| Preface |
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ix | |
| Preface to Second Edition |
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xi | |
| Acknowledgements |
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xii | |
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1 | (7) |
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1 | (2) |
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Calculators and computers |
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3 | (2) |
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5 | (3) |
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8 | (26) |
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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 | (3) |
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Roots and fractional powers |
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26 | (3) |
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29 | (5) |
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34 | (29) |
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34 | (2) |
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36 | (2) |
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Simplification: addition and subtraction |
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38 | (2) |
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Simplification: multiplication |
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40 | (5) |
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Simplification: factorizing |
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45 | (4) |
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49 | (2) |
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51 | (5) |
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56 | (3) |
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59 | (4) |
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63 | (46) |
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63 | (2) |
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65 | (3) |
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Graphs of linear functions |
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68 | (5) |
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73 | (3) |
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76 | (5) |
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81 | (5) |
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86 | (4) |
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90 | (5) |
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Using Excel to plot functions |
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95 | (4) |
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Functions with two independent variables |
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99 | (5) |
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Summing functions horizontally |
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104 | (5) |
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109 | (59) |
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Simultaneous linear equation systems |
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109 | (1) |
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Solving simultaneous linear equations |
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110 | (1) |
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110 | (2) |
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Equating to same variable |
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112 | (3) |
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115 | (1) |
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116 | (2) |
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118 | (3) |
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121 | (5) |
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Comparative statics and the reduced form of an economic model |
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126 | (9) |
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135 | (6) |
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141 | (27) |
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Appendix: linear programming |
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148 | (20) |
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168 | (21) |
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Solving quadratic equations |
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168 | (1) |
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169 | (4) |
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173 | (3) |
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176 | (2) |
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Quadratic simultaneous equations |
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178 | (4) |
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182 | (7) |
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Financial mathematics: series, time and investment |
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189 | (58) |
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Discrete and continuous growth |
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189 | (2) |
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191 | (5) |
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Part year investment and the annual equivalent rate |
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196 | (6) |
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Time periods, initial amounts and interest rates |
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202 | (5) |
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Investment appraisal: net present value |
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207 | (11) |
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The internal rate of return |
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218 | (6) |
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Geometric series and annuities |
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224 | (6) |
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230 | (4) |
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234 | (6) |
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Other applications of growth and decline |
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240 | (7) |
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247 | (25) |
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The differential calculus |
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247 | (2) |
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Rules for differentiation |
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249 | (3) |
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Marginal revenue and total revenue |
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252 | (6) |
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Marginal cost and total cost |
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258 | (3) |
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261 | (2) |
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263 | (2) |
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Point elasticity of demand |
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265 | (2) |
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267 | (2) |
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269 | (3) |
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Unconstrained optimization |
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272 | (19) |
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First-order conditions for a maximum |
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272 | (1) |
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Second-order condition for a maximum |
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273 | (3) |
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Second-order condition for a minimum |
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276 | (1) |
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Summary of second-order conditions |
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277 | (3) |
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280 | (2) |
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282 | (3) |
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Comparative static effects of taxes |
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285 | (6) |
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291 | (43) |
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Partial differentiation and the marginal product |
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291 | (5) |
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Further applications of partial differentiation |
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296 | (11) |
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Second-order partial derivatives |
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307 | (5) |
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Unconstrained optimization: functions with two variables |
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312 | (13) |
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Total differentials and total derivatives |
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325 | (9) |
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334 | (30) |
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Constrained optimization and resource allocation |
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334 | (1) |
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Constrained optimization by substitution |
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334 | (8) |
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The Lagrange multiplier: constrained maximization with two variables |
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342 | (6) |
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The Lagrange multiplier: second-order conditions |
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348 | (2) |
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Constrained minimization using the Lagrange multiplier |
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350 | (5) |
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Constrained optimization with more than two variables |
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355 | (9) |
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Further topics in calculus |
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364 | (31) |
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364 | (1) |
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364 | (8) |
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372 | (5) |
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377 | (4) |
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381 | (3) |
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384 | (4) |
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388 | (7) |
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Dynamics and difference equations |
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395 | (37) |
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Dynamic economic analysis |
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395 | (1) |
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The cobweb: iterative solutions |
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396 | (9) |
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The cobweb: difference equation solutions |
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405 | (9) |
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The lagged Keynesian macroeconomic model |
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414 | (12) |
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426 | (6) |
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Exponential functions, continuous growth and differential equations |
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432 | (33) |
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Continuous growth and the exponential function |
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432 | (2) |
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Accumulated final values after continuous growth |
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434 | (3) |
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Continuous growth rates and initial amounts |
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437 | (3) |
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440 | (6) |
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Differentiation of logarithmic functions |
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446 | (1) |
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Continuous time and differential equations |
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447 | (1) |
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Solution of homogeneous differential equations |
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448 | (4) |
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Solution of non-homogeneous differential equations |
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452 | (4) |
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Continuous adjustment of market price |
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456 | (5) |
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Continuous adjustment in a Keynesian macroeconomic model |
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461 | (4) |
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465 | (45) |
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Introduction to matrices and vectors |
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465 | (4) |
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Basic principles of matrix multiplication |
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469 | (3) |
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Matrix multiplication -- the general case |
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472 | (6) |
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The matrix inverse and the solution of simultaneous equations |
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478 | (3) |
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481 | (3) |
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Minors, cofactors and the Laplace expansion |
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484 | (3) |
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The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula |
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487 | (5) |
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Application of the matrix inverse to the solution of linear simultaneous equations |
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492 | (5) |
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497 | (2) |
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Second-order conditions and the Hessian matrix |
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499 | (6) |
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Constrained optimization and the bordered Hessian |
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505 | (5) |
| Answers |
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510 | (13) |
| Symbols and terminology |
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523 | (2) |
| Index |
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525 | |
