James Stewart’s CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart’s trademark style, while instructors have turned to his approach time and time again. In the Sixth Edition of CALCULUS, Stewart continues to set the standard for the course while adding new diagnostic tools, carefully revised content, and all-new course management tools built on the foundation of Stewart’s renowned content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart’s texts best-sellers continue to provide a strong foundation for the Sixth Edition. From the most unprepared student to the most mathematically gifted, Stewart’s writing and presentation serve to enhance understanding and build confidence.

10. Parametric Equations and Polar Coordinates.
Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Tangents and Areas. Laboratory Project: Bezier Curves. Arc Length and Surface Area. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Applied Project: Transfer Orbits. Review. Problems Plus.
11. 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
The Binomial Series. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.
12. 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. Quadric Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Problems Plus.
13. Vector Functions.
Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Keplers Laws. Review. Problems Plus.
14. Partial Derivatives
Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Differentials. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. Problems Plus.
15. Multiple Integrals.
Double Integrals Over Rectangles. Iterated Integrals. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical and Spherical Coordinates. Applied Project: Roller Derby. Discovery Project: The Intersection of Three Cylinders. Change of Variables in Multiple Integrals. Review. Problems Plus.
16. Vector Calculus.
Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Greens Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus.
17. Second-Order Differential Equations.
Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus.
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: The Logarithm Defined as an Integral. H: Complex Numbers. I: Answers to Odd-Numbered Exercises