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.
Course Learning Outcomes
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.
College level readiness in reading and writing
Willliam Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz; Calculus, Early Transcendentals, 3rd ed.; Pearson
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;
ISBN for hard copies of access codes: 9780134856926
Hardbound text (optional), ISBN: 9780134995991
Loose Leaf text + free MyMathLab access, ISBN: 9780134996684
Calculators may be required for some assignments/assessments at the discrection of the Instructor. Refer to class syllabus for details.
Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.
Chapter 13. Vectors and the Geometry of Space
13.1 Vectors in the Plane
13.2 Vectors in Three Dimensions
13.3 Dot Products
13.4 Cross Products
13.5 Lines and Planes in Space
13.6 Cylinders and Quadric Surfaces
Chapter 14. Vector-Valued Functions
14.1 Vector-Valued Functions
14.2 Calculus for Vector-Valued Functions
14.3 Motion in Space
14.4 Length of Curves
14.5 Curvature and Normal Vectors
Chapter 15. Functions of Several Variables
15.1 Graphs and Level Curves
15.2 Limits and Continuity
15.3 Partial Derivatives
15.4 The Chain Rule
15.5 Directional Derivatives and the Gradient
15.6 Tangent Planes and Linear Approximation
15.7 Maximum / Minimum Problems
Chapter 16. Multiple Integration
16.1 Double Integrals Over Rectangular Regions
16.2 Double Integrals Over General Regions
16.3 Double Integrals in Polar Coordinates
16.4 Triple Integrals
16.5 Triple Integrals in Cylindrical and Spherical Coordinates