Homework Help for Multivariable Calculus 18.02SC MIT
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Details
MIT Recitation Instructors take viewers step-by-step through solving homework problems related to Multivariable Calculus.
Resources: OpenCourseware from MIT, UC Berkeley, Stanford along with many of the World's finest University's.
Language: English
Professors: Joshua Coleman, Michael Williams
Units: 70
Lesson content
- Coordinate free proofs: centroid of a triangle
- Dot products and angles
- Components of a vector
- Area of a parallelogram
- Determinants
- Volume of a parallelepiped
- Finding area using cross products
- Matrix multiplication practice
- Solve a linear system using matrices
- Equations of planes
- Distance of a point to a plane
- Systems of linear equations
- Parametrized lines and intersections
- Parametric line intersecting a plane
- Differentiating a vector valued function
- Parametric curves: velocity, acceleration, length
- Graphing surfaces
- Level curves
- Level curves and critical points
- Partial derivatives
- Tangent plane approximation
- Least squares
- Second derivative test
- Max/Min
- Total differentials and the chain rule
- Tangent planes
- Gradient and directional derivative
- Lagrange multipliers
- Lagrange multipliers (3 variables)
- The chain rule with constraints
- Gradients - composition
- Regions of integration
- Changing the order of integration
- Integration in polar coordinates
- Integrals with density
- Change of variables
- Integral of exp(-x^2)
- Change of variables
- Line integrals: path dependence
- Line integrals: parametrization independence
- Line integrals by geometric reasoning
- Fundamental theorem of line integrals
- Non-conservative vector fields
- Potentials of gradient fields
- Green's Theorem: an off center circle
- Green's Theorem: area under an arch
- Application of Green's theorem
- Flux across a curve
- Green's Theorem in normal form
- Extended Green's Theorem
- Domains of vector fields
- Volume in cylindrical coordinates
- Average height
- Moment of inertia of a cylinder
- Average distance on a sphere
- Gravity and a half-sphere
- Flux through easy surfaces
- Flux through a square
- Flux through surfaces
- Flux
- Flux and the divergence theorem
- Extended Gauss' Theorem
- Del and the product rule
- Line integral on a helix
- Conservative fields and exact differentials
- Stokes' Theorem
- Extended Stokes' Theorem
- Simply connected regions
- More Stokes' Theorem
- Consequences of Stokes' Theorem
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