MTH2301 Multivariable Calculus

MTH2301 is a course in multivariable calculus, which is the study of calculus with functions of multiple variables. It covers topics such as vectors, partial differentiation, and multiple integration.

Mathematics

Tác giả: Veronique Van Lierde
Nhà xuất bản: Al Akhawayn University
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 150 mục

09: Sequences and Series
9.00: Prelude to Sequence and Series
9.01: Sequences
9.1E: Exercises for Sequences
9.02: Infinite Series
9.2E: Exercises for Infinite Series
9.03: The Divergence and Integral Tests
9.3E: Exercises for Divergence and Integral Tests
9.04: Comparison Tests
9.4E: Exercises for Comparison Test
9.05: Alternating Series
9.5E: Exercises for Alternating Series
9.06: Ratio and Root Tests
9.6E: Exercises for Ratio and Root Tests
9.07: Chapter 9 Review Exercises
10: Power Series
10.00: Prelude to Power Series
10.01: Power Series and Functions
10.1E: Exercises for Section 10.1
10.02: Properties of Power Series
10.2E: Exercises for Section 10.2
10.03: Taylor and Maclaurin Series
10.3E: Exercises for Taylor Polynomials and Taylor Series
10.04: Working with Taylor Series
10.4E: Exercises for Section 10.4
10.05: Chapter 10 Review Exercises
11: Vectors and the Geometry of Space
11.00: Prelude to Vectors in Space
11.01: Vectors in the Plane
11.1E: Exercises for Vectors in the Plane
11.02: Vectors in Space
11.2E: Exercises for Vectors in Space
11.03: The Dot Product
11.3E: Exercises for The Dot Product
11.04: The Cross Product
11.4E: Exercises for The Cross Product
11.05: Equations of Lines and Planes in Space
11.5E: Exercises for Equations of Lines and Planes in Space
11.06: Quadric Surfaces
11.6.00: Quadric surfaces - explore the ellipsoid
11.6.01: Quadric surfaces - explore the hyperboloid of one sheet
11.6.02: Quadric surfaces - explore the hyperboloid of two sheets
11.6.03: Quadric surfaces - explore the elliptic cone
11.6.04: Quadric surfaces - explore the elliptic paraboloid
11.6.05: Quadric surfaces - explore the hyperbolic paraboloid
11.6E: Exercises for Quadric Surfaces
11.07: Cylindrical and Spherical Coordinates
11.7.00: Cylindrical Coordinates
11.7.01: Spherical Coordinates
11.7E: Exercises for Cylindrical and Spherical Coordinates
11.08: Chapter 11 Review Exercises
12: Vector-valued Functions
12.00: Prelude to Vector-valued Functions
12.01: Vector-Valued Functions and Space Curves
12.1E: Exercises for Vector-valued Functions and Space Curves
12.02: The Calculus of Vector-Valued Functions
12.2E: Exercises for The Calculus of Vector-valued Functions
12.03: Arc Length and Curvature
12.3E: Exercises for Arc Length and Curvature
12.04: Motion in Space
12.4E: Exercises for Motion in Space
12.05: Acceleration and Kepler's Laws (optional)
12.5E: Exercises for Acceleration and Kepler's Law
12.06: Review Exercises for Chapter 12
12.07: More Review Exercises for Chapter 12
13: Functions of Multiple Variables and Partial Derivatives
13.00: Introduction to Functions of Multiple Variables
13.01: Functions of Multiple Variables
13.1E: Functions of Multiple Variables (Exercises)
13.02: Limits and Continuity
13.2E: Exercises for Limits and Continuity
13.03: Partial Derivatives
13.3E: Partial Derivatives (Exercises)
13.04: Tangent Planes Linear Approximations and the Total Differential
13.4E: Tangent Planes Linear Approximations and the Total Differential (Exercises)
13.05: The Chain Rule for Multivariable Functions
13.5.00: The Chain Rule for Functions of Multiple Variables (Exercises)
13.06: Directional Derivatives and the Gradient
13.6E: Directional Derivatives and the Gradient (Exercises)
13.07: (OPTIONAL) Taylor Polynomials of Functions of Two Variables
13.7E: Taylor Polynomials of Functions of Two Variables (Exercises)
13.08: Optimization of Functions of Several Variables
13.8E: Optimization of Functions of Several Variables (Exercises)
13.09: Applications of Optimization Constrained Optimization and Absolute Extrema
13.9E: Optimization of Functions of Several Variables (Exercises)
13.10: Lagrange Multipliers
13.10E: Exercises for Lagrange Multipliers
13.11: Chapter 13 Review Exercises
14: Multiple Integration
14.00: Iterated Integrals and Area
14.0E: Iterated Integrals and Area (Exercises)
14.01: Double Integrals Over Rectangular Regions
14.1.00: Double Integrals Part 1 (Exercises)
14.02: Double Integrals Over General Regions
14.2.00: Double Integrals Part 2 (Exercises)
14.03: Double Integration with Polar Coordinates
14.3b: Double Integrals in Polar Coordinates
14.3E: Double Integrals in Polar Coordinates (Exercises)
14.04: Triple Integrals
14.4E: Triple Integrals (Exercises)
14.05: Triple Integrals in Cylindrical and Spherical Coordinates
14.5E: Exercises for Section 14.5
14.06: Calculating Centers of Mass and Moments of Inertia
14.6E: Exercises for Section 14.6
14.07: Change of Variables in Multiple Integrals (Jacobians)
14.7E: Exercises for Section 14.7
14.08: Review Exercises for Chapter 14
14.09: More Chapter 14 Review Exercises
15: Vector Fields Line Integrals and Vector Theorems
15.00: Introduction to Vector Field Chapter
15.01: Vector Fields
15.1E: Exercises for Section 15.1
15.02: Line Integrals
15.2.00: Line Integrals - Part 2
15.2E: Exercises for Section 15.2
15.03: Conservative Vector Fields
15.3E: Exercises for Section 15.3
15.04: Green's Theorem
15.4E: Exercises for Section 15.4
15.05: Divergence and Curl
15.5E: Divergence and Curl (Exercises)
15.06: Surface Integrals
15.6E: Exercises for Section 15.6
15.07: Stokes' Theorem
15.7E: Exercises for Section 15.7
15.08: The Divergence Theorem
15.8E: Exercises for Section 15.8
16: Appendices
16.00: Trigonometric Identities
16.01: Review of Derivative Rules
16.02: Table of Derivatives
16.03: Table of Integrals
17: Visualizations
17.00: Geogebra visual- ellipsoid and its traces
17.01: Geogebra visual- hyperboloid of one sheet and its traces
17.02: Geogebra visual- hyperboloid of two sheets and its traces
17.03: Geogebra visual- elliptic cone and its traces
17.04: Geogebra visual- elliptic paraboloid and its traces
17.05: Geogebra visual- hyperbolic paraboloid and its traces
17.06: Geogebra visual- cylindrical coordinates
17.07: Geogebra visual- spherical coordinates
17.08: Geogebra visual- helix
17.09: New Page
17.10: Animating Motion on a Helix
17.11: Geogebra visual- level surfaces
17.12: Geogebra visual - gradient
17.13: Geogebra visual - partial derivatives and contour plot
17.14: Geogebra visual- parametric equations of an ellipse in a horizontal plane
17.15: Geogebra visual- parametric equations of a line segment in space
Section 17.16: Geogebra visual - vector field in two variables, curl, divergence