Higher Engineering Mathematics, 7th ed

Introduction; Preface; Website information; Syllabus guidance; 1. Algebra; 2. Partial fractions; 3. Logarithms; 4. Exponential functions; 5. Inequalities; Revision Test 1; 6. Arithmetic and geometric progressions; 7. The binomial series; Revision Test 2; 8. Maclaurin's series; 9. Solving equations by iterative methods; 10. Binary, octal and hexadecimal numbers; 11. Boolean algebra and logic circuits; Revision Test 3; 12. Introduction to trigonometry; 13. Cartesian and polar co-ordinates; 14. The circle and its properties; Revision Test 4; 15. Trigonometric waveforms; 16. Hyperbolic functions; 17. Trigonometric identities and equations; 18. The relationship between trigonometric and hyperbolic functions; 19. Compound angles; Revision Test 5; 20. Functions and their curves; 21. Irregular areas, volumes and mean values of waveforms; Revision Test 6; 22. Complex numbers; 23. De Moivre's theorem; 24. The theory of matrices and determinants; 25. Applications of matrices and determinants; Revision Test 7; 26. Vectors; 27. Methods of adding alternating waveforms; 28. Scalar and vector products; Revision Test 8; 29. Methods of differentiation; 30. Some applications of differentiation; 31. Differentiation of parametric equations; 32. Differentiation of implicit functions; 33. Logarithmic differentiation; Revision Test 9; 34. Differentiation of hyperbolic functions; 35. Differentiation of inverse trigonometric and hyperbolic functions; 36. Partial differentiation; 37. Total differential, rates of change and small changes; 38. Maxima, minima and saddle points for functions of two variables; Revision Test 10; 39. Standard integration; 40. Some applications of integration; 41. Integration using algebraic substitutions; Revision Test 11; 42. Integration using trigonometric and hyperbolic substitutions; 43. Integration using partial fractions; 44. The t = tan substitution; Revision Test 12; 45. Integration by parts; 46. Reduction formulae; 47. Double and triple integrals; 48. Numerical integration; Revision Test 13; 49. Solution of first order differential equations by separation of variables; 50. Homogeneous first order differential equations; 51.Linear first order differential equations; 52. Numerical methods for first order differential equations; Revision Test 14; 53. First order differential equations of the form; 54. First order differential equations of the form; 55. Power series methods of solving ordinary differential equations; 56. An introduction to partial differential equations; Revision Test 15; 57. Presentation of statistical data; 58. Mean, median, mode and standard deviation; 59. Probability; Revision Test 16; 60. The binomial and Poisson distributions; 61. The normal distribution; 62. Linear correlation; 63. Linear regression; Revision Test 17; 64. Sampling and estimation theories; 65. Significance testing; 66. Chi-square and distribution-free tests; Revision Test 18; 67. Introduction to Laplace transforms; 68. Properties of Laplace transforms; 69. Inverse Laplace transforms; 70. The Laplace transform of the Heaviside function; 71. The solution of differential equations using Laplace transforms; 72. The solution of simultaneous differential equations using Laplace transforms; Revision Test 19; 73. Fourier series for periodic functions of period 2p; 74. Fourier series for a non-periodic function over period 2p; 75. Even and odd functions and half-range Fourier series ; 76. Fourier series over any range; 77. A numerical method of harmonic analysis; 78. The complex or exponential form of a Fourier series; Revision Test 20; Essential formulae; Answers to Practise Exercises; Index