Nguồn ngoài
Vector Calculus
The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. The content in this Textmap is complemented by Vector Calculus Modules in the Core and the Vector Calculus (UCD Mat 21D) Libretext.
- Tác giả
- Michael Corral
- Nhà xuất bản
- Schoolcraft College
- Nguồn
- LibreTexts
- Giấy phép
- GNU FDL
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 37 mục
- 01: Vectors in Euclidean Space
- 1.01: Introduction
- 1.02: Vector Algebra
- 1.03: Dot Product
- 1.04: Cross Product
- 1.05: Lines and Planes
- 1.06: Surfaces
- 1.07: Curvilinear Coordinates
- 1.08: Vector-Valued Functions
- 1.09: Arc Length
- 1.E: Vectors in Euclidian Space (Exercises)
- 02: Functions of Several Variables
- 2.01: Functions of Two or Three Variables
- 2.02: Partial Derivatives
- 2.03: Tangent Plane to a Surface
- 2.04: Directional Derivatives and the Gradient
- 2.05: Maxima and Minima
- 2.06: Unconstrained Optimization- Numerical Methods
- 2.07: Constrained Optimization - Lagrange Multipliers
- 2.E: Functions of Several Variables (Exercises)
- 03: Multiple Integrals
- 3.01: Double Integrals
- 3.02: Double Integrals Over a General Region
- 3.03: Triple Integrals
- 3.04: Numerical Approximation of Multiple Integrals
- 3.05: Change of Variables in Multiple Integrals
- 3.06: Application- Center of Mass
- 3.07: Application- Probability and Expectation Values
- 3.E: Multiple Integrals (Exercises)
- 04: Line and Surface Integrals
- 4.01: Line Integrals
- 4.02: Properties of Line Integrals
- 4.03: Greens Theorem
- 4.04: Surface Integrals and the Divergence Theorem
- 4.05: Stokes Theorem
- 4.06: Gradient Divergence Curl and Laplacian
- 4.E: Line and Surface Integrals (Exercises)