Concept of indefinite integration,basic integration formulas,the methods of change of variables, n by part. 2 Master the methods of change of variables and integtation by part for indefinite integrals. Chapter 6.definite Integration(16 class hours) Concept of definite integration,basic properties of definitive integration,basic integration formulas,the Newton-Leibniz formula,the methods of change of variables,integration by part.Application of definite equireme ot of definite and n of ir 9 al a Be famili正 n-Leibniz for eorem M erthemethodsofchangeofvariablesandintegrationby.partforhothindefiniteanddefinite nt Be able to compute the area of the plane graph and the volume of the rotation bodies.Be able to solve the simple applying problem about economics. 6. Comprehend the concept of general integration.Be able to compute the general integration. Chapter 7.Multivariate Differentiation and Integration (38 class hours) Conce vec curved surtace plane and multvarable function,directional derivatives, tion,partial derivative for c Basic tio high orders partia derivative,extreme value equirem +h。 etric idea of multi 2 Co and the erties of continuous function on a closed bounded set mprehend omrehend the concents of partial derivative and total differentiation Be able to compute 3 first order and second order partial derivative and total differentiation for composite functions.Be able to solve the partial derivative for implicit functions 4. Understand the concepts of extreme value and conditional extreme value of a multivariate function be able to solve the extreme value of a bi-variate function:know the Legrand's multiplier method:be able to solve some simple multivariate functions'maximum and minimum value problem and simple application problem in practice 5. omprehend the conc nstant series,positiv eseries,real number series,power series Comprehend the concepts of convergence diver gence and summation of an infinite series Master the basic properties of an infinite series and the necessary condition for its convergence Be familiar with geometric series and p-series and their convergence property Master its comparison test and ratio test 3. Understand the Leibniz theorem for alternate series:Know the concepts of absolute convergence and conditional convergence of an infinite series and their relationshin. Be able to calculate the convergence ratio.convergent interval and convergent fields Comprehend the basic properties of power series on its convergence interval (continuity of sum function.successive term differentiation and integration)Master the method to solve certain 6. urin expansion of to expand some basic functions in to power series. Chapter 9.Ordinary Differe s orde homogenous linear differential equation ith ic Reo quir al equation applications in the economic ent Concept of indefinite integration, basic integration formulas, the methods of change of variables, integration by part. Basic Requirement 1. Understand the concept and properties of indefinite integrals. Master the basic properties and basic formula of indefinite integration. 2. Master the methods of change of variables and integration by part for indefinite integrals. Chapter 6. definite Integration (16 class hours) Concept of definite integration, basic properties of definitive integration, basic integration formulas, the Newton-Leibniz formula, the methods of change of variables, integration by part. Application of definite integration, generalized integration. Basic Requirement 1. Comprehend the concept of definite integration, basic properties and mean value of integration. 2. Understand the definite integral as a function of its integration limits and its derivative theorem. 3. Be familiar with the Newton-Leibniz formula. 4. Master the methods of change of variables and integration by part for both indefinite and definite integrals. 5. Be able to compute the area of the plane graph and the volume of the rotation bodies. Be able to solve the simple applying problem about economics. 6. Comprehend the concept of general integration. Be able to compute the general integration. Chapter 7. Multivariate Differentiation and Integration (38 class hours) Concept of vector Algebra, curved surface , plane and multivariable function, directional derivatives, partial derivative and total differentiation, partial derivative for composite functions and implicit functions, higher orders partial derivative, extreme value of a multivariate function, double integrals. Basic Requirement 1. Comprehend the concept and the geometric idea of multivariable function. 2. Comprehend concept of limit and continuity for bivariate functions.Comprehend properties of continuous function on a closed bounded set. 3. Comprehend the concepts of partial derivative and total differentiation. Be able to compute the first order and second order partial derivative and total differentiation for composite functions,. Be able to solve the partial derivative for implicit functions. 4. Understand the concepts of extreme value and conditional extreme value of a multivariate function; be able to solve the extreme value of a bi-variate function; know the Legrand’s multiplier method; be able to solve some simple multivariate functions' maximum and minimum value problem and simple application problem in practice. 5. Comprehend the concepts of double integrals and their properties. Master the method to calculate the double integrals (under Euclidean and polar coordinate system). Chapter 8. Series (16 class hours) Concepts and properties of constant series, positive series, real number series, power series. Basic Requirement 1. Comprehend the concepts of convergence, divergence and summation of an infinite series. 2. Master the basic properties of an infinite series and the necessary condition for its convergence. Be familiar with geometric series and p-series and their convergence property. Master its comparison test and ratio test. 3. Understand the Leibniz theorem for alternate series; Know the concepts of absolute convergence and conditional convergence of an infinite series and their relationship. 4. Be able to calculate the convergence ratio, convergent interval and convergent fields . 5. Comprehend the basic properties of power series on its convergence interval (continuity of sum function , successive term differentiation and integration ). Master the method to solve certain simple power series. 6. Be able to use Maclaurin expansion of to expand some basic functions in to power series. Chapter 9. Ordinary Differential Equation (16 class hours ) Basic concept, differential equation, the second order homogenous linear differential equation with constant coefficients, differential equation applications in the economics. Basic Requirement