Essentials Engineering Mathematics

This popular self-study/supplementary textbook covers in detail all mathematical requirements common to first year engineering students of every discipline. Thoroughly revised for the second edition, the book provides more worked examples and exercises, and more material on numerical computation and includes an introduction to using MATLAB and Maple software. It is organized into short sections specific to certain topics, which allows students to identify subjects of interest that they can study separately, with little background reading. The author provides numerous worked examples throughout the text, and for reference, includes lists of mathematical formulae, standard integrals, and Laplace transform pairs.

First published in 1992, Essentials of Engineering Mathematics is a widely popular reference ideal for self-study, review, and fast answers to specific questions. While retaining the style and content that made the first edition so successful, the second edition provides even more examples, new material, and most importantly, an introduction to using two of the most prevalent software packages in engineering: Maple and MATLAB. Specifically, this edition includes:Introductory accounts of Maple and MATLAB that offer a quick start to using symbolic software to perform calculations, explore the properties of functions and mathematical operations, and generate graphical outputNew problems involving the mean value theorem for derivativesExtension of the account of stationary points of functions of two variablesThe concept of the direction field of a first-order differential equationIntroduction to the delta function and its use with the Laplace transformThe author includes all of the topics typically covered in first-year undergraduate engineering mathematics courses, organized into short, easily digestible sections that make it easy to find any subject of interest. Concise, right-to-the-point exposition, a wealth of examples, and extensive problem sets at the end each chapter--with answers at the end of the book--combine to make Essentials of Engineering Mathematics, Second Edition ideal as a supplemental textbook, for self-study, and as a quick guide to fundamental concepts and techniques.

Real numbers, inequalities and intervalsFunction, domain and rangeBasic coordinate geometryPolar coordinatesMathematical inductionBinomial theoremCombination of functionsSymmetry in functions and graphsInverse functionsComplex numbers; real and imaginary formsGeometry of complex analysisModulus-argument form of a complex numberRoots of complex numbersLimitsOne-sided limitsDerivativesLeibniz's formulaDifferentialsDifferentiation of inverse trigonometric functionsImplicit differentiationParametrically defined curves and parametric differentiationThe exponential functionThe logarithmic functionHyperbolic functionsInverse hyperbolic functionsProperties and applications of differentialabilityFunctions of two variablesLimits and continuity of functions of two real variablesPartial differentiationThe total differentialThe chain ruleChange of variable in partial differentiationAntidifferentiation (integration)Integration by substitutionSome useful standard formsIntegration by partsPartial fractions and integration of rational functionsThe definite integralThe fundamental theorem of integral calculus and the evaluation of definite integralsImproper integralsNumerical integrationGeometrical applications of definite integralsCentre of mass of a plane laminaApplications of integration to he hydrostatic pressure on a plateMoments of inertiaSequencesInfinite numerical seriesPower seriesTaylor and Maclaurin seriesTaylor's theorem for functions of two variable: stationary points and their identificationFourier seriesDeterminantsMatricesMatrix multiplicationThe inverse matrixSolution of a system of linear equations: Gaussian eliminationThe Gauss-Seidel iterative methodThe algebraic eigenvalue problemScalars, vectors and vector additionVectors in component formThe straight lineThe scalar product (dot product)The planeThe vector product (cross product)Applications of the vector productDifferentiation and integration of vectorsDynamics of a particle and the motion of a particle in a planeScalar and vector fields and the gradient of a scalar functionOrdinary differential equations: order and degree, initial and boundary conditionsFirst order differential equations solvable by separation of variablesThe method of isoclines and Euler's methodsHomogeneous and near homogeneous equationsExact differential equationsThe first order linear differential equationThe Bernoulli equationThe structure of solutions of linear differential equations of any orderDetermining the complementary function for constant coefficient equationsDetermining particular integrals of constant coefficient equationsDifferential equations describing oscillationsSimultaneous first order linear constant coefficient different equationsThe Laplace transform and transform pairsThe Laplace transform of derivativesThe shift theorems and the Heaviside step functionSolution of initial value problemsThe Delta function and its use in initial value problems with the Laplace transformEnlarging the list of Laplace transform pairsSymbolic Algebraic Manipulation by Computer SoftwareAnswersReferences

Alan Jeffrey