TECHNICAL COLLEGE SERIES... (Catlett, VA)

TECHNICAL COLLEGE SERIES...

...NATIONAL CERTIFICATE MATHEMATICS VOLUME II 2ND YEAR COURSELocal pick-up preferred but will ship at the buyer s expenseKingston IMG_4515 250.00 or Best OfferCharts Graphs Tables Illustrations FormulasAuthors P. ABBBOTT B.A. and H. MARSHALL B.A.Completely Revised byW.E. Fisher O. B. E. D.Sc A.M.I. Mech.E.Formerly Principal Wolverhampton and Stafford College of TechnologyPublisher THE ENGLISH UNIVERSITIES PRESS LTD 102 NEWGATE STREET LONDON E.C.1GENERAL EDITOR S FOREWORDThe last twenty years have seen far-reaching changes in technical education changes whose objectives have been to meet the ever increasing demands of technology. A new pattern of technical education is now emerging as a result of a series of Government committees and white papers. Initially attention was directed more intensely to the education of technologists resulting in the expansion of universities a greater emphasis on the teaching of science in schools and the establishment of the Colleges of Advanced Technology. The training of technologists has hitherto fallen into two broad categories university courses and National Certificate Courses arranged on a part-time basis for apprentices in industry. These part-time courses have become the route through the majority of professional engineers have received their training. It is however that this state of affairs will continue in the future. The professional Institutions have rightly raised their entrance requirements to a level which the part-time day release student will find extremely difficult to achieve at the same time the greatly increased facilities for full-time and sandwich courses will provide a much more satisfactory educational system for those wishing to attain professional status.Latterly more attention has been given to better training of technicians craftsman and operatives The Government White Paper Better Opportunities in Technical Education seeks establish a new pattern for technical courses at these levels. The very high failure rate in Ordinary and Higher National Certificate courses which has caused such concern in recent years is it is hoped to be avoided to be avoided by the introduction of the new General Course. This is designed as a diagnostic course to determine whether a student is best suited to continue with an Ordinary National Certificate course a craft or operative course or a technician course. The City and Guilds of London Institute are making radical changes in their existing courses and designing new technician courses to fulfill these objectives.The Technical College series of books covers this very wide field of technician craft and operative courses. Many of the books of the series are now standard works having stood the test of time over a long period of years. Such books are reviewed from time to time and new editions published to keep them up-to-date both in respect of new technological developments and changing examination requirements. New works are constantly being added to the list as new courses are arranged and new techniques are developed. The publishers are fully aware of the part that well written up-to-date textbooks can play in supplementing teaching and it is their intention that the Technical College Series shall continue to make a substantial contribution to the development of technical educationContents by ChapterINDICES AND LOGARITHMS The index notationLaws of indicesFractional and negative indicesMeaning of a logarithmLaws of logarithmsLogarithms To Other Bases Than 10 MeaningGeneral relation between logarithms of a number to two different basesNapier logarithmsRelation to common logarithmsQUADRATIC EQUATIONS Methods of SolutionImaginary rootsSimultaneous quadraticsMENSURATION I Areas of plane rectilinear figuresFormula for area of triangleRegular polygonsIrregular rectilinear figuresAreas of irregular curved figures by trapezoidal mid-ordinate and Simpson s rulesVolumes of irregular solidsMENSURATION II The circleIntersecting chords and their propertiesArea of sector and of segmentAngular velocityMENSURATION III Area and volume of prism and cylinderVolume of frustumArea and volume of pyramid and coneArea and volume of frustumArea and volume of spherePROGRESSIONS Meaning of a seriesArithmetic seriesGeometric seriesSum of n termsApproach to infinitySum to infinityTHE TRIGONOMETRICAL RATIOS Sines of angles up to 360 degreesNegative anglesThe sine graphCosines of angles up to 360 degreesThe cosine graphTangents of angles up to 360 degreesWell known identitiesTrigonometrical functionsSOLUTIONS OF TRIANGLES Sine ruleThe ambiguous caseCosine ruleTHE ADDITION FORMULA Expansion of sin (A - B) cos (A - B)Ratios of multiple and sub-multiple anglesTrigonometrical equationsTHE PLOTTING OF MORE DIFFICULT GRAPHS Recapitulation of previous workGraphs of cubic expressionsAlternative methodsThe graphs of y x (x-a) (x b) y ax3 bx2 cx dAlternative method of graphical solutionThe graphs of y 3.5x2.8 y 3e2xDETERMINATION OF LAWS The linear lawLaws other than linear and their reduction to a straight line13. THE BINOMIAL LAWMeaning of binomial expressionSimple expressions of (a b)Expansion of (a b)n FUNCTIONS RATE OF INCREASE DIFFERENTATION Meaning of functionDependent and independent variablesFunctional notationGradient and slopeGradient of a straight lineGradient of a curveVelocity at a pointDifferentiation from first principlesDifferential coefficientDifferentiation of simple functionsDifferentiation of y axnDifferentiation of a sumVelocity and acceleration by differentiationMAXIMA AND MINIMA The sign of the differential coefficientStationary valuesTurning pointsMaximum and minimum pointsApplications to practical problemsCONSTANTSTABLESANSWERSHardcover 412 pages Printed in Great Britain for the English Universities Press Limited by Richard Clay and Company Ltd. Bungay. Suffolk. Copyright W.E Fisher 1960