Essentials Of Engineering Mathematics

This work gives an introduction to mathematical topics needed in first-year engineering mathematics courses. It can be used both as a supplement to a lecture course and as a text for private study. The book is divided into a large number of specific topic-based sections, which can be studied separately. Each section uses a group of worked examples to demonstrate theories and techniques, with comprehensive problem sets to reinforce understanding of the subject. Answers to over 1300 separate problems are also included.

Table of Contents:
Real numbers, inequalities and intervals; function, domain and range; basic co-ordinate geometry; polar co-ordinates; mathematical induction; binomial theorem; combination of functions; symmetry in functions and graphs; inverse functions; complex numbers - real and imaginary form; geometry of complex numbers; limits; on-sided limits - continuity; derivatives; Leibniz's formula; differentials; differentiation of inverse trigonometric functions; implicit differentiation; parametrically defined curves and parametric differentiation; the exponential function; the logarithmic function; hyperbolic functions; inverse hyperbolic functions; properties and applications of differentiability; functions of two variables; limits of continuity of functions of two real variables; partial differentiation; the total differential; the chain rule; change of variable in partial differentiation; antidifferentiation (integration); integration by substitution; some useful standard forms; integration by parts; partial fractions and integration of rational functions; the definite integral; the fundamental theorem of integral calculus and the evaluation of definite integrals; improper integrals; numerical integration; geometrical applications of definite integrals; centre of mass of a plane lamina (centroid); applications of integration to the hydrostatic pressure on a plate; moments of inertia; sequences; infinite numerical series; power series; Taylor and Maclaurin series; Taylor's theorem for functions of two variables - stationery points and their identification; Fourier series; determinants; matrices - equality, addition, subtraction, scaling and transposition; matrix multiplication; the inverse matrix; solution of a system of linear equations - Gaussian elimination; the Gauss-Seidel iterative method; the algebraic eigenvalue problem; scalars, vectors and vector addition; vectors in component form; the straight line; the scalar product (dot product); the plane; the vector product (cross product); applications of the vector product; differentiation and integration of vectors; dynamics of a particle and the motion of a particle in a plane; scalar and vector fields and the gradient of a scalar function; ordinary differential equations - order and degree, initial an boundary conditions; first order differential equations solvable by separation of variables; the method of isoclines and Euler's methods; homogeneous and near homogeneous equations; exact differential equations; the first order linear differential equation. (Part Contents)