University of Houston
Department of Mathematics
Math 2433

Text: CALCULUS, 9^th edition . Authors: Salas, Hille, Etgen. Publisher: John Wiley & Sons, Inc.
Text is in electronic form .

Homework Assignments: html pdf

Syllabus

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

EXAM I

Chapter 14. FUNCTIONS OF SEVERAL VARIABLES

Section 14.1 Elementary Examples
Section 14.2 A Brief Catalogue 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 Exreme Values
Section 15.7 Maxima and Minima with Side Conditions
Section 15.8 Differentials
Section 15.9 Reconstructing a Function from its Gradient

EXAM II

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 16.6 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 Line Integrals with Respect to Arc Length
Section 17.5 Green's Theorem

EXAM III