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.