Week 12: Triple integrals in rectangular coordinates, Masses and moments in three dimensions, Triple integrals in cylindrical and spherical coordinates.
Thomas Calculus, 11 th edition, pages: 1098 - 1127
Sec 15.4 Triple Integrals in Rectangular Coordinates
Just as double integrals allow us to deal with more general situations than could be handled by single integrals, triple integrals enable us to solve still more general problems. We use triple integrals to calculate the volumes of three-dimensional shapes, the masses and moments of solids of varying density, and the average value of a function over a threedimensional region. Triple integrals also arise in the study of vector fields and fluid flow in three dimensions, as we will see in Chapter 16.
Sec 15.5 Masses and Moments in Three Dimensions
This section shows how to calculate the masses and moments of three-dimensional objects in Cartesian coordinates. The formulas are similar to those for two-dimensional objects.
Sec 15.6 Triple integrals in cylindrical and spherical coordinates
When a calculation in physics, engineering, or geometry involves a cylinder, cone, or sphere, we can often simplify our work by using cylindrical or spherical coordinates, which are introduced in this section. The procedure for transforming to these coordinates and evaluating the resulting triple integrals is similar to the transformation to polar coordinates in the plane studied in Section 15.3.
- 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
