Contents
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