals. 9. Further Applications of Integration. Arc Length / Discovery Project: Arc Length Contest / Area of a Surface of Revolution / Discovery Project: Rotating on a Slant / Applications to Physics and Engineering / Discovery Project: Complementary Coffee Cups / Applications to Economics and Biology / Probability. 10. Differential Equations. Modeling with Differential Equations / Direction Fields and Euler's Method / Separable Equations / Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth / Applied Project: Calculus and Baseball / Linear Equations / Predator-Prey Systems. 11. Parametric Equations and Polar Coordinates. Curves Defined by Parametric Equations / Laboratory Project: Families of Hypocycloids / Calculus with Parametric Curves / Laboratory Project: Bezier Curves / Polar Coordinates / Areas and Lengths in Polar Coordinates / Conic Sections / Conic Sections in Polar Coordinates. 12. 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 / Writing Project: How Newton Discovered the Binomial Series / Applications of Taylor Polynomials / Applied Project: Radiation from the Star. Appendixes. A: Intervals, 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: Answers to Odd-Numbered Exercises.