| 1 | Standard functions and techniques | 1 |
| 2 | Differentiation | 29 |
| 3 | Further techniques for differentiation | 47 |
| 4 | Applications of differentiation | 64 |
| 5 | Taylor series and approximations | 84 |
| 6 | Complex numbers | 97 |
| 7 | Matrix algebra | 114 |
| 8 | Determinants | 132 |
| 9 | Vectors in two and three dimensions | 146 |
| 10 | Linear equations | 170 |
| 11 | Eigenvalues and eigenvectors | 189 |
| 12 | Antidifferentiation and area | 215 |
| 13 | The definite and indefinite integral | 226 |
| 14 | Applications involving the integral as a sum | 245 |
| 15 | Systematic techniques for integration | 257 |
| 16 | Unforced linear differential equations with constant coefficients | 276 |
| 17 | Forced linear differential equations | 292 |
| 18 | Harmonic functions and the harmonic oscillator | 309 |
| 19 | Steady forced oscillations: phasors, impedance, transfer functions | 323 |
| 20 | Graphical, numerical and other aspects of first-order equations | 335 |
| 21 | Introduction to the phase plane | 352 |
| 22 | The Laplace transform | 371 |
| 23 | Applications of the Laplace transform | 390 |
| 24 | Fourier series | 409 |
| 25 | Differentiation of functions of two variables | 427 |
| 26 | Functions of two variables: geometry and formulae | 445 |
| 27 | Chain rules, restricted maxima, coordinate systems | 462 |
| 28 | Functions of any number of variables | 480 |
| 29 | Double integration | 502 |
| 30 | Line integrals | 519 |
| 31 | Sets | 542 |
| 32 | Boolean algebra: logic gates and switching functions | 554 |
| 33 | Graph theory: circuit analysis and signal flow | 565 |
| 34 | Difference equations | 583 |
| 35 | Applications projects using symbolic computing | 600 |
| App. A Some algebraical rules | 618 |
| App. B Trigonometric formulae | 619 |
| App. C Areas and volumes | 620 |
| App. D A table of derivatives | 621 |
| App. E A table of integrals | 621 |
| App. F A table of Laplace transforms and inverses | 622 |
| App. G Answers to selected problems | 624 |
| Index | 651 |
Format: Hardcover, 2nd ed., 806 pages
