§14.1 The elements of nitrogen family 14.1.5 The compounds of As, Sb and Bi 14.1.4 The compounds of phosphorus 14.1.3 The compounds of nitrogen 14.1.2 The elemental substances of nitrogen family 14.1.1 Outline on nitrogen family §14.2 The elements of oxygen 14.2.3 Sulfur and the related compounds 14.2.2 Oxygen and the related 14.2.1 Outline on oxygen family
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:
1 Financial Crisis: A Hardy Perennial 1 2 Anatomy of a Typical Crisis 24 3 Speculative Manias 38 4 Fueling the Flames: The Expansion of Credit 64 5 The Critical Stage 90 6 Euphoria and Economic Booms 113 7 International Contagion 123 8 Bubble Contagion: Tokyo to Bangkok to New York 142 9 Frauds, Swindles, and the Credit Cycle 165 10 Policy Responses: Letting It Burn Out, and Other Devices 203 11 The Domestic Lender of Last Resort 225 12 The International Lender of Last Resort 243 13 The Lessons of History and the Most Tumultuous
6.1 Source terms in momentum equations and two key issues in numerically solving momentum equation 6.1.1 Introduction 6.1.2 Source in momentum equations 6.1.3 Two key issues in solving flow field 6.2 Staggered grid system and discretization of momentum equation 6.2.1 Staggered grid(交叉网格) 6.2.2 Discretization of momentum equation in staggered grid 6.2.3 Interpolation in staggered grid 6.2.4 Remarks 1. Flow rate at a node 2. Density at interface 3. Conductance at interface 6.3 Pressure correction methods for N-S equation 6.3.1 Basic idea of pressure correction methods 6.3.2 Equations for velocity corrections of u ’, v ’ 6.3.3 Derivation of equation of pressure correction p ’ 6.3.4 Boundary condition for pressure correction
