Math 2415 Calculus III Information
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
College level readiness in reading and writing
Textbook: Willliam Briggs, Lyle Cochran, Bernard Gillett; Calculus for Scientists and Engineers, Early Transcendentals; Pearson, 2013
Required: Students must buy an access code to MyMathLab, an online course management system which includes a complete eBook; students will first need a Course ID provided by the instructor in order to register; online purchase of MyMathLab access at www.mymathlab.com; hard copies of access codes available with ISBN: 9780321199911
Hardbound text (optional), ISBN: 9780321785374
Hardbound text + free MyMathLab access + Student Edition of Maple Software, ISBN: 9780321844545
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 PDA’s can be used as calculators. Calculators may be cleared before tests.
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 Green’s Theorem
15.5 Divergence and Curl
15.6 Surface Integrals
15.7 Stoke's Theorem
15.8 Divergence Theorem