Math 2433 Topics
University of Houston
Department of Mathematics
Math 2433
Text: CALCULUS, 9^th 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