Nguồn ngoài

Multivariable Calculus

Mathematics

Tác giả: Jessica Kuang
Nhà xuất bản: Oxnard College
Nguồn: LibreTexts
Giấy phép: CC BY
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 83 mục

01: Vectors and the Geometry of Space
1.01: Vectors in the Plane
1.1E: Exercises for Vectors in the Plane
1.02: Vectors in Space
1.2E: Exercises for Vectors in Space
1.03: The Dot Product
1.3E: Exercises for The Dot Product
1.04: The Cross Product
1.4E: Exercises for The Cross Product
1.05: Equations of Lines and Planes in Space
1.5E: Exercises for Equations of Lines and Planes in Space
1.06: Quadric Surfaces
1.6E: Exercises for Quadric Surfaces
1.07: Cylindrical and Spherical Coordinates
1.7E: Exercises for Cylindrical and Spherical Coordinates
1.E: Chapter 1 Review Exercises
02: Functions of Multiple Variables and Partial Derivatives
2.01: Introduction to Functions of Multiple Variables
2.02: Functions of Multiple Variables
2.2E: Functions of Multiple Variables (Exercises)
2.03: Limits and Continuity
2.3E: Exercises for Limits and Continuity
2.04: Partial Derivatives
2.4E: Partial Derivatives (Exercises)
2.05: Tangent Planes Linear Approximations and the Total Differential
2.5E: Tangent Planes Linear Approximations and the Total Differential (Exercises)
2.06: The Chain Rule for Functions of Multiple Variables
2.6E: The Chain Rule for Functions of Multiple Variables (Exercises)
2.07: Directional Derivatives and the Gradient
2.7E: Directional Derivatives and the Gradient (Exercises)
2.08: Taylor Polynomials of Functions of Two Variables
2.8E: Taylor Polynomials of Functions of Two Variables (Exercises)
2.09: Optimization of Functions of Several Variables
2.9E: Optimization of Functions of Several Variables (Exercises)
2.10: Constrained Optimization
2.10E: Optimization of Functions of Several Variables (Exercises)
2.11: Lagrange Multipliers
2.11E: Exercises for Lagrange Multipliers
03: Multiple Integration
3.01: Iterated Integrals and Area
3.1E: Iterated Integrals and Area (Exercises)
3.02: Double Integrals Over Rectangular Regions
3.2.01: Double Integrals Part 1 (Exercises)
3.03: Double Integrals Over General Regions
3.3.01: Double Integrals Part 2 (Exercises)
3.04: Double Integration with Polar Coordinates
3.4b: Double Integrals in Polar Coordinates
3.4E: Double Integrals in Polar Coordinates (Exercises)
3.05: Triple Integrals
3.5E: Triple Integrals (Exercises)
3.06: Triple Integrals in Cylindrical and Spherical Coordinates
3.07: Calculating Centers of Mass and Moments of Inertia
3.08: Change of Variables in Multiple Integrals (Jacobians)
3.E: Chapter 3 Review Exercises
04: Vector-valued Functions
4.01: Vector-Valued Functions and Space Curves
4.1E: Exercises for Section 12.1
4.02: The Calculus of Vector-Valued Functions
4.2E: Exercises for Section 12.2
4.03: The Calculus of Vector-Valued Functions II
4.04: Motion in Space
4.4E: Exercises for Section 12.3
4.05: Arc Length and Curvature
4.5E: Exercises for Section 12.4
4.06: Acceleration and Kepler's Laws
4.6E: Exercises for Section 12.5
4.E: Chapter 4 Review Exercises
05: Vector Fields Line Integrals and Vector Theorems
5.01: Introduction to Vector Field Chapter
5.02: Vector Fields
5.2E: Vector Fields (Exercises)
5.03: Line Integrals
5.3.01: Line Integrals - Part 2
5.3E: Line Integrals (Exercises)
5.04: Conservative Vector Fields
5.4E: Conservative Vector Fields (Exercises)
5.05: Green's Theorem
5.5E: Green's Theorem (Exercises)
5.06: Divergence and Curl
5.6E: Divergence and Curl (Exercises)
5.07: Surface Integrals
5.08: Stokes' Theorem
5.09: The Divergence Theorem