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| CHAPTER1 NUMBER,VARIABLE,FUNETION 1.1 REAL NUMBERS.REAL NUMBERS AS POINTS ON A NUMBER SCALE 1.2 THE ABSOLUTE VALUE OF S REAL NUMBER 1.3 VARIABLES AND CONSTANTS 1.4 THE RANGE OF A VARIABLE 1.5 FUNCTION 1.6 ALGEBRAIC FUNCTION 1.6.1 Power function 1.6.2 The rational integral function or poly nomial 1.6.3 Frsctional rational function 1.6.4 Irrational function 1.7 EXPONETIAL,LOGARITHMIC AND TRIGONOMETRIC FUNCTION 1.7.1 General exponential function 1.7.2 Logarithmic function 1.7.3 Trigonometric functions 1.8 ELEMENTARY FUNCTION 1.9 INVERSE FUNCTIONS EXERCISES ON CHAPTER1 CGHAPTER2 LIMITS AND CONTINUITY OF FUNCTIONS 2.1 THE LIMIT OF AN ORDERED VARIABLE 2.2 THE LIMIT FUNCTION 2.3 PROPERTIES OF THE LIMIT FUNCTION 2.4 A FUNCTION APPROACHES INFINITY 2.5 INFINITESIMALS AND THEIR BASIC PROPERTIES 2.6 BASIC THEOREMS ON LIMITS 2.7 THE LIMOF TWO FUNCTIONS 2.8 CONTINUIY OF FUNCTIONS 2.9 CERTAIN PROPERTIES OF CONTINUOUS FUNCTIONS EXERCISES ON CHAPTER2 CHARTER3 DERIVE AND DIFFERENTIAL 3.1 VELOCITY OF MOTION 3.2 THE DEFINITION OF A DERIVATIVE 3.3 THE DERIVATIVE OF:A CONSTANT,THE FUNCTION,n A POSITIVE INTEGER 3.4 DERIVATIVES OF:A SUM,APRODUCT AND APUOTIENT 3.5 THE DERIVATIVE OF A COMPOSITE FUNCTION 3.6 DERIVATIVES OF THE FUNCTIONS 3.7 AN INPLICIT FUNCTION AND ITS DIFFERENTIATION 3.8 DERIVATIVESOF A LOGARITHMIC FUNCTION,A GENERAL EXPONENTIAL FUNCTION 3.9 AN INVERSE FUNETION’S DIFFERENTIATION 3.10 BASEC DIFFERENTIATION FORMULAS 3.11 THE DERIVATIVE OF A FUNCTION REPRSENTED PARAMETRICALLY 3.12 THE DIFFERENTIAL 3.13 DERIV ATIVES OF DIFFERENT ORDERS 3.13.1 Derivatives of dlementary functions 3.13.2 Derivatives of implicit functions 3.13.3 Derivatives of functions represented parametrically 3.14 THE EQUATIONS OF A TANGENT AND A NORMAL 3.14.1 The geometric meaning of the differential 3.14.2 The equations of a tangent and a normal EXERCISES ON CHAPTER3 CHAPTER4 SOME THEOREMS ON DIFFERENTIABLE FUNCTIONS CHAPTER5 THE INDEFINITE INTEGRAL CHAPTER6 THE DEFINITE INTEGRAL CHAPTER7 DIFERENTIAL EQUATIONS CHAPTER8 VECTORS AND SOLID ANALYTIC GEOMETRY CHAPTER9 FUNCTIONS OF SEVERAL VARIABLES CHAPTER10 MRLTIPLE INTEGRALS CHAPTER11 SERIES ANSWER TO EXERCISES REFERENCES |
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