Section number: This information applies to all sections.
Delivery format: face-to-face lecture or online.
Prerequisites: MATH 1432
Course Description: Calculus of functions of several variables: calculus of vector-valued functions, partial differentiation, multiple integrals. *Note: TCCNS Equivalent: MATH 2415
Textbook: Calculus, 9th Edition, by Salas, Hille, and Etgen, Wiley. Available in electronic form (PDF) through CASA for all enrolled students via an Access Code.
The information contained in this class outline is an abbreviated description of the course. Additional important information is contained at your instructor’s personal webpage. You are responsible for knowing all of this information.
Chapter 11. VECTORS
Section 11.1 Cartesian Space Coordinates
Section 11.2 Vectors
Section 11.3 The Dot Product
Section 11.4 The Cross Product
Section 11.5 Lines 11.6 Planes
Chapter 12. VECTOR CALCULUS
Section 12.1 Vector Functions
Section 12.2 Differentiation Formulas
Section 12.3 Curves
Section 12.4 Arc Length
Section 12.5 Curvilinear Motion; Curvature
Chapter 13. FUNCTIONS OF SEVERAL VARIABLES
Section 13.1 Basic Terms and Examples
Section 13.2 Graphs; Level Curves and Level Surfaces
Section 13.3 Limits and Continuity
Section 13.4 Partial Derivatives
Chapter 14. GRADIENTS; EXTREME VALUES; DIFFERENTIALS
Section 14.1 Differentiability and Gradient
Section 14.2 Gradients and Directional Derivatives
Section 14.3 The Mean-Value Theorem; Chain Rules
Section 14.4 The Gradient as a Normal; Tangent Lines and Tangent Planes
Section 14.5 Local Extreme Values
Section 14.6 Absolute Extreme Values
Section 14.7 LaGrange Multipliers; Maxima and Minima with Side Conditions
Section 14.8 Increments and Differentials
Section 14.9 Reconstructing a Function from Its Gradient
Chapter 15. DOUBLE AND TRIPLE INTEGRALSSection 15.1 Double Integrals
Section 15.2 The Evaluation of Double Integrals by Repeated Integrals
Section 15.3 Evaluating Double Integrals Using Polar Coordinates
Section 15.4 Some Applications of Double Integration
Section 15.5 Triple Integrals
Section 15.6 Reduction to Repeated Integrals
Section 15.7 Cylindrical Coordinates
Section 15.8 Spherical Coordinates
Section 15.9 Jacobians; Changing Variables in Multiple Integration
Chapter 16. LINE INTEGRALS AND SURFACE INTEGRALS
Section 16.1 Line Integrals
Section 16.2 The Fundamental Theorem for Line Integrals
Section 16.3 Line Integrals With Respect to Arc Length
Section 16.4 Green’s Theorem
Section 16.5 Parameterized Surfaces; Surface Area
Section 16.6 Surface Integrals
Section 16.7 The Vector Differential Operator
Section 16.8 The Divergence Theorem
Section 16.9 Stokes’s Theorem
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