Essentials Engineering Mathematics

"The book is intended for first year engineering students and presumably this choice of subjects is a reflection of the course on which the author lectured. The book fulfills this purpose in a very satisfactory manner and can be warmly recommended for this purpose. The explanations are good and there is an adequacy of worked examples. …A welcome feature is that indefinite integrals mentioned in the text all have included an arbitrary constant. …Much of the book would be found useful for those in the last years at school."-Zentralblatt MATH"Each of the short sections covers the amount of material one would hope to get through in a lecture or two, typically giving a short introduction to the relevant theory and several worked examples. …Jeffrey's book could be easily adopted as a course text, and the sections can be divided naturally into groups for shorter modules."-Times Higher Education Supplementead> Concise explanations and a wealth of examples form an ideal study guide and reference

• 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