책소개

"`This book is intended to help readers understand spatial geometry through vectors and to apply vector methods to a wide range of physical phenomena. The concepts of differentiation and integration introduced in single-variable calculus are extended to functions of several variables, enabling readers to solve problems involving the maximum and minimum values of multivariable functions as well as applications such as computing the volume of solids. In addition, vector-valued functions are introduced to facilitate a better understanding of various physical phenomena. Therefore, a basic knowledge of single-variable calculus is assumed.
This book consists of seven chapters.
Chapter 1 introduces sequences and series.
Chapter 2 presents vectors and vector spaces from a conceptual point of view.
Chapter 3 introduces vectors and discusses lines and planes using the dot product and the cross product.
Chapter 4 extends the study of lines and planes to curves and surfaces. Particular emphasis is placed on quadric surfaces, the arc length of space curves, and curvature.
Chapter 5 deals with limits, continuity, and partial derivatives of multivariable functions. It also introduces tangent planes and the chain rule for functions of two variables. Furthermore, the concept of the gradient vector and its applications are presented, including problems involving tangent planes and the determination of maximum and minimum values.
Chapter 6 focuses on multiple integrals. It explains the computation of double and triple integrals in various coordinate systems and discusses the evaluation of multiple integrals through changes of variables.
Chapter 7 introduces differential equations, which have numerous applications in science, engineering, economics, and many other fields.
Finally, I would like to express my sincere gratitude to Freedom Academy for making the publication of this book possible. Any corrections or updates identified after publication will be made available in the Resources section of the Freedom Academy website(www.freeaca.com) for reference. I also hope that this book will help students develop a deeper understanding of calculus and apply what they have learned effectively in their major fields of study."

저자소개

목차

"`01 Sequences and Series
1.1 Sequence
1.2 Infinite series
1.3 Power series
02 Parametric Equation and Polar Coordinate
2.1 Parametric Equation
2.2 Polar Coordinates
2.3 Conic Curve
03 Vectors and the Geometry of Space
3.1 Vectors
3.2 Space Coordinate and Vectors in Space Coordinates in Space
3.3 The Dot Product of Two Vectors
3.4 The Cross Product
3.5 Equations of Lines and Planes
04 Calculus of Vector Functions
4.1 Vector Functions and Limits
4.2 Differentiation and Integration of Vector Functions
4.3 Arc length, Unit tangent vector, Unit normal vector
4.4 Curvature and Radius of Curvature
4.5 Velocity and Acceleration in Space
05 Partial Derivatives
5.1 Functions of Several Variables
5.2 Limits and Continuity
5.3 Partial Derivatives
5.4 The Chain Rule
5.5 Directional Derivatives and Gradients
5.6 Extrema of functions of Two variables
5.7 Lagrange Multipliers
06 Multiple Integration
6.1 Double Integrals and Volume
6.2 Double Integrals in Polar Coordinate
6.3 Triple Integrals
6.4 Triple Integrals in Cylindrical and Spherical Coordinates
6.5 Change of Variables for Double Integrals
07 Differential Equation
7.1 Gradient Fields and Euler`s Theorem
7.2 Differential Equation with Separation of Variables
7.3 Homogeneous Differential Equation
7.4 Total Differential Equation
7.5 Linear Differential Equation
7.6 Applications of Linear Differential Equations
Solution
Index"