Calculus (1)
Pre-order courses:
Course description:
This course is a scientific, systematic introduction to the functions, limits and continuity, derivative and differential, derivative value theorem and applications, indefinite integral, definite integral, multi-function calculus, infinite series, differential equations and differential equations and other content preliminary and discusses the relevant application examples and economic model. In addition to each section is equipped with basic exercises, each chapter is also equipped with a comprehensive selection of exercises.
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: Chapter1. Functions
§ 1.1. Preliminaries
Real number, the absolute value, interval, neighborhood, a collection.
§ 1.2. The concept of a function
Constants and variables; function definitions
§ 1.3. Geometric characteristics of the function
Monotonicity, boundedness, parity, periodicity.
§ 1.4. Inverse function
Definition and its inverse function graph, inverse trigonometric functions and their principal values.
Week2: § 1.5. Composite function definition
§ 1.6. Basic elementary functions
The definition of basic elementary functions, domain and range of functions; elementary function definition.
§ 1.7. Establish function examples
Economic function ---- total cost function, the total revenue function, the total profit function, demand function, supply function and so on.
Week3: Chapter Limits and Continuity
§2.1. Limit of a sequence
The concept of the sequence,
geometric meaning for limit of a sequence ,
Monotone bounded principle.
§ 2.2. Limit of a function
First, the limit of a function
Second, understanding the limit of a function by it's graph
Third, recognize limit of a function by the function value
Week4: § 2.3. The nature of the limit of a function and four arithmetic operations of functional limit
The nature of the limit of a function;
Four arithmetic operations of functional limit
Week5:§ 2.4. Infinitesimals and infinitely large number
Infinitesimal definition and basic properties of infinitesimal compared; infinite number of definitions; infinitesimal and infinite number of relationships.
Week6: § 2.5. Continuity of a function
Function of the amount of change; function continuity, left continuous and right continuous; relationship between continuity and limits.
Function and classification of discontinuities.
Inverse function and composite function continuity; elementary functions continuity; piecewise continuity.
§ 2.6. Continuous function on a closed interval
Boundedness theorem, the most value theorem, intermediate value theorem, Zero Theorem.
Week 7: Derivative and differential
§ 3.1. Concept of derivative
Speed linear motion speed;
plane tangent to the curve slope;
derivative definition and geometric meaning;
derivable with continuous relationship.
§ 3.2. Derivative operation with the derivation formula
I. four arithmetic of derivative
Second, the anti-derivative of a function
Third, the basic derivative formula
Week8: § 3.3. Composite function derivative rule
First, composite function derivation rules
Second, the logarithmic derivative method
Third, the implicit function rule
§ 3.4. Differential its calculation
Differential definition and geometry meaning; derivable relationship with differentiable; parametric equation derivation formula; differential form invariance.
Week9: § 3.5. Higher-order derivatives and higher-order differential
First, the higher-order derivatives
Leibniz derivation formula
Second, the high-order differential
§ 3.6 Simple application of derivative and differential
Concept of marginal andelasticity.
Week10: Mean Value Theorem and Applications of Derivatives
§ 4.1. Differential Mean Value Theorem
Rolle mean value theorem, Lagrange mean value theorem, Cauchy mean value theorem.
Week 11: § 4.2 Taylor formula
Taylor's formula and its application in the limit
Week12：§ 4.3. L'Hospital's Rule
Week13: § 4.4. Monotonicity and convexity
One, a sign of the first-order derivative and monotonicity
Second, a sign of the second-order derivative of the convexity of the function symbols
Week14: § 4.5 Function extreme value and maximum (small) value
Definition of function extreme value,
Necessary conditions for the extreme value
Sufficient condition for the extreme value ;
Concept of most value of function, to find the most value of the function basic steps.
§ 4.6 Graphing a function
Asymptotic lines, plotted as a function
Week 15: Indefinite integral
§ 5.1. Concept of indefinite integral
The concept of the original function; indefinite integral definition and geometric meaning; basic properties of indefinite integrals.
§ 5.2. Basic integral formula
Week 16: § 5.3 Minato differentiation and integration by parts
§ 5.4 Integration bysubstitution
Week 17: Final Examination