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> calculus 3 subject checklist
calculus 3 subject checklist
Vectors
Vector basics (magnitude, direction, addition, subtraction)
Dot product and its properties
Cross product and its properties
Scalar triple product
Vector functions and their derivatives
Arc length and curvature of a vector function
Multivariable Functions
Domain and range of a function
Level curves and level surfaces
Partial derivatives and their properties
Gradient vector and directional derivatives
Chain rule for multivariable functions
Optimization problems (finding local/global extrema)
Lagrange multipliers
Multiple Integration
Double integrals and their properties
Area and volume using double integrals
Polar coordinates and their conversion
Triple integrals and their properties
Volume using triple integrals
Cylindrical and spherical coordinates and their conversion
Vector Calculus
Line integrals and their properties
Green's theorem and its applications
Surface integrals and their properties
Divergence theorem and its applications
Stokes' theorem and its applications
Additional Topics
Taylor series and Maclaurin series
Convergence and divergence of series
Power series and their applications
Fourier series and Fourier transformations
Calculus of vector fields
Parametric surfaces and their curvature
Please note that this checklist is not exhaustive and can vary based on the specific curriculum or course requirements.
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