Engineering MathematicsThe best-selling introductory mathematics textbook for students on engineering and science degree and pre-degree courses. Sales stand at more than half a million copies world-wide. Its unique programmed approach really works! Many thousands of students have found that they understand and excel through using this book. It takes you through the mathematics in a step-by-step fashion with a wealth of examples and exercises. The text demands that you engage with it by asking you to complete steps that you should be able to manage from previous examples or knowledge you have acquired, while carefully introducing new steps. By working with the authors through the examples, you become proficient as you go. By the time you come to trying examples on your own, confidence is high. Aimed at undergraduates on Foundation and First Year degree programmes in all Engineering disciplines and Science. The Foundation section covers mathematics from GCSE onwards to allow for revision and gap-filling, and so means the book can be used for a range of abilities and all levels of access. New to this Edition: - A general revision of the entire contents - In Matrices an emphasis on eigenvalues and eigenvectors and the introduction of the Cayley Hamilton theorem - New review summaries plus a new easy reference to help check back when you need more help - Key chapters improved yet further as a result of detailed student feedback |
Contents
| 2 | |
| 3 | |
Programme F2 Introduction to algebra | 63 |
Programme F3 Expressions and equations | 97 |
Programme F4 Graphs | 123 |
Programme F5 Linear equations | 157 |
Programme F6 Polynomial equations | 173 |
Programme F7 Binomials | 187 |
Programme 10 Sequences | 607 |
Programme 11 Series 1 | 642 |
Programme 12 Series 2 | 666 |
Programme 13 Curves and curve fitting | 692 |
Programme 14 Partial differentiation 1 | 736 |
Programme 15 Partial differentiation 2 | 757 |
Programme 16 Integration 1 | 773 |
Programme 17 Integration 2 | 800 |
Programme F8 Partial fractions | 215 |
Programme F9 | 235 |
Programme F10 Functions | 259 |
Programme F11 Trigonometric and exponential functions | 279 |
Programme F12 Differentiation | 309 |
Programme F13 Integration | 347 |
PART II | 378 |
Programme 1 Complex numbers 1 | 379 |
Programme 2 Complex numbers 2 | 406 |
Programme 3 Hyperbolic functions | 431 |
Programme 4 Determinants | 453 |
Programme 5 Matrices | 484 |
Programme 6 Vectors | 519 |
Programme 7 Differentiation | 544 |
Programme 8 Differentiation applications | 563 |
Programme 9 Tangents normals and curvature | 585 |
Programme 18 Reduction formulas | 828 |
Programme 19 Integration applications 1 | 841 |
Programme 20 Integration applications 2 | 859 |
Programme 21 Integration applications 3 | 881 |
Programme 22 Approximate integration | 910 |
Programme 23 Polar coordinate systems | 929 |
Programme 24 Multiple integrals | 951 |
Programme 25 Firstorder differential equations | 977 |
Programme 26 Secondorder differential equations | 1013 |
Programme 27 Introduction to Laplace transforms | 1036 |
Programme 28 Data handling and statistics | 1054 |
Programme 29 Probability | 1085 |
Answers | 1126 |
| 1153 | |
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Common terms and phrases
algebraic angle Argand diagram arithmetic asymptote binomial expansion calculator cell check your results coefficient column complex number constant convergent cos² cosh cosx curve d²y decimal denominator derivative determine difference equation differentiate dx ¼ dx dx dx dy dy dx dz dz Evaluate example expression ffiffiffiffiffiffiffiffiffiffiffiffiffiffi find the value formula function geometric sequence given gives gradient graph hexadecimal integral inverse l'Hôpital's rule linear loga matrix multiply obtain octal parametric equations partial fractions PERSONAL TUTOR PERSONAL polar curves polar form polynomial powers radians radius Review exercise Review summary sec² sequence sides Simpson's rule sin x sin² sinh sinx solution Solve straight line substitute subtraction tangent tanh Test exercise triangle trigonometric TUTOR PERSONAL TUTOR variables vector x-axis x2 þ y-axis zero δχ бу дх ду