Week 15: Surface area and surface Integrals, Parameterized surfaces.
Thomas Calculus, 11th edition, pages: 1182 - 1200
Sec 16.5 Surface Area and Surface Integral
We know how to integrate a function over a flat region in a plane, but what if the function is defined over a curved surface? To evaluate one of these so-called surface integrals, we rewrite it as a double integral over a region in a coordinate plane beneath the surface. Surface integrals are used to compute quantities such as the flow of liquid across a membrane or the upward force on a falling parachute.
Sec 16.6 Parameterized Surfaces
In the present section, we extends the investigation of surface area and surface integrals to surfaces described parametrically.
Course Material
- Week 1: Three-Dimensional Coordinate Systems, Vectors, The Dot Product.
- Week 2: The Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces
- Week 3: Vector functions, Modeling projectile motion, Arc length and the unit tangent vector T.
- Week 4: Curvature and the unit normal vector N, Torsion and the unit binormal vector B, Planetary motion and satellites
- Week 5: Functions of several variables, Limits and continuity in higher dimensions, Partial derivatives,
- Week 6: The chain rule, Directional derivatives and gradient vectors, Tangent planes and differentials
- Week 7: Extreme values and Saddle points, Lagrange multipliers,
- Week 8: Partial derivatives with constrained variables, Taylor's formula for two variables
- Week 9: Double integrals, Areas, Moments and centers of mass, Double integrals in polar form
- Week 10: Mid Term, December 14 - 18,2020 Week 11: Winter Break, December 21 - 24, 2020
- Week 12: Triple integrals in rectangular coordinates, Masses and moments in three dimensions, Triple integrals in cylindrical and spherical coordinates.
- Week 13: Substitution in multiple integrals, Line integrals, Vector fields, Work, Circulation and Flux,
- Week 14: Path independence, Potential functions and conservative fields, Green's theorem in the plane
- Week 15: Surface area and surface Integrals, Parameterized surfaces.
- Week 16: Stokes' Theorem, The Divergence theorem and a unified theory
- Chapters 15
- Department Chemistry
- Teacher
Dr. Uzma Ahmad
