1 Preliminary 11 Introduction 12 Cardinality 13 Topology of the Euclidean space 14 Metric space and Baire Category theorem 15 Continuous functions and Distance in metric space 151 Hausdorff distance and Gromov-Hausdorff distance 152 Invariant of domain 2 Lebesgue measure 21 Exterior measure 22 Measure 23 Borel sets and Measurable sets 24 Linear transformation of measurable sets 25 Sets of positive measure 3 Measurable functions 31 Measurable functions 32 Simple functions 33 Littlewood’s Three principles 4 Lebesgue’s integration theory 41 Integration 42 Interchanging limits with integrals 43 Lebesgue vs Riemann 44 Fubini’s Theorem 5 Differentiation 51 Monotone functions 52 Fundamental theorem of Calculus I 521 A detour: Bounded variation functions 53 Fundamental theorem of Calculus II 54 Lebesgue Differentiation Theorem 6 Function spaces 61 L P spaces 611 Normed vector space 612 A detour: Convexity and Jensen’s inequality 613 Completeness: Banach space 614 Separability 62 Hilbert space:
《大学计算机基础》 《英语阅读》 《英语写作》 《英语听力》 《英语口语》 《雅思专项培训》 《高等数学》 《管理学》 《财务管理》 《Marketing Principles》 《Statistics Analysis》 《Introduction to Business Law》 《Introduction to Accounting》 《Financial Information for Decision Making》 《Quantitative Analysis for Business》 《运筹学》
Chapter 12 Time Series Analysis 12.1 Stochastic processes A stochastic process is a family of random variables {Xt,t ET}. Example{St,t 0, 1,2,...} where St i=o X; and iid(0,2). St has a different distribution at each point t
To use regression analysis to predict the value of a dependent variable based on an independent variable The meaning of the regression coefficients bo and b . To evaluate the assumptions of regression analysis and know what to do if the assumptions are violated . To make inferences about the slope and correlation coefficient . To estimate mean values and predict individual values
Mesh analysis is applicable only to those networks, which are planar. If it is possible to draw the diagram of a circuit on a plane surface in such a way that no branch passes over or under any other branch, then that circuit is said to be planar circuit. (Non-planar-circuit