Engineering Analysis

Preface
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Contents
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1. Applications of Differential Calculus 1
...1-1. Introduction 1
...1-2. Functions 2
...1-3. Checking equations 6
...1-4. The limit of a function 11
...1-5. Continuity offunctions 14
...1-6. The first derivative of a function 14
...1-7. Problems involving related time rates 16
...1-8. Maxima and minima 19
...1-9. Differentials 24
...1-10. Higher derivatives 27
...1-11. Indeterminate forms 28
...1-12. Taylor's expansion of a function 30
...1-13. Remainder in Taylor's series 34
...1-14. Convergence of Taylor's series 37
...1-15. Approximating functions by means of series 39
...1-16. Numerical differentiation 46
...1-17. Numerical differentiation (continued) 52
...1-18. Functions of several variables 55
2. Vector Algebra 62
...2-1. Vectors and vector analysis 62
...2-2. Addition and subtraction of vectors 63
...2-3. Statics of a particle 67
...2-4. Vector addition\emAlgebraic methods 71
...2-5. Scalar product of two vectors 78
...2-6. Vector product of two vectors 84
...2-7. Equilibrium of bodies of finite size 89
...2-8. Derivative of a vector 100
3. Applications of Integral Calculus 103
...3-1. The definite integral 103
...3-2. The indefinite integral 104
...3-3. Bending moments and shearing forces on beams 112
...3-4. Double integrals by iteration 118
...3-5. Centroid of a plane area 126
...3-6. The second moments of a plane area 132
...3-7. Hydrostatic pressure on plane surfaces 145
...3-8. Triple integrals by iteration 150
...3-9. Polar-cylindrical and polar-spherical coordinates 155
...3-10. Electrostatic field, magnetic field, etc. 159
...3-11. Line integrals and potentials 171
...3-12. Integration by means of infinite series-elliptic integrals 178
...3-13. Numerical integration 186
4. Ordinary Differential Equations 197
...4-1. Definitions 197
...4-2. First-order ordinary differential equations of first degree 198
...4-3. Setting up differential equations 209
...4-4. Derivation by using differentials 219
...4-5. One-dimensional steady flow of heat and electricity 229
...4-6. Hyperbolic functions 236
...4-7. First-order ordinary differential equations of the second degree 239
...4-8. Graphical and numerical methods of solving first-order equations 244
...4-9. Higher-order ordinary differential equations 251
...4-10. Deflection of slender beams under bending 259
...4-11. Dynamics of a particle 266
...4-12. Homogenevus linear equations with constant coefficients 273
...4-13. Non-homogeneous linear equations with constant coefficients 284
...4-14. Mechanical and electrical vibrations. Linearization 301
...4-15. Characteristic functions of boundary problems 309
...4-16. Simultaneous linear equations with constant coefficients 318
...4-17. Homogeneous linear equations with variable coefficients 322
...4-18. Non-homogeneous linear equations with variable coefficients 332
5. Fourier Series 339
...5-1. Expansion in trigonometric series 339
...5-2. Harmonic analysis\emNumerical methods 351
Index 359