Chapter 7 Differential Equations
7.1 Basic Concepts of Differential Equations
7.1.1 Examples of Differential Equations
7.1.2 Basic Concepts
7.1.3 Geometric Interpretation of the First-Order Differential Equation
Exercises 7.1
7.2 First-Order Differential Equations
7.2.1 First-Order Separable Differential Equation
7.2.2 Homogeneous First-Order Equations
7.2.3 Linear First-Order Equations
7.2.4 Bernoulli's Equation
7.2.5 Some Other Examples that can be Reduced to Linear First-Order Equations
Exercises 7.2
7.3 Reducible Second-Order Differential Equations
Exercises 7.3
7.4 Higher-Order Linear Differential Equations
7.4.1 Some Examples of Linear Differential Equation of Higher-Order
7.4.2 Structure of Solutions of Linear Differential Equations
Exercises 7.4
7.5 Higher-Order Linear Equations with Constant Coefficients
7.5.1 Higher-Order Homogeneous Linear Equations with Constant Coefficients
7.5.2 Higher-Order Nonhomogeneous Linear Equations with Constant Coefficients
Exercises 7.5
7.6 Euler's Differential Equation
Exercises 7.6
7.7 Applications of Differential Equations
Exercises 7.7
Chapter 8 Vectors and Solid Analytic Geometry
8.1 Vectors in Plane and in Space
8.1.1 Vectors
8.1.2 Operations on Vectors
8.1.3 Vectors in Plane
8.1.4 Rectangular Coordinate System
8.1.5 Vectors in Space
Exercises 8.1
Part A
Part B
8.2 Products of Vectors
8.2.1 Scalar Product of two Vectors
8.2.2 Vector Product of two Vectors
8.2.3 Triple Scalar Product of three Vectors
8.2.4 Applications of Products of Vectors
Exercises 8.2
Part A
Part B
8.3 Planes and Lines in Space
8.3.1 Equations of Planes
8.3.2 Equations of Lines in Space
Exercises 8.3
Part A
Part B
8.4 Surfaces and Space Curves
8.4.1 Cylinders
8.4.2 Cones
8.4.3 Surfaces of Revolution
8.4.4 Quadric Surfaces
8.4.5 Space Curves
……
Chapter 9 The Differential Calculus for Multi-variable Functions
Chapter 10 Applications of Multi-variable Functions
Chapter 11 Multiple Integrals
Chapter 12 Line Integrals and Surface Integrals
Bibliography
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