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Chapter 8 Infinitive series 8.1 The concepts and characters of infinite series 8.1.1 The concepts of constant term progression 8.1.2 The convergence and divergence of infinite series 8.1.3 The characters of convergent series Exercises 8.2 Positive series and its convergence test 8.2.1 The basic characters of positive series 8.2.2 The comparison test of positive series 8.2.3 d'Alembert method of positive series 8.2.4 The root test of positive series Exercises 8.3 Arbitrary term progression 8.3.1 Alternating series and Leibniz Principle 8.3.2 The absolute value method of arbitrary term progression Exercises 8.4 Power series 8.4.1 Function series 8.4.2 Power series and its convergent interval 8.4.3 The properties of power series Exercises 8.5 Unfold functions into power series 8.5.1 Taylor series 8.5.2 The method to unfold functions into power series Exercises Summary Quiz Exercises Chapter 9 Differential equations 9.1 Basic concepts of differential equation Exercises 9.2 First-order differential equation 9.2.1 Separable differential equation 9.2.2 Homogeneous differential equation 9.2.3 First-order linear differential equation 9.2.4 Bernoulli equation Exercises 9.3 Reducible high-order differential equation 9.3.1 The formy("~=f(x) 9.3.2 The form y"= f(x,y') 9.3.3 The formy"=f(y,y') Exercises 9.4 High-order linear differential equation 9.4.1 The property and structure of solution of second-order linear differential equation 9.4.2 The property and structure of solution of high-order linear differential equation Exercises 9.5 Second-order linear differential equation with constant coefficients 9.5.1 Second-order homogeneous linear differential equation with constant