Stewart’s MULTIVARIABLE CALCULUS: CONCEPTS AND CONTEXTS, THIRD EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems.
MULTIVARIABLE CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because it has successfully brought peace to departments that were split between reform and traditional approaches to teaching calculus. Not only does the text help reconcile the two schools of thought by skillfully merging the best of traditional calculus with the best of the reform movement, it does so with innovation and meticulous accuracy.
Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representation of Functions as Power Series. Taylor and Maclaurin Series. The Binomial Series. Applications of Taylor Polynomials. Review. Focus on Problem Solving.
9. VECTORS AND THE GEOMETRY OF SPACE.
Three Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Functions and Surfaces. Cylindrical and Spherical Coordinates. Review. Focus on Problem Solving.
10. VECTOR FUNCTIONS.
Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space. Parametric Surfaces. Review. Focus on Problem Solving.
11. PARTIAL DERIVATIVES.
Functions 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. Lagrange Multipliers. Review. Focus on Problem Solving.
12. MULTIPLE INTEGRALS.
Double Integrals over Rectangles. Interated Integrals. Double Integrals over General Regions. 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. Review. Focus on Problem Solving.
13. VECTOR CALCULUS.
Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green’s Theorem. Curl and Divergence. Surface Integrals. Stokes’ Theorem. The Divergence Theorem. Summary. Review. Focus on Problem Solving.
Appendix A: Intervals, Inequalities, And Absolute Values.
Appendix B: Coordinate Geometry.
Appendix C: Trigonometry.
Appendix D: Precise Definitions Of Limits.
Appendix E: A Few Proofs.
Appendix F: Sigma Notation.
Appendix G: Integration Of Rational Functions By Partial Fractions.
Appendix H: Polar Coordinates.
Appendix I: Complex Numbers.
Appendix J: Answers To Odd-Numbered Exercises.