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 MeanValue 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 
WorkEnergy Formula; Conservation of Mechanical
Energy 


Section 17.4 
Another Notation for Line Integrals; Line Integrals
With Respect to Arc Length 


Section 17.5 
GreenŐs 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 
StokesŐ Theorem 
