Calculus 3
Master multivariable calculus, partial derivatives, and multiple integrals in 3D space.
Model higher-dimensional constraints with OrgFlow and share annotated diagrams through DiagramDB as you collaborate.
📐 Vectors and 3D Space
Extend calculus concepts into three dimensions with vectors, planes, and surfaces.
Key Concepts:
- • Vector operations (dot product, cross product)
- • Equations of lines and planes
- • Cylindrical and spherical coordinates
- • Vector-valued functions
∂ Partial Derivatives
Analyze functions of multiple variables by taking derivatives with respect to one variable at a time.
Topics:
- • Partial derivatives ∂f/∂x, ∂f/∂y
- • Gradient vectors and directional derivatives
- • Tangent planes and linear approximation
- • Chain rule for multivariable functions
- • Critical points and second derivative test
∫∫ Multiple Integrals
Extend integration to functions of multiple variables for calculating volumes, masses, and more.
Integration Methods:
- • Double integrals over rectangles and general regions
- • Triple integrals and volumes
- • Change of variables (Jacobian)
- • Cylindrical and spherical coordinates
∇ Vector Calculus
Study vector fields and their properties using line integrals, surface integrals, and fundamental theorems.
Major Theorems:
- • Line integrals and work
- • Green's Theorem
- • Divergence and curl
- • Stokes' Theorem
- • Divergence Theorem (Gauss's Theorem)
Need help with 3D visualizations? Check out DiagramDB (diagramdb.com) for collaborative diagrams.