Bird, John. creator text Electronic books. xx 2021 9th ed. monographic eng 1 online resource (934 pages) Over 600 practical engineering examples and applications underpin undergraduate and upper-level vocational courses. The companion website provides of essential formulae, and full solutions to 2,000 further questions from the 277 practice exercises; and answers to revision tests for adopting course instructors. Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Syllabus guidance -- Section A: Number and algebra -- 1. Algebra -- 1.1. Introduction -- 1.2. Revision of basic laws -- 1.3. Revision of equations -- 1.4. Polynomial division -- 1.5. The factor theorem -- 1.6. The remainder theorem -- 2. Partial fractions -- 2.1. Introduction to partial fractions -- 2.2. Partial fractions with linear factors -- 2.3. Partial fractions with repeated linear factors -- 2.4. Partial fractions with quadratic factors -- 3. Logarithms -- 3.1. Introduction to logarithms -- 3.2. Laws of logarithms -- 3.3. Indicial equations -- 3.4. Graphs of logarithmic functions -- 4. Exponential functions -- 4.1. Introduction to exponential functions -- 4.2. The power series for e x -- 4.3. Graphs of exponential functions -- 4.4. Napierian logarithms -- 4.5. Laws of growth and decay -- 4.6. Reduction of exponential laws to linear form -- Revision Test 1 -- 5. The binomial series -- 5.1. Pascal's triangle -- 5.2. The binomial series -- 5.3. Worked problems on the binomial series -- 5.4. Further worked problems on the binomial series -- 5.5. Practical problems involving the binomial theorem -- 6. Solving equations by iterative methods -- 6.1. Introduction to iterative methods -- 6.2. The bisection method -- 6.3. An algebraic method of successive approximations -- 7. Boolean algebra and logic circuits -- 7.1. Boolean algebra and switching circuits -- 7.3. Laws and rules of Boolean algebra -- 7.2. Simplifying Boolean expressions -- 7.4. De Morgan's laws -- 7.5. Karnaugh maps -- 7.6. Logic circuits -- 7.7. Universal logic gates -- Revision Test 2 -- Section B: Geometry and trigonometry -- 8. Introduction to trigonometry -- 8.1. Trigonometry -- 8.2. The theorem of Pythagoras -- 8.3. Trigonometric ratios of acute angles. 8.4. Evaluating trigonometric ratios -- 8.5. Solution of right-angled triangles -- 8.6. Angles of elevation and depression -- 8.7. Sine and cosine rules -- 8.8. Area of any triangle -- 8.9. Worked problems on the solution of triangles and finding their areas -- 8.10. Further worked problems on solving triangles and finding their areas -- 8.11. Practical situations involving trigonometry -- 8.12. Further practical situations involving trigonometry -- 9. Cartesian and polar co-ordinates -- 9.1. Introduction -- 9.2. Changing from Cartesian into polar co-ordinates -- 9.3. Changing from polar into Cartesian co-ordinates -- 9.4. Use of Pol/Rec functions on calculators -- 10. The circle and its properties -- 10.1. Introduction -- 10.2. Properties of circles -- 10.3. Radians and degrees -- 10.4. Arc length and area of circles and sectors -- 10.5. The equation of a circle -- 10.6. Linear and angular velocity -- 10.7. Centripetal force -- Revision Test 3 -- 11. Trigonometric waveforms -- 11.1. Graphs of trigonometric functions -- 11.2. Angles of any magnitude -- 11.3. The production of a sine and cosine wave -- 11.4. Sine and cosine curves -- 11.5 Sinusoidal form A sin(!t ) -- 11.6. Harmonic synthesis with complex waveforms -- 12. Hyperbolic functions -- 12.1. Introduction to hyperbolic functions -- 12.2. Graphs of hyperbolic functions -- 12.3. Hyperbolic identities -- 12.4. Solving equations involving hyperbolic functions -- 12.5. Series expansions for cosh x and sinh x -- 13. Trigonometric identities and equations -- 13.1. Trigonometric identities -- 13.2. Worked problems on trigonometric identities -- 13.3. Trigonometric equations -- 13.4. Worked problems (i) on trigonometric equations -- 13.5. Worked problems (ii) on trigonometric equations -- 13.6. Worked problems (iii) on trigonometric equations -- 13.7. Worked problems (iv) on trigonometric equations. 14. The relationship between trigonometric and hyperbolic functions -- 14.1. The relationship between trigonometric and hyperbolic functions -- 14.2. Hyperbolic identities -- 15. Compound angles -- 15.1. Compound angle formulae -- 15.2. Conversion of a sin !t + b cos !t into R sin(!t + ) -- 15.3. Double angles -- 15.4. Changing products of sines and cosines into sums or differences -- 15.5. Changing sums or differences of sines and cosines into products -- 15.6. Power waveforms in a.c. circuits -- Revision Test 4 -- Section C: Graphs -- 16. Functions and their curves -- 16.1. Standard curves -- 16.2. Simple transformations -- 16.3. Periodic functions -- 16.4. Continuous and discontinuous functions -- 16.5. Even and odd functions -- 16.6. Inverse functions -- 16.7. Asymptotes -- 16.8. Brief guide to curve sketching -- 16.9. Worked problems on curve sketching -- 17. Irregular areas, volumes and mean values of waveforms -- 17.1. Areas of irregular figures -- 17.2. Volumes of irregular solids -- 17.3. The mean or average value of a waveform -- Revision Test 5 -- Section D: Complex numbers -- 18. Complex numbers -- 18.1. Cartesian complex numbers -- 18.2. The Argand diagram -- 18.3. Addition and subtraction of complex numbers -- 18.2. The Argand diagram -- 18.4. Multiplication and division of complex numbers -- 18.5. Complex equations -- 18.6. The polar form of a complex number -- 18.7. Multiplication and division in polar form -- 18.8. Applications of complex numbers -- 19. De Moivre's theorem -- 19.1. Introduction -- 19.2. Powers of complex numbers -- 19.3. Roots of complex numbers -- 19.4. The exponential form of a complex number -- 19.5. Introduction to locus problems -- Section E: Matrices and determinants -- 20. The theory of matrices and determinants -- 20.1. Matrix notation -- 20.2. Addition, subtraction and multiplication of matrices. 20.3. The unit matrix -- 20.4. The determinant of a 2 by 2 matrix -- 20.5. The inverse or reciprocal of a 2 by 2 matrix -- 20.6. The determinant of a 3 by 3 matrix -- 20.7. The inverse or reciprocal of a 3 by 3 matrix -- 21. Applications of matrices and determinants -- 21.1. Solution of simultaneous equations by matrices -- 21.2. Solution of simultaneous equations by determinants -- 21.3. Solution of simultaneous equations using Cramer's rule -- 21.4. Solution of simultaneous equations using the Gaussian elimination method -- 21.5. Stiffness matrix -- 21.6. Eigenvalues and eigenvectors -- Section F: Vector geometry -- 22. Vectors -- 22.1. Introduction -- 22.2. Scalars and vectors -- 22.3. Drawing a vector -- 22.4. Addition of vectors by drawing -- 22.5. Resolving vectors into horizontal and vertical components -- 22.6. Addition of vectors by calculation -- 22.7. Vector subtraction -- 22.8. Relative velocity -- 22.9. i, j and k notation -- 23. Methods of adding alternating waveforms -- 23.1. Combination of two periodic functions -- 23.2. Plotting periodic functions -- 23.3. Determining resultant phasors by drawing -- 23.4. Determining resultant phasors by the sine and cosine rules -- 23.5. Determining resultant phasors by horizontal and vertical components -- 23.6. Determining resultant phasors by using complex numbers -- 24. Scalar and vector products -- 24.1. The unit triad -- 24.2. The scalar product of two vectors -- 24.3. Vector products -- 24.4. Vector equation of a line -- Revision Test 7 -- Section G: Differential calculus -- 25. Methods of differentiation -- 25.1. Introduction to calculus -- 25.2. The gradient of a curve -- 25.3. Differentiation from first principles -- 25.4. Differentiation of common functions -- 25.5. Differentiation of a product -- 25.6. Differentiation of a quotient -- 25.7. Function of a function. 25.8. Successive differentiation -- 26. Some applications of differentiation -- 26.1. Rates of change -- 26.2. Velocity and acceleration -- 26.3. The Newton-Raphson method -- 26.4. Turning points -- 26.5. Practical problems involving maximum and minimum values -- 26.6. Points of inflexion -- 26.7. Tangents and normals -- 26.8. Small changes -- Revision Test 8 -- 27. Differentiation of parametric equations -- 27.1. Introduction to parametric equations -- 27.2. Some common parametric equations -- 27.3. Differentiation in parameters -- 27.4. Further worked problems on differentiation of parametric equations -- 28. Differentiation of implicit functions -- 28.1. Implicit functions -- 28.2. Differentiating implicit functions -- 28.3. Differentiating implicit functions containing products and quotients -- 28.4. Further implicit differentiation -- 29. Logarithmic differentiation -- 29.1. Introduction to logarithmic differentiation -- 29.2. Laws of logarithms -- 29.4. Differentiation of further logarithmic functions -- 29.3. Differentiation of logarithmic functions -- 29.5. Differentiation of [f(x)]x -- Revision Test 9 -- 30. Differentiation of hyperbolic functions -- 30.1. Standard differential coefficients of hyperbolic functions -- 30.2. Further worked problems on differentiation of hyperbolic functions -- 31. Differentiation of inverse trigonometric and hyperbolic functions -- 31.1. Inverse functions -- 31.2. Differentiation of inverse trigonometric functions -- 31.3. Logarithmic forms of inverse hyperbolic functions -- 31.4. Differentiation of inverse hyperbolic functions -- 32. Partial differentiation -- 32.1. Introduction to partial derivatives -- 32.2. First-order partial derivatives -- 32.3. Second-order partial derivatives -- 33. Total differential, rates of change and small changes -- 33.1. Total differential -- 33.2. Rates of change. 33.3. Small changes. Engineering mathematics TA330 510.2462 Bird, John Milton : CRC Press LLC,c2021 9781000353037 https://ebookcentral-proquest-com.mlisicats.remotexs.co/lib/ppks/detail.action?docID=6466951 https://ebookcentral-proquest-com.mlisicats.remotexs.co/lib/ppks/detail.action?docID=6466951 MiAaPQ 260525 20260623164149.0 EBC6466951 eng