Book:H.V. Lowry/Advanced Mathematics for Technical Students, Part II/Second Edition

Contents

 * PREFACE


 * PREFACE TO SECOND EDITION


 * CHAPTER I
 * Indeterminate forms. Leibnitz's theorem. Integral relations. Reduction formulae. Infinite integrals. Gamma function. Mean value theorems. Differentiation of an integral. Moments and products of inertia. Principal axes of inertia


 * CHAPTER II
 * Envelopes. Evolute of a curve. Contact of curves. Plane motion of a lamina. Instantaneous centre of rotation. Space and body centroids. Epicyclics


 * CHAPTER III
 * First order differential equations. Orthogonal families of curves. Simple second order equations. Linear differential equations with constant coefficients. Referential operators


 * CHAPTER IV
 * Forced mechanical and electrical oscillations. Buckling of clamped struts. Bending of loaded struts and ties. Simultaneous differential equations. Oscillation of coupled springs. Normal modes of oscillation. Stress in a rotating disc. General theory of coupled electric circuits. Use of Laplace transforms for the solution of linear differential equations with constant coefficients


 * CHAPTER V
 * Recurrence relations. Difference equations. Electrical filters. Newton's interpolation formula. Continued fractions


 * CHAPTER VI
 * Determinants. Solution of linear equations. Consistency of equations. Linear dependence of a set of equations. Matrices. Solution of linear equations by matrices. Linear transformations. Invariants. Tensors


 * CHAPTER VII
 * Co-ordinates of a point in space. Direction cosines. Rotation of axes. Scalar and vector products. Differentiation of vectors. Equation of a plane. Equations of a straight line. Surfaces. Momental ellipsoid. Tangent plane to a surface. Space curves. Curvature and torsion


 * CHAPTER VIII
 * Spherical triangles. Principle of duality. Sine and cosine formulae. Napier's rules for right-angled triangles. Further trigonometric formulae. Solution of triangles


 * CHAPTER IX
 * Differentiation of functions of several variables. Taylor's series. Superposition of small increments. Change of independent variables. Inverse functions. Jacobians. Exact differentials. Application to thermodynamics. Homogeneous functions. Normal and tangent plane to a surface. Directional derivative of a scalar field. Gradient of a function. Maxima and minima. Curvature of surface. Functions of a complex variable. Conjugate functions. Conformal transformations


 * CHAPTER X
 * Integration of functions of several variables. Line, surface and space integrals. Double integrals in Cartesian and polar coordinates. Centre of pressure. Change of variable in a double integral. Triple integrals. Moments and products of inertia. Space integrals in cylindrical and polar co-ordinates. Dependence of a line integral on the path of integration. Green's theorem. Two-dimensional flow of liquid. Divergence and curl of a vector. Gauss's and Stokes's theorems. Cauchy's theorems


 * CHAPTER XI
 * Fourier series. Expansion of odd and even functions. Sum at a point of discontinuity. Approximation by successive harmonics. Half-range series. Differentiation and integration of Fourier series. Harmonic analysis


 * CHAPTER XII
 * Motion of a system of particles and of a rigid body. Components of acceleration in plane motion. Angular momentum. Kinetic and potential energies. Motion of a rigid body. Energy equation. Impulsive motion


 * CHAPTER XIII
 * Energy methods. Virtual work. Stability of equilibrium. Small oscillations. Strain energy. Potential energy of an electrostatic field. Potential energy of mechanical forces on circuits. Carnot's cycle. Entropy. Stability of a floating body. Bernoulli's theorem


 * CHAPTER XIV
 * Solution of differential equations by infinite series. Bessel's equation. Partial differential equations. Transverse oscillations of a string. Electric waves along a cable. Conduction of heat


 * Answers


 * Index