AVIATION MATHEMATICS (GC_1)

COURSE OBJECTIVEStudents will get an overview of aviation mathematics as perThe requirement of regulatory bodiesThe application of mathematical concepts the field

ALLOTTED TIME AND DELIVERYDuration 40 hours theoryDeliveryLecture discussionClass exerciseReading and class exercisesHome take exams/exercises

COURSE CONTENTArithmeticAlgebraGeometryTrigonometryPractical problems on charts and graphs

TEXT BOOKS AND REFERENCESAc 65 9A, Airframe and Powerplant Series, General HandbookTechnical Mathematics with CalculusShop Mathematics

EVALUATIONClass testsAssignmentsFinal testPassing mark70%

DISCIPLINEPunctualityGood appearanceI'D. cards in proper placeSchool regualtion

ArithmeticObjectiveAddition, subtraction, multiplication and division of:FractionsDecimalsConversion of Metric System to British SystemCalculation of ratio, average and percentageApplication of logarithms and indices

Basic OperationsAddition +Subtraction -Multiplication x () *Division ,/,Grouping signs

TermsNumberSumMinuendSubtrahendDifferenceMultiplicandMultiplierProduct

Terms (Contd.)DividendDivisorQuotientRemainderDigitsDenominatorNumerator5 2 =37 x 3 = 2127 / 5 = 5 and 2Product Quotient Difference Subtrahend Multiplier Minuend Multiplicand Divisor Dividend Remainder

Number SystemCounting Numbers{ 1,2,3,4,}Whole Numbers{ 0,1,2,3,4,}Integers (I){,-3,-2,-1,0,1,2,3,}Rational Numbers

Fractions a/b , a I, b IProper , ab 4/3Mixed , a c/b 3 2/3Decimals , 0.5, 2.33, 4.1111Irrational numbers , 3.030030003, Real Numbers = R U IR

Significant DigitsMeasured dataReliability of a numberPrecision position of last reliable digitAccuracy number of significant figureE.g. 56.78, 0.0034, 5.600, 3.0080, 50,000Rounding off a numberEven and odd case

Rules Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant. Round the final result to the least number of significant figures of any one term.

Examples 1) 3.0800 - five significant figures. All the rules are illustrated by this problem. Rule one - the 3 and the 8. Rule Two - the zero between the 3 and 8. Rule three - the two trailing zeros after the 8.2) 0.00418 - three significant figures: the 4, the 1, and the 8. This is a typical type of problem where the student errs by giving five significant figures as the answer.3) 7.09 x 105 - three significant figures. When a number is written in scientific notation, only significant figures are placed into the numerical portion. If this number were taken out of scientific notation, it would be 0.0000709.4) 91,600 - three significant figures. The last two zeros are not considered to be significant (at least normally). Suppose you had information that showed the zero in the tens place to be significant. How would you show it to be different from the zero in the ones place, which is not significant? The answer is scientific notation. Here is how it would be written: 9.160 x 104. This CLEARLY indicates the presence of four significant figures.5) 0.003005- four significant figures. No matter how many zeros there are between two significant figures, all the zeros are to be considered significant. A number like 70.000001 would have 8 significant figures.6) 3.200 x 109 - four significant figures. Notice the use of scientific notation to indicate that there are two zeros which should be significant. If this number were to be written without scientific notation (3,200,000,000) the significance of those two zeros would be lost and you would - wrongly - say that there were only two significant figures.

Multiples and FactorsFactors 27 : 1,3,9,27Multiple3 : 3,6,9,12,Prime factors36 : 2,3Greatest common factor (GCF)Least common multiple (LCM)

Exercise 3 + 4 2 x 5 + 4 = 5 + 1/100 + 7/1000 = Change 3.333 to fractional formChange 4/3 to decimal formGo to drill for significant figures

Exercises (Cont.) Round off the result of the following calculations to three significant digits2.4x6.5x10.3721.3x0.054/(97.4x3.80)Find the GCF of the following10,15,3018,30,12,42Find the LCM of the following3,4,5

Measurement Systems Metric system (SI)MeterKilogramsecondBritish system (BS)InchPoundSecond

Area And VolumeA = BHA = BHA = BH/2A = R2V = R2HV = BHDV = R2H/3V = 4R3/3A = 4R2

Comparison Ratio : by dividing one number by another15 to 3 15:3=15/3=5Proportion : equality of two ratiosa/b = c/d 15:3::25:5Variation : the result one when the other changesDirect Inverse

Percentage and AveragePercentage : by the hundred2 = 200%, 1.5 = 150%50 = 25% of 40015% of 60 = 9Average : Average of 3,4,5,6,7 is (3+4+5+6+7)/5 = 5RateDivision by time

Rate

Powers and RootsPower = root exponent 9 = 32Root = index Power3 = 327Rulesax ay = a x+yax/ay = ax-y(ax)y = axy1/ax = a-xxa = a1/x

Logarithms 100 = 1022 is the logarithm of 100 on the base 10Log(ab) = loga + logbLog(a/b) = log(a) log(b) Log(ab) = b*log(a)43 x 69 = x use logarithm tables to solve

Exercises

Algebra Objective : To do algebraic operationsTo solve linear equations, simultaneous equations, and quadratic equations

Algebraic OperationAlgebra : Relations and properties of numbers by means of letters, signs of operations and other symbols.3x + 4y Expression Coefficient Term

Laws Associative law3a + (2b 3c) = (3a +2b) 3c (a x b) x c = a x (b x c) Commutative law3a x 2b = 2b x 3aDistributive law a(b + c) = ab + ac

Special Products(a + b) (a + b) = a2 +2ab + b2 (a - b) (a - b) = a2 - 2ab + b2(a + b) (a - b) = a2 - b2(a + b) (a + ) = a2 +a(b + c) + bc(a + b) (c + d) = ac + ad + bc + bda3 + b3= (a + b) (a2 - ab + b2)a3 - b3= (a - b) (a2 + ab + b2)

Simplification of ExpressionsExercises

Equations Linear equations3x + 5 = 9x 7Word problemsSimultaneous equations

Algebraic sentence

Quadratic Equationsax2 + bx + c = 0SolutionsBy plotting graphsBy completing the squareBy quadratic formula

Review Problems

Geometry Objective : To evaluate the areas and volumes of different geometric shapes.To understand the relationship of angular, linear and irregular geometric figures.

Fundamental ConceptsPoint Designation ., + , x, Line One dimensionalPath traced by a pointTypes SegmentStraightcurved

Fundamental Concepts (Contd.)Plane Two dimensionalPath traced by a lineVolume Three dimensionalPath traced by surfaces

Angles Made by two straight lines which are intersectingAcuteObtuseRight MeasurementDegreeRadianGradientRevolutions

Triangles Right

Isosceles

Equilateral

Scalene

Polygons Square

Pentagon

Hexagon

Heptagon

Circles and Arcs

Trigonometry

Charts & Graphs

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