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CLP-3 Multivariable Calculus
This textbook covers multivariable Calculus. There are chapters on vectors and geometry in 2 and 3 dimensions, partial derivatives, and multivariable integrals.
- Author
- Joel Feldman, Andrew Rechnitzer, & Elyse Yeager
- Publisher
- University of British Columbia
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 43 sections
- 01: Vectors and Geometry in Two and Three Dimensions
- 1.01: Points
- 1.02: Vectors
- 1.03: Equations of Lines in 2d
- 1.04: Equations of Planes in 3d
- 1.05: Equations of Lines in 3d
- 1.06: Curves and their Tangent Vectors
- 1.07: Sketching Surfaces in 3d
- 1.08: Cylinders
- 1.09: Quadric Surfaces
- 02: Partial Derivatives
- 2.01: Limits
- 2.02: Partial Derivatives
- 2.03: Higher Order Derivatives
- 2.04: The Chain Rule
- 2.05: Tangent Planes and Normal Lines
- 2.06: Linear Approximations and Error
- 2.07: Directional Derivatives and the Gradient
- 2.08: Optional Solving the Wave Equation
- 2.09: Maximum and Minimum Values
- 2.10: Lagrange Multipliers
- 03: Multiple Integrals
- 3.01: Double Integrals
- 3.02: Double Integrals in Polar Coordinates
- 3.03: Applications of Double Integrals
- 3.04: Surface Area
- 3.05: Triple Integrals
- 3.06: Triple Integrals in Cylindrical Coordinates
- 3.07: Triple Integrals in Spherical Coordinates
- 3.08: Optional Integrals in General Coordinates
- 04: Appendices
- 4.01: A Appendices
- 4.1.01: A.1: Trigonometry
- 4.1.02: A.2: Powers and Logarithms
- 4.1.03: A.3: Table of Derivatives
- 4.1.04: A.4: Table of Integrals
- 4.1.05: A.5:Table of Taylor Expansions
- 4.1.06: A.6: 3d Coordinate Systems
- 4.1.07: A.7: ISO Coordinate System Notation
- 4.1.08: A.8: Conic Sections and Quadric Surfaces
- 4.02: B: Hints for Exercises
- 4.03: C: Answers to Exercises
- 4.04: D: Solutions to Exercises