| Preface |
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| Preface to second edition |
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| Preface to third edition |
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| Acknowledgements |
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1 | (7) |
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1.1 Why study mathematics? |
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1 | (2) |
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1.2 Calculators and computers |
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3 | (2) |
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5 | (3) |
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8 | (24) |
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2.1 Revision of basic concepts |
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8 | (1) |
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9 | (2) |
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11 | (1) |
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12 | (3) |
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15 | (3) |
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18 | (3) |
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21 | (2) |
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23 | (2) |
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2.9 Roots and fractional powers |
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25 | (3) |
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28 | (4) |
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3 Introduction to algebra |
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32 | (31) |
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32 | (3) |
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35 | (2) |
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3.3 Simplification: addition and subtraction |
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37 | (2) |
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3.4 Simplification: multiplication |
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39 | (4) |
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3.5 Simplification: factorizing |
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43 | (4) |
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3.6 Simplification: division |
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47 | (2) |
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3.7 Solving simple equations |
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49 | (5) |
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3.8 The summation sign S and price indexes |
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54 | (5) |
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59 | (4) |
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63 | (44) |
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63 | (3) |
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66 | (2) |
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4.3 Graphs of linear functions |
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68 | (5) |
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4.4 Fitting linear functions |
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73 | (3) |
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76 | (5) |
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81 | (5) |
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86 | (2) |
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88 | (5) |
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4.9 Using a spreadsheet to plot functions |
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93 | (4) |
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4.10 Functions with two independent variables |
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97 | (5) |
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4.11 Summing functions horizontally |
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102 | (5) |
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5 Simultaneous linear equations |
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107 | (61) |
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5.1 Systems of simultaneous linear equations |
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107 | (1) |
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5.2 Solving simultaneous linear equations |
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108 | (1) |
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108 | (2) |
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5.4 Equating to same variable |
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110 | (2) |
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112 | (2) |
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114 | (2) |
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5.7 More than two unknowns |
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116 | (3) |
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119 | (5) |
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5.9 Comparative statics and the reduced form of an economic model |
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124 | (9) |
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5.10 Price discrimination |
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133 | (7) |
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140 | (28) |
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5A Appendix: linear programming |
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148 | (1) |
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5A.1 Constrained maximization |
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148 | (10) |
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5A.2 Constrained minimization |
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158 | (7) |
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165 | (2) |
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5A.4 More than two variables |
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167 | (1) |
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168 | (21) |
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6.1 Solving quadratic equations |
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168 | (2) |
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170 | (4) |
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174 | (2) |
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6.4 The quadratic formula |
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176 | (1) |
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6.5 Quadratic simultaneous equations |
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177 | (5) |
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182 | (7) |
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7 Financial mathematics -- series, time and investment |
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189 | (91) |
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7.1 Discrete and continuous growth |
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189 | (2) |
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191 | (5) |
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7.3 Part year investment and the annual equivalent rate |
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196 | (6) |
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7.4 Time periods, initial amounts and interest rates |
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202 | (5) |
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7.5 Investment appraisal: net present value |
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207 | (10) |
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7.6 The internal rate of return |
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217 | (7) |
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7.7 Geometric series and annuities |
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224 | (6) |
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230 | (4) |
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7.9 Pension pots, annuity income and drawdown pensions |
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234 | (8) |
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7.10 Drawdown pension income |
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242 | (2) |
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7.11 Loan repayments and mortgages |
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244 | (8) |
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252 | (5) |
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7.13 Sinking fund savings schemes |
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257 | (3) |
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7.14 Other applications of growth and decline |
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260 | (20) |
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7A Appendix: asset valuation |
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267 | (1) |
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267 | (6) |
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273 | (7) |
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8 Introduction to calculus |
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280 | (25) |
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8.1 Differential calculus |
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280 | (2) |
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8.2 Rules for differentiation |
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282 | (4) |
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8.3 Marginal revenue and total revenue |
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286 | (5) |
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8.4 Marginal cost and total cost |
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291 | (2) |
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293 | (2) |
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8.6 Re-specifying functions |
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295 | (2) |
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8.7 Point elasticity of demand |
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297 | (3) |
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300 | (3) |
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8.9 The Keynesian multiplier |
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303 | (2) |
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9 Unconstrained optimization |
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305 | (21) |
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9.1 First-order conditions for a maximum |
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305 | (1) |
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9.2 Second-order conditions for a maximum |
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306 | (3) |
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9.3 Second-order conditions for a minimum |
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309 | (1) |
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9.4 Summary of second-order conditions |
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310 | (3) |
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313 | (3) |
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316 | (4) |
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9.7 Comparative static effects of taxes |
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320 | (6) |
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10 Partial differentiation |
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326 | (48) |
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10.1 Partial differentiation and the marginal product |
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326 | (6) |
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10.2 Further applications of partial differentiation |
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332 | (12) |
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10.3 Second-order partial derivatives |
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344 | (5) |
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10.4 Unconstrained optimization: functions with two variables |
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349 | (15) |
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10.5 Total differentials and total derivatives |
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364 | (10) |
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11 Constrained optimization |
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374 | (33) |
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11.1 Constrained optimization and resource allocation |
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374 | (1) |
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11.2 Constrained optimization by substitution |
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375 | (8) |
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11.3 The Lagrange multiplier: constrained maximization with two variables |
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383 | (6) |
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11.4 The Lagrange multiplier: second-order conditions |
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389 | (3) |
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11.5 Constrained minimization using the Lagrange multiplier |
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392 | (6) |
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11.6 Constrained optimization with more than two variables |
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398 | (9) |
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12 Further topics in differentiation and integration |
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407 | (42) |
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407 | (1) |
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407 | (9) |
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416 | (6) |
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422 | (7) |
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429 | (6) |
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435 | (7) |
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12.7 Integration by substitution and integration by parts |
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442 | (7) |
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13 Dynamics and difference equations |
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449 | (39) |
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13.1 Dynamic economic analysis |
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449 | (1) |
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13.2 The cobweb: iterative solutions |
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450 | (10) |
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13.3 The cobweb: difference equation solutions |
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460 | (10) |
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13.4 The lagged Keynesian macroeconomic model |
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470 | (12) |
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13.5 Duopoly price adjustment |
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482 | (6) |
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14 Exponential functions, continuous growth and differential equations |
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488 | (38) |
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14.1 Continuous growth and the exponential function |
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488 | (3) |
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14.2 Accumulated final values after continuous growth |
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491 | (3) |
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14.3 Continuous growth rates and initial amounts |
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494 | (5) |
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499 | (5) |
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14.5 Differentiation of logarithmic functions |
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504 | (2) |
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14.6 Continuous time and differential equations |
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506 | (1) |
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14.7 Solution of homogeneous differential equations |
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507 | (4) |
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14.8 Solution of non-homogeneous differential equations |
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511 | (5) |
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14.9 Continuous adjustment of market price |
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516 | (5) |
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14.10 Continuous adjustment in a Keynesian macroeconomic model |
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521 | (5) |
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526 | (63) |
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15.1 Introduction to matrices and vectors |
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526 | (5) |
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15.2 Basic principles of matrix multiplication |
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531 | (3) |
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15.3 Matrix multiplication -- the general case |
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534 | (6) |
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15.4 The matrix inverse and the solution of simultaneous equations |
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540 | (4) |
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544 | (3) |
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15.6 Minors, cofactors and the Laplace expansion |
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547 | (4) |
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15.7 The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula |
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551 | (5) |
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15.8 Application of the matrix inverse to the solution of linear simultaneous equations |
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556 | (6) |
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562 | (2) |
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15.10 Second-order conditions and the Hessian matrix |
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564 | (7) |
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15.11 Constrained optimization and the bordered Hessian |
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571 | (4) |
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15.12 Input-output analysis |
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575 | (6) |
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15.13 Multiple industry input-output models |
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581 | (8) |
| Answers |
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589 | (11) |
| Index |
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600 | |
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