Math 2433 Topics University of Houston Department of Mathematics Math 2433 Text:  CALCULUS, 9th edition.  Authors: Salas, Hille, Etgen.  Publisher: John Wiley & Sons, Inc. Chapter 12.   VECTORS Section 12.1 Cartesian Space Coordinates Section 12.2 Displacements and Forces Section 12.3 Vectors Section 12.4 The Dot Product Section 12.5 The Cross Product Section 12.6 Lines Section 12.7 Planes Chapter 13.   VECTOR CALCULUS Section 13.1 Vector Functions Section 13.2 Differentiation Formulas Section 13.3 Curves Section 13.4 Arc Length Section 13.5 Curvilinear Motion; Curvature Chapter 14.   FUNCTIONS OF SEVERAL VARIABLES Section 14.1 Elementary Examples Section 14.2 A Brief Catalog of Quadric Surfaces; Projections Section 14.3 Graphs; Level Curves and Level Surfaces Section 14.4 Partial Derivatives Section 14.5 Open and Closed Sets Section 14.6 Limits and Continuity; Equality of Mixed Partials Chapter 15.   GRADIENTS; EXTREME VALUES; DIFFERENTIALS Section 15.1 Differentiability and Gradient Section 15.2 Gradients and Directional Derivatives Section 15.3 The Mean-Value Theorem; Chain Rules Section 15.4 The Gradient as a Normal; Tangent Lines and Tangent Planes Section 15.5 Local Extreme Values Section 15.6 Absolute Extreme Values Section 15.7 Maxima and Minima with Side Conditions Section 15.8 Differentials Section 15.9 Reconstruction a Function from its Gradient Chapter 16.   DOUBLE AND TRIPLE INTEGRALS Section 16.2 The Double Integral Section 16.3 The Evaluation of Double Integrals by Repeated Integrals Section 16.4 Double Integrals in Polar Coordinates Section 16.5 Some Applications of Double Integration Section 16.6 Triple Integrals Section 16.7 Reduction to Repeated Integrals Section 16.8 Triple Integrals in Cylindrical Coordinates Section 16.9 The Triple Integral as a Limit of Riemann Sums; Spherical Coordinates Section 16.10 Jacobians; Changing Variables in Multiple Integration

 Chapter 17.   LINE INTEGRALS AND SURFACE INTEGRALS Section 17.1 Line Integrals Section 17.2 The Fundamental Theorem for Line Integrals Section 17.3 Work-Energy Formula; Conservation of Mechanical Energy Section 17.4 Another Notation for Line Integrals; Line Integrals With Respect to Arc Length Section 17.5 Green’s Theorem Section 17.6 Parameterized Surfaces; Surface Area Section 17.7 Surface Integrals Section 17.8 The Vector Differential Operator Section 17.9 The Divergence Theorem Section 17.10 Stokes’ Theorem