Engineering Analysis

The material covered in this book has been the basis of a course taught by the author at The Johns Hopkins University. Its purpose is to present mathematics, as a technical language and a practical tool, to engineering undergraduates. Examples of this application of mathematics are drawn from various branches of engineering and physics. The student is trained to formulate problems mathematically and to arrive at their solutions. The student will need only an elementary knowledge of the Calculus as a prerequisite. In fact, the material covered in the first three chapters has been so arranged that it can be taught to students who are taking Integral Calculus concurrently. Chapter 4 is self-contained and can be used as a text for an introductory course of ordinary differential equations. Copyright Preface Contents 1. Applications of Differential Calculus 1-1. Introduction 1-2. Functions 1-3. Checking equations 1-4. The limit of a function 1-5. Continuity offunctions 1-6. The first derivative of a function 1-7. Problems involving related time rates 1-8. Maxima and minima 1-9. Differentials 1-10. Higher derivatives 1-11. Indeterminate forms 1-12. Taylor's expansion of a function 1-13. Remainder in Taylor's series 1-14. Convergence of Taylor's series 1-15. Approximating functions by means of series 1-16. Numerical differentiation 1-17. Numerical differentiation (continued) 1-18. Functions of several variables 2. Vector Algebra 2-1. Vectors and vector analysis 2-2. Addition and subtraction of vectors 2-3. Statics of a particle 2-4. Vector addition—Algebraic methods 2-5. Scalar product of two vectors 2-6. Vector product of two vectors 2-7. Equilibrium of bodies of finite size 2-8. Derivative of a vector 3. Applications of Integral Calculus 3-1. The definite integral 3-2. The indefinite integral 3-3. Bending moments and shearing forces on beams 3-4. Double integrals by iteration 3-5. Centroid of a plane area 3-6. The second moments of a plane area 3-7. Hydrostatic pressure on plane surfaces 3-8. Triple integrals by iteration 3-9. Polar-cylindrical and polar-spherical coordinates 3-10. Electrostatic field, magnetic field, etc. 3-11. Line integrals and potentials 3-12. Integration by means of infinite series-elliptic integrals 3-13. Numerical integration 4. Ordinary Differential Equations 4-1. Definitions 4-2. First-order ordinary differential equations of first degree 4-3. Setting up differential equations 4-4. Derivation by using differentials 4-5. One-dimensional steady flow of heat and electricity 4-6. Hyperbolic functions 4-7. First-order ordinary differential equations of the second degree 4-8. Graphical and numerical methods of solving first-order equations 4-9. Higher-order ordinary differential equations 4-10. Deflection of slender beams under bending 4-11. Dynamics of a particle 4-12. Homogenevus linear equations with constant coefficients 4-13. Non-homogeneous linear equations with constant coefficients 4-14. Mechanical and electrical vibrations. Linearization 4-15. Characteristic functions of boundary problems 4-16. Simultaneous linear equations with constant coefficients 4-17. Homogeneous linear equations with variable coefficients 4-18. Non-homogeneous linear equations with variable coefficients 5. Fourier Series 5-1. Expansion in trigonometric series 5-2. Harmonic analysis—Numerical methods Index