LSC-CyFair Math Department

Advanced topics in calculus, including three dimensional coordinate systems, limits and continuity of multivariable functions, partial derivatives, directional derivatives, the gradient, extreme values, multiple integration, the calculus of vector valued functions and line and surface integrals.

The student will:

Perform calculus operations on vector-valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.

Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.

Find extrema and tangent planes.

Solve problems using the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.

Apply the computational and conceptual principles of calculus to the solutions of real-world problems.

Explore selected topics of solid analytic geometry pertaining to lines and planes.

Use the cylindrical and spherical coordinate systems.

Use three space vector operations.

Acquire a graphic and algebraic understanding of quadratic surfaces.

Analyze and apply the concepts of limits and continuity to multivariable functions.

Credit Hours: 4

Lecture Hours: 3

Lab Hours: 2

External Hours: 0

Total Contact Hours: 80

MATH 2414;

ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing;

ENGL 0307

**Required Materials**

** Textbook: **Willliam Briggs, Lyle Cochran, Bernard Gillett

Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.

Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.

Neither cell phones nor PDAs can be used as calculators. Calculators may be cleared before tests.

**Textbook Sections**

**Chapter 12. Vectors and Vector-Valued Functions**

12.1 Vectors in the Plane

12.2 Vectors in Three Dimensions

12.3 Dot Products

12.4 Cross Products

12.5 Lines and Curves in Space

12.6 Calculus of Vector-Valued Functions

12.7 Motion in Space

12.8 Length of Curves

12.9 Curvature and Normal Vectors

**Chapter 13. Functions of Several Variables**

**13.1 Planes and Surfaces**

13.2 Graphs and Level Curves

13.3 Limits and Continuity

13.4 Partial Derivatives

13.5 The Chain Rule

13.6 Directional Derivatives and the Gradient

13.7 Tangent Planes and Linear Approximation

13.8 Maximum / Minimum Problems

Chapter 14. Multiple Integration

14.1 Double Integrals Over Rectangular Regions

14.2 Double Integrals Over General Regions

14.3 Double Integrals in Polar Coordinates

14.4 Triple Integrals

14.5 Triple Integrals in Cylindrical and Spherical Coordinates

14.6 Integrals for Mass Calculations

**Chapter 15. Vector Calculus**

15.1 Vector Fields

15.2 Line Integrals

15.3 Conservative Vector Fields

15.4 Greens Theorem

15.5 Divergence and Curl

15.6 Surface Integrals

15.7 Stoke's Theorem

15.8 Divergence Theorem