| Preface to the Third Edition |
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vii | |
| Preface to the First Edition |
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ix | |
| I Interpolation |
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1 | (105) |
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1 Graphical interpolation |
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1 | (1) |
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2 | (1) |
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3 Interpolation polynomial |
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3 | (1) |
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4 | (27) |
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5 Interpolation by using the least square-fitting |
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31 | (15) |
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46 | (19) |
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7 Lagrange's interpolation |
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65 | (10) |
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8 Hermite's interpolation |
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75 | (2) |
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77 | (6) |
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10 Interpolation by using differences |
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83 | (5) |
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11 Gregory-Newton difference interpolation |
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88 | (4) |
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12 Gauss formulas for interpolation |
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92 | (5) |
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97 | (1) |
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98 | (2) |
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100 | (2) |
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16 Problems and questions |
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102 | (4) |
| II Differentiation |
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106 | (33) |
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1 Differentiation by the least square fitting |
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106 | (12) |
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2 Differentiation by Lagrange's interpolation |
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118 | (4) |
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3 Differentiation by Newton's interpolation |
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122 | (3) |
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4 Differentiation by Gregory-Newton difference interpolation |
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125 | (5) |
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5 Differentiation using Newton's forward difference formula |
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130 | (2) |
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6 Differentiation using Newton's backward difference formula |
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132 | (2) |
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7 Differentiation using Stirling's formula |
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134 | (3) |
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8 Derivative near the end of difference-table |
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137 | (1) |
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137 | (2) |
| III Integration |
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139 | (42) |
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139 | (1) |
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2 Integration with Lagrange's interpolation |
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140 | (1) |
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3 Newton-Cotes expression for integral |
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141 | (1) |
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142 | (5) |
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147 | (4) |
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6 Newton's three-eight rule |
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151 | (4) |
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155 | (4) |
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159 | (3) |
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162 | (3) |
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10 Euler's formula of summation and quadrature |
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165 | (1) |
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11 Gauss quadrature method |
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166 | (8) |
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174 | (2) |
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13 Numerical double integration |
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176 | (3) |
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14 Problems and questions |
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179 | (2) |
| IV Roots of an Equation |
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181 | (64) |
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181 | (9) |
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2 Transcendental equations |
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190 | (1) |
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3 Some theorems about functions |
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191 | (1) |
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191 | (1) |
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5 Limits for roots of a polynomial equation |
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192 | (4) |
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196 | (9) |
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205 | (9) |
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214 | (10) |
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224 | (2) |
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10 Direct substitution method |
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226 | (5) |
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231 | (2) |
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12 Bairstow's method for complex roots |
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233 | (9) |
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13 Problems and questions |
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242 | (3) |
| V Simultaneous Equations |
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245 | (46) |
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246 | (3) |
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249 | (1) |
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250 | (2) |
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4 Gauss elimination method |
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252 | (7) |
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5 Pivotal condensation method |
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259 | (5) |
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264 | (5) |
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7 Gauss-Seidel iteration method |
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269 | (8) |
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8 Matrix inversion method |
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277 | (3) |
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9 Gauss-Jordan matrix inversion method |
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280 | (7) |
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10 When number of linear equations is larger than that of unknowns |
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287 | (1) |
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11 Problems and questions |
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288 | (3) |
| VI Eigenvalues and Eigenvectors |
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291 | (61) |
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1 Determinant of a matrix |
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292 | (8) |
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2 Characteristic equation |
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300 | (15) |
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3 Eigenvalues and eigenvectors of a matrix |
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315 | (20) |
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335 | (11) |
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5 Eigenvalues and eigenvectors of a real symmetric matrix of order 2 x 2 |
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346 | (3) |
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349 | (3) |
| VII Differential Equations |
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352 | (35) |
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354 | (3) |
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357 | (3) |
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360 | (4) |
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364 | (3) |
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5 Predictor-corrector method |
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367 | (6) |
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6 Predictor-corrector methods with difference schemes |
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373 | (7) |
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7 Runge-Kutta method for second order first degree linear differential equation |
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380 | (4) |
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384 | (3) |
| VIII Partial Differential Equations |
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387 | (33) |
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1 Elliptic partial differential equations |
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387 | (20) |
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2 Parabolic partial differential equations |
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407 | (6) |
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3 Hyperbolic partial differential equations |
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413 | (6) |
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419 | (1) |
| IX Monte Carlo Simulation |
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420 | (11) |
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420 | (3) |
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423 | (1) |
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424 | (5) |
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429 | (2) |
| X Some Functions |
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431 | (29) |
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431 | (5) |
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436 | (4) |
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3 Associated Legendre function |
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440 | (1) |
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441 | (1) |
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441 | (2) |
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6 Associated Laguerre function |
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443 | (1) |
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444 | (3) |
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8 Hypergeometric function |
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447 | (4) |
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451 | (3) |
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454 | (4) |
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11 Problems and questions |
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458 | (2) |
| XI Accuracy of Calculations |
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460 | (27) |
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460 | (2) |
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462 | (1) |
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3 Rounding off the numbers |
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462 | (3) |
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465 | (1) |
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466 | (1) |
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6 General formula for errors |
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467 | (1) |
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7 Application of error formula |
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468 | (8) |
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8 Accuracy in evaluation of a formula |
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476 | (4) |
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9 Accuracy of series approximation |
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480 | (5) |
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10 Problems and questions |
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485 | (2) |
| Bibliography |
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487 | (2) |
| Index |
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489 | |
| 9781457303227 |
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| Introduction |
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vii | |
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CLEP Study Materials: A Word of Warning |
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viii | |
|
American Council on Education (ACE) |
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viii | |
| I The College-Level Examination Program |
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1 | (1) |
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1 | (1) |
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What the Examinations Are Like |
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2 | (1) |
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Where to Take the Examinations and How to Register |
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2 | (1) |
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ACE's College Credit Recommendation Service |
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2 | (1) |
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How Your Score Is Reported |
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3 | (2) |
| II Approaching a College about CLEP |
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How to Apply for College Credit |
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5 | (3) |
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Questions to Ask about a College's CLEP Policy |
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8 | (3) |
| III Deciding Which Examinations to Take |
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If You're Taking the Examinations for College Credit or Career Advancement |
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11 | (2) |
| IV Preparing to Take CLEP Examinations |
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Using the Examination Guides |
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13 | (2) |
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Assessing Your Readiness for a CLEP Examination |
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15 | (1) |
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16 | (2) |
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18 | (2) |
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Accommodations for Students with Disabilities |
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20 | (1) |
| V Taking the Examinations |
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Test-Taking Strategies for Multiple-Choice Questions |
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21 | (2) |
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Answering Essay Questions |
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23 | (1) |
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Test-Taking Strategies for Essay Writing |
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23 | (2) |
| VI Interpreting Your Scores |
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How CLEP Scores Are Computed |
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25 | (1) |
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25 | (4) |
| VII Examination Guides |
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Composition and Literature |
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29 | (22) |
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Analyzing and Interpreting Literature |
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51 | (20) |
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College Composition/College Composition Modular |
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71 | (30) |
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101 | (20) |
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121 | (22) |
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143 | (26) |
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169 | (18) |
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187 | (28) |
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History and Social Sciences |
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215 | (16) |
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History of the United States I: Early Colonization to 1877 |
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231 | (18) |
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History of the United States II: 1865 to the Present |
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249 | (20) |
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Human Growth and Development |
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269 | (14) |
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Introduction to Educational Psychology |
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283 | (18) |
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Principles of Macroeconomics |
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301 | (18) |
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Principles of Microeconomics |
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319 | (18) |
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337 | (16) |
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353 | (14) |
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Social Sciences and History |
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367 | (18) |
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Western Civilization I: Ancient Near East to 1648 |
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385 | (18) |
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Western Civilization II: 1648 to the Present |
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403 | (18) |
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421 | (18) |
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439 | (16) |
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455 | (16) |
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471 | (16) |
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487 | (14) |
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501 | (16) |
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517 | (16) |
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533 | (16) |
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Information Systems and Computer Applications |
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549 | (16) |
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Introductory Business Law |
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565 | (16) |
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581 | (18) |
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599 | (14) |
| Appendix: What Your CLEP Score Means |
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613 | |
