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Full Description
In Calculus: Multivariable, 12th Edition, an expert team of mathematicians delivers a rigorous and intuitive exploration of calculus, introducing concepts like derivatives and integrals of multivariable functions. Using the Rule of Four, the authors present mathematical concepts from verbal, algebraic, visual, and numerical points of view. The book includes numerous exercises, applications, and examples that help readers learn and retain the concepts discussed within.
Contents
PREFACE ix
SUPPLEMENTS x
ACKNOWLEDGMENTS xi
THE ROOTS OF CALCULUS xv
11 Three-Dimensional Space; Vector 657
11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 657
11.2 Vectors 663
11.3 Dot Product; Projections 673
11.4 Cross Product 682
11.5 Parametric Equations of Lines 692
11.6 Planes in 3-Space 698
11.7 Quadric Surfaces 705
11.8 Cylindrical and Spherical Coordinates 715
12 Vector-Valued Functions 723
12.1 Introduction to Vector-Valued Functions 723
12.2 Calculus of Vector-Valued Functions 729
12.3 Change of Parameter; Arc Length 738
12.4 Unit Tangent, Normal, and Binormal Vectors 746
12.5 Curvature 751
12.6 Motion Along a Curve 759
12.7 Kepler's Laws of Planetary Motion 771
13 Partial Derivatives 781
13.1 Functions of Two or More Variables 781
13.2 Limits and Continuity 791
13.3 Partial Derivatives 800
13.4 Differentiability, Differentials, and Local Linearity 812
13.5 The Chain Rule 820
13.6 Directional Derivatives and Gradients 830
13.7 Tangent Planes and Normal Vectors 840
13.8 Maxima and Minima of Functions of Two Variables 845
13.9 Lagrange Multipliers 856
14 Multiple Integrals 866
14.1 Double Integrals 866
14.2 Double Integrals Over Nonrectangular Regions 873
14.3 Double Integrals in Polar Coordinates 882
14.4 Surface Area; Parametric Surfaces 889
14.5 Triple Integrals 902
14.6 Triple Integrals in Cylindrical and Spherical Coordinates 909
14.7 Change of Variables in Multiple Integrals; Jacobians 918
14.8 Centers of Gravity Using Multiple Integrals 930
15 Topics in Vector Calculus 942
15.1 Vector Fields 942
15.2 Line Integrals 951
15.3 Independence of Path; Conservative Vector Fields 966
15.4 Green's Theorem 976
15.5 Surface Integrals 983
15.6 Applications of Surface Integrals; Flux 990
15.7 The Divergence Theorem 999
15.8 Stokes' Theorem 1008
A Appendices
A Trigonometry Review (Summary) App-1
B Functions (Summary) App-8
C New Functions From Old (Summary) App-11
D Families of Functions (Summary) App-16
E Inverse Functions (Summary) App-23
READY REFERENCE RR-1
ANSWERS TO ODD-NUMBERED EXERCISES Ans-1
INDEX Ind-1
Web Appendices (online only)
Available in WileyPLUS
A Trigonometry Review
B Functions
C New Functions From Old
D Families of Functions
E Inverse Functions
F Real Numbers, Intervals, and Inequalities
G Absolute Value
H Coordinate Planes, Lines, and Linear Functions
I Distance, Circles, and Quadratic Equations
J Solving Polynomial Equations
K Graphing Functions Using Calculators and Computer Algebra Systems
L Selected Proofs
M Early Parametric Equations Option
N Mathematical Models
O The Discriminant
P Second-Order Linear Homogeneous Differential Equations
Chapter Web Projects: Expanding the Calculus Horizon (online only)
Available in WileyPLUS
Blammo the Human Cannonball -- Chapter 12
Hurricane Modeling -- Chapter 15
