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22

Centers of Mass for Variable Density

Lecture no. 22 from the course: Understanding Multivariable Calculus: Problems, Solutions, and Tips

Centers of Mass for Variable Density

Taught by Professor Bruce H. Edwards | 29 min | Categories: The Great Courses Plus Online Mathematics Courses

With these new methods of evaluating integrals over a region, we can apply these concepts to the realm of physics. Continuing from the previous lecture, learn the formulas for mass and moments of mass for a planar lamina of variable density, and find the center of mass for these regions.

36 Lectures

1
Image of A Visual Introduction to 3-D Calculus
A Visual Introduction to 3-D Calculus
0 of 33 min
2
Image of Functions of Several Variables
Functions of Several Variables
0 of 30 min
3
Image of Limits, Continuity, and Partial Derivatives
Limits, Continuity, and Partial Derivatives
0 of 30 min
4
Image of Partial Derivatives—One Variable at a Time
Partial Derivatives—One Variable at a Time
0 of 30 min
5
Image of Total Differentials and Chain Rules
Total Differentials and Chain Rules
0 of 31 min
6
Image of Extrema of Functions of Two Variables
Extrema of Functions of Two Variables
0 of 30 min
7
Image of Applications to Optimization Problems
Applications to Optimization Problems
0 of 30 min
8
Image of Linear Models and Least Squares Regression
Linear Models and Least Squares Regression
0 of 31 min
9
Image of Vectors and the Dot Product in Space
Vectors and the Dot Product in Space
0 of 29 min
10
Image of The Cross Product of Two Vectors in Space
The Cross Product of Two Vectors in Space
0 of 29 min
11
Image of Lines and Planes in Space
Lines and Planes in Space
0 of 31 min
12
Image of Curved Surfaces in Space
Curved Surfaces in Space
0 of 31 min
13
Image of Vector-Valued Functions in Space
Vector-Valued Functions in Space
0 of 31 min
14
Image of Kepler’s Laws—The Calculus of Orbits
Kepler’s Laws—The Calculus of Orbits
0 of 30 min
15
Image of Directional Derivatives and Gradients
Directional Derivatives and Gradients
0 of 30 min
16
Image of Tangent Planes and Normal Vectors to a Surface
Tangent Planes and Normal Vectors to a Surface
0 of 28 min
17
Image of Lagrange Multipliers—Constrained Optimization
Lagrange Multipliers—Constrained Optimization
0 of 30 min
18
Image of Applications of Lagrange Multipliers
Applications of Lagrange Multipliers
0 of 29 min
19
Image of Iterated integrals and Area in the Plane
Iterated integrals and Area in the Plane
0 of 30 min
20
Image of Double Integrals and Volume
Double Integrals and Volume
0 of 29 min
21
Image of Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
0 of 30 min
22
Image of Centers of Mass for Variable Density
Centers of Mass for Variable Density
0 of 29 min
23
Image of Surface Area of a Solid
Surface Area of a Solid
0 of 31 min
24
Image of Triple Integrals and Applications
Triple Integrals and Applications
0 of 29 min
25
Image of Triple Integrals in Cylindrical Coordinates
Triple Integrals in Cylindrical Coordinates
0 of 30 min
26
Image of Triple Integrals in Spherical Coordinates
Triple Integrals in Spherical Coordinates
0 of 29 min
27
Image of Vector Fields—Velocity, Gravity, Electricity
Vector Fields—Velocity, Gravity, Electricity
0 of 30 min
28
Image of Curl, Divergence, Line Integrals
Curl, Divergence, Line Integrals
0 of 31 min
29
Image of More Line Integrals and Work by a Force Field
More Line Integrals and Work by a Force Field
0 of 31 min
30
Image of Fundamental Theorem of Line Integrals
Fundamental Theorem of Line Integrals
0 of 31 min
31
Image of Green’s Theorem—Boundaries and Regions
Green’s Theorem—Boundaries and Regions
0 of 30 min
32
Image of Applications of Green’s Theorem
Applications of Green’s Theorem
0 of 30 min
33
Image of Parametric Surfaces in Space
Parametric Surfaces in Space
0 of 32 min
34
Image of Surface Integrals and Flux Integrals
Surface Integrals and Flux Integrals
0 of 31 min
35
Image of Divergence Theorem—Boundaries and Solids
Divergence Theorem—Boundaries and Solids
0 of 29 min
36
Image of Stokes’s Theorem and Maxwell's Equations
Stokes’s Theorem and Maxwell's Equations
0 of 33 min

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