Book:A. Geary/Advanced Mathematics for Technical Students, Part I

Contents

 * CHAPTER I
 * Functions. Limits. Infinitesimals. Continuity. Derivatives of standard functions. Methods of differentiation. Hyperbolic functions. Higher derivatives. Implicit functions. Connected rates


 * CHAPTER II
 * Convergence of infinite series. Simple tests for convergence. Power series. Maclaurin's series. Series for standard functions. Taylor's series. Small increments and percentage errors. Differentials. Points of inflexion. Maxima and minima. Functions of several variables. Partial derivatives. Total differential


 * CHAPTER III
 * Standard integrals. Expansion in series by integration. Definite integrals. Areas. Infinite integrals. Length of a curve. Integration by substitution and by parts. Partial fractions. Integration of fractions, trigonometric functions and functions containing surds. Wallis's formulae


 * CHAPTER IV
 * Co-ordinates. Equation of a straight line. Perpendicular distance of a point from a line. Angle between two lines. Equations of tangent and normal to a curve. Equation of a pair of straight lines. Equation of a circle. Radical axis. Coaxal systems of circles. Pole and polar. Parametric equations


 * CHAPTER V
 * Length of a curve in polar co-ordlnates. Curvature and radius of curvature. Newton's formula for radius of curvature. Transition curves. Cycloid, epicycloid and hypocycloid. Centre of curvature. Evolute and involute


 * CHAPTER VI
 * Conic sections. Parabola. Ellipse. Orthogonal projection. Hyperbola. Asymptotes. Change of axes. General equation of the second degree. Polar equations


 * CHAPTER VII
 * Volume and surface of a solid. First and second momenta of areas and volumes. Centroids. Pappus' theorems. Moments of inertia and radii of gyration. Centre of pressure. Mean value and root-mean-square. Electric and magnetic force. Exponential law of growth or decay. Catenary


 * CHAPTER VIII
 * Algebraic operations with complex numbers, and their geometric representation. Polar form of a complex number. Alternating currents. De Moivre's theorem. Roots of a complex number. Exponential form of sine and cosine. Summation of trigonometric series. Connection between trigonometric and hyperbolic functions


 * CHAPTER IX
 * Elementary theory of equations. Remainder theorem and factor theorem. Relations between roots and coefficients. Complex roots. Graphical solution of cubic equations


 * CHAPTER X
 * Methods of approximation to a root of an equation. Newton's formula and Graeffe's root squaring method. Approximate evaluation of first and second derivatives. Approximate integration by Simpson's rule and by expansion in series. Planimeter


 * CHAPTER XI
 * First order differential equations in which the variables can be separated. Motion of a body in a straight line under a varying force. Solution of $a \dfrac {d^2 y} {d x^2} + b \dfrac {d y} {d x} + c y = 0$. Simple harmonic motion. Damped and forced oscillations. Energy and momentum equations. Potential energy


 * CHAPTER XII
 * Chain rule for vector. Rate of change of a vector. Hodograph. Relative velocity and acceleration. Motion of a particle in a plane. Energy equation. Equilibrium of coplanar forces. Virtual work. Rotational motion. Bending of beams. Shearing force and bending couple. Tensile and shear strain. Bending of a thin rod. Buckling of a thin rod


 * Answers


 * Index