Math 2415 Calculus III Information
LSC-CyFair Math Department
Catalog Description
The algebra and geometry of vectors; topics from the calculus of multivariable functions including limits, continuity, partial derivatives, directional derivatives, the gradient, extreme values, multiple integration and vector calculus.
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:
Joel Hass, Maurice Weir, George Thomas, Jr.; University Calculus, Alternate Edition., with Maple Software and MyMathLab Portal Access; Pearson, 2008, ISBN Numbers:
Textbook Plus Maple Software and MyMathLab Portal Access: 9781256368731
Textbook Only: 9780321471963
MyMathLab Portal Access Only: 9780558357603
Calculator:
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 11. Vectors and the Geometry of Space
11.1 Three-Dimensional Coordinate Systems
11.2 Vectors
11.3 The Dot Product
11.4 The Cross Product
11.5 Lines and Planes in Space (delete the distance from a point to a line in space and the distance from a point to a plane)
11.6 Cylinders and Quadric Surfaces
Chapter 12. Vector Valued Functions and Motion in Space
12.1 Vector Functions and Their Derivatives
12.2 Integrals of Vector Functions
12.3 Arc Length in Space
12.4 Curvature of a Curve
Chapter 13. Partial Derivatives
13.1 Functions of Several Variables
13.2 Limits and Continuity in Higher Dimensions
13.3 Partial Derivatives
13.4 The Chain Rule
13.5 Directional Derivatives and Gradient Vectors
13.6 Tangent Planes and Differentials
13.7 Extreme Values and Saddle Points
Chapter 14. Multiple Integrals
14.1 Double and Iterated Integrals over Rectangles
14.2 Double Integrals over General Regions
14.3 Area by Double Integration
14.4 Double Integrals in Polar Form
14.5 Triple Integrals in Rectangular Coordinates
14.6 Moments and Centers of Mass
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
Chapter 15. Integration in Vector Fields
15.1 Line Integrals
15.2 Vector Fields, Work, Circulations and Flux
15.3 Path Independence, Potential Functions and Conservative Fields
15.4 Greens Theorem in the Plane
15.5 Surfaces and Area
15.6 Surface Integrals and Flux
15.7 Stoke's Theorem
15.8 The Divergence Theorem and a Unified Theory
