Author(s): Joel Feldman, Andrew Rechnitzer and Elyse Yeager
Series: CLP Calculus 03
Edition: Exercises
Publisher: University of British Columbia
Year: 2021
Language: English
Tags: mathematics; maths; math; calc; calculus; single variable; limits; differentiation; differential; integration; integral; continuity; differentiability; analysis; real; complex; multiple variables; multivariable; multivariate; several variables; many variables
How to use this book
I The questions
Vectors and Geometry in Two and Three Dimensions
Points
Vectors
Equations of Lines in 2d
Equations of Planes in 3d
Equations of Lines in 3d
Curves and their Tangent Vectors
Sketching Surfaces in 3d
Partial Derivatives
Limits
Partial Derivatives
Higher Order Derivatives
The Chain Rule
Tangent Planes and Normal Lines
Linear Approximations and Error
Directional Derivatives and the Gradient
A First Look at Partial Diferential Equations
Maximum and Minimum Values
Lagrange Multipliers
Multiple Integrals
Double Integrals
Double Integrals in Polar Coordinates
Applications of Double Integrals
Surface Area
Triple Integrals
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
II Hints to problems
1.1 Points
1.2 Vectors
1.3 Equations of Lines in 2d
1.4 Equations of Planes in 3d
1.5 Equations of Lines in 3d
1.6 Curves and their Tangent Vectors
1.7 Sketching Surfaces in 3d
2.1 Limits
2.2 Partial Derivatives
2.3 Higher Order Derivatives
2.4 The Chain Rule
2.5 Tangent Planes and Normal Lines
2.6 Linear Approximations and Error
2.7 Directional Derivatives and the Gradient
2.8 A First Look at Partial Diferential Equations
2.9 Maximum and Minimum Values
2.10 Lagrange Multipliers
3.1 Double Integrals
3.2 Double Integrals in Polar Coordinates
3.3 Applications of Double Integrals
3.4 Surface Area
3.5 Triple Integrals
3.6 Triple Integrals in Cylindrical Coordinates
3.7 Triple Integrals in Spherical Coordinates
III Answers to problems
1.1 Points
1.2 Vectors
1.3 Equations of Lines in 2d
1.4 Equations of Planes in 3d
1.5 Equations of Lines in 3d
1.6 Curves and their Tangent Vectors
1.7 Sketching Surfaces in 3d
2.1 Limits
2.2 Partial Derivatives
2.3 Higher Order Derivatives
2.4 The Chain Rule
2.5 Tangent Planes and Normal Lines
2.6 Linear Approximations and Error
2.7 Directional Derivatives and the Gradient
2.8 A First Look at Partial Diferential Equations
2.9 Maximum and Minimum Values
2.10 Lagrange Multipliers
3.1 Double Integrals
3.2 Double Integrals in Polar Coordinates
3.3 Applications of Double Integrals
3.4 Surface Area
3.5 Triple Integrals
3.6 Triple Integrals in Cylindrical Coordinates
3.7 Triple Integrals in Spherical Coordinates
IV Solutions to problems
1.1 Points
1.2 Vectors
1.3 Equations of Lines in 2d
1.4 Equations of Planes in 3d
1.5 Equations of Lines in 3d
1.6 Curves and their Tangent Vectors
1.7 Sketching Surfaces in 3d
2.1 Limits
2.2 Partial Derivatives
2.3 Higher Order Derivatives
2.4 The Chain Rule
2.5 Tangent Planes and Normal Lines
2.6 Linear Approximations and Error
2.7 Directional Derivatives and the Gradient
2.8 A First Look at Partial Diferential Equations
2.9 Maximum and Minimum Values
2.10 Lagrange Multipliers
3.1 Double Integrals
3.2 Double Integrals in Polar Coordinates
3.3 Applications of Double Integrals
3.4 Surface Area
3.5 Triple Integrals
3.6 Triple Integrals in Cylindrical Coordinates
3.7 Triple Integrals in Spherical Coordinates
