Title Details

12 FUNCTIONS OF SEVERAL VARIABLES

12.1 FUNCTIONS OF TWO VARIABLES

12.2 GRAPHS AND SURFACES

12.3 CONTOUR DIAGRAMS

12.4 LINEAR FUNCTIONS

12.5 FUNCTIONS OF THREE VARIABLES

12.6 LIMITS AND CONTINUITY

REVIEW PROBLEMS

PROJECTS

13 A FUNDAMENTAL TOOL: VECTORS

13.1 DISPLACEMENT VECTORS

13.2 VECTORS IN GENERAL

13.3 THE DOT PRODUCT

13.4 THE CROSS PRODUCT

REVIEW PROBLEMS

PROJECTS

14 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES

14.1 THE PARTIAL DERIVATIVE

14.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY

14.3 LOCAL LINEARITY AND THE DIFFERENTIAL

14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE

14.5 GRADIENTS AND DIRECTIONAL DERIVATIVES IN SPACE

14.6 THE CHAIN RULE

14.7 SECOND-ORDER PARTIAL DERIVATIVES

14.8 DIFFERENTIABILITY

REVIEW PROBLEMS

PROJECTS

15 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA

15.1 CRITICAL POINTS: LOCAL EXTREMA AND SADDLE POINTS

15.2 OPTIMIZATION

15.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS

REVIEW PROBLEMS

PROJECTS

16 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES

16.1 THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES

16.2 ITERATED INTEGRALS

16.3 TRIPLE INTEGRALS

16.4 DOUBLE INTEGRALS IN POLAR COORDINATES

16.5 INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES

16.6 APPLICATIONS OF INTEGRATION TO PROBABILITY

REVIEW PROBLEMS

PROJECTS

17 PARAMETERIZATION AND VECTOR FIELDS

17.1 PARAMETERIZED CURVES

17.2 MOTION, VELOCITY, AND ACCELERATION

17.3 VECTOR FIELDS

17.4 THE FLOW OF A VECTOR FIELD

REVIEW PROBLEMS

PROJECTS

18 LINE INTEGRALS

18.1 THE IDEA OF A LINE INTEGRAL

18.2 COMPUTING LINE INTEGRALS OVER PARAMETERIZED CURVES

18.3 GRADIENT FIELDS AND PATH-INDEPENDENT FIELDS

18.4 PATH-DEPENDENT VECTOR FIELDS AND GREEN’S THEOREM

REVIEW PROBLEMS

PROJECTS

19 FLUX INTEGRALS AND DIVERGENCE

19.1 THE IDEA OF A FLUX INTEGRAL

19.2 FLUX INTEGRALS FOR GRAPHS, CYLINDERS, AND SPHERES

19.3 THE DIVERGENCE OF A VECTOR FIELD

19.4 THE DIVERGENCE THEOREM

REVIEW PROBLEMS

PROJECTS

20 THE CURL AND STOKES’ THEOREM

20.1 THE CURL OF A VECTOR FIELD

20.2 STOKES’ THEOREM

20.3 THE THREE FUNDAMENTAL THEOREMS

REVIEW PROBLEMS

PROJECTS

21 PARAMETERS, COORDINATES, AND INTEGRALS

21.1 COORDINATES AND PARAMETERIZED SURFACES

21.2 CHANGE OF COORDINATES IN A MULTIPLE INTEGRAL

21.3 FLUX INTEGRALS OVER PARAMETERIZED SURFACES

REVIEW PROBLEMS

PROJECTS

APPENDIX

A ROOTS, ACCURACY, AND BOUNDS

B COMPLEX NUMBERS

C NEWTON’S METHOD

D VECTORS IN THE PLANE

E DETERMINANTS

READY REFERENCE

ANSWERS TO ODD-NUMBERED PROBLEMS

INDEX