Calculus (2)

Pre-order courses: Calculus (1)

Course description:

This course is a scientific, systematic introduction to the functions, limits and continuity, derivative and differential, mean value theorem of differentials and the application of derivative , indefinite integral, definite integral, multivariate function calculus, infinite series, initial of differential equations, and difference equations, etc, and discussed the application of relevant examples and economic model. In addition to each section is equipped with the basic exercises, each chapter is also equipped with selected after a comprehensive exercise.

PROGRESSIVE ASSESSMENT

Coursework assignment (30%)

2 hour examination (70%)

Textbooks and References:

1 Zhu Laiyi. Calculus (21st Century course, colleges and universities mathematical foundations of economic management disciplines), Beijing: Higher Education Press, 2010

2. Liu Jianya, Wu Zhen, Jiang Xiaoyun. Calculus (2nd Edition) Higher Education Press, 2011.

3. Tongji University, Department of Mathematics, College Mathematics (Sixth Edition) Higher Education Press

4. Guo Dajun, Chen Yumei. Mathematical Analysis, Shandong Science and Technology Press, 2004

5. Fudan University, Department of Mathematics. Ou Yangguangzhong, Zhu Xueyan, Jin Fulin, Chen ChuanZhang. "Mathematical Analysis (third edition)," Higher Education Press. 2007

6, East China Normal University. "Mathematical Analysis (fourth edition)," Higher Education Press, 2010

7 (America) Tom M.Aposto. Mathematical Analysis, Second mathematical analysis (English • 2nd Edition) Addison-Wesley 2004 . 07 . 26

Teaching content:

Week1: The Definite Integral

§ 6.1 Concepts and properties of definite integrals

First, two examples

Second, the definition of the definite integral

Third, the geometric meaning of the definite integral

Fourth, the basic properties of the definite integral

Week2: § 6.2 Fundamental Theorem of The Calculus

First,variable limit integral with the original function;

Second, the Fundamental Theorem of The Calculus; Newton - Leibniz formula.

Week3: § 6.3 The integration by substitution and integration by parts

First, integration bysubstitution

Second, integration by parts

§ 6.4 Application of definite integral

First, the area of ​​plane figures;

Second, the three-dimensional volume;

Third, the simple economic application problems.

Week4: § 6.5 Improper integrals

First, the infinite integral

Second,defect integral

Three, Gfunction and BFunction

Week5:The Calculus of Multivariate Function

§ 7.1 Preliminaries

Spatial Cartesian coordinate system, spatial distance between two points, surface equation. Plane-regional, interior point, exterior point, the boundary point, open set, open domain and closed domain.

§ 7.2 The concept of multivariate function

First, definition of multivariate function;

Second, domain of bivariate function and geometric meaning of bivariate function;

Third, the limits and continuity of bivariate function .

Week 6: § 7.3 Directional derivative, partial derivative and total differential

First, the direction ofderivative andpartial derivative;

Second, the total differential

Third, the gradient

Week 7: § 7.4 Differential of multiple composite function and implicit differentiation

First, differential of multiple composite function

Second, total differential form invariance

Third, implicit differentiation

§ 7.5 Higher-order derivative and high-order total differential

First, the high-order partial derivatives

Second, the high-order total differential

Third, the Taylor formula function bivariate function

Week 8: § 7.6 Multivariate function extreme value

One, multi-function extreme value;

Definition of bivariate function extreme value;

Necessary conditions of bivariate function extreme value;

Sufficient conditions of bivariate function extreme value;

Second,Conditional extreme value and Lagrange multiplier method.

Week 9: § 7.7 Double integrals

First, the concept and nature of double integrals

Second, the calculation of double integrals

Third, the unbounded domains double integrals

Week 10: § 8.1 Infinite series

First, the concept of Infinite series，Convergence and divergence of infinite series;

geometric progression and harmonic series;

Second, the basic properties of convergent series；

A necessary condition for convergence of infinite series; convergent series of basic properties.

§ 8.2 Positive Series

First, the concept of positive series converges; positive series converges necessary and sufficient condition;

Second, D'Alembert ratio test, Cauchy root test, P-series convergence and divergence.

Week 11: § 8.3General series

The concept of alternating series; Leibniz test; absolutely convergent series ; conditional convergence series;

Week 12: § 8.4 Power Series

First, the concept of Functional Series

Second, the power series and its convergence

Third, the basic nature of power series

Fourth, the Taylor series and its applications

Week 13: § 9.1 The basic concepts of differential equations

First, the definition of differential equations,

Second, the differential equations (general solution, particular solution), boundary conditions and initial value problems, and other basic concepts.

§ 9.2 First-order differential equations

First, separable differential equation of variables;

Second, the homogeneous differential equation;

Third, the first-order linear differential equations.

Week 14: § 9.3 Second-order linear differential equations with constant coefficients

First, second-order homogeneous linear equations with constant coefficients;

Second, the second-order constant coefficient non-homogeneous linear equations.

§ 9.4 Application of differential equations in economics

First, the new product promotion model

Second, the price adjustment model

Three, personnel allocation model

Week 15 § 10.1 The basic concepts of difference equations

The concept of difference and difference equations, the order of the difference equation, the solution (general solution, particular solution).

§10.2 first-order linear difference equations with constant coefficients

First, general solution for first-order homogeneous difference equation;

Second, particular solution and the general solution for first-order inhomogeneous difference equation .

Third, the general solution for second-order homogeneous equation with constant coefficients;

Week 16 § 10.3 Simple applications of difference equation in economics

First, the "raising educational funds" model

Second, the price and inventory model

Third, the stability of the national income analysis model

Week 17: Final Examination