# Math 2433 - Calculus III

**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, 9^{th} 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.**

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**Syllabus**

**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 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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