Mathematics-1, Basics of Calculus

Ata Atun

 

Contents

Title                                                                                                                           i

Copyright                                                                                                                  ii

Preface                                                                                                                      iii

Table of Contents                                                                                                     iv

 

SYMBOLS AND NOMENCLATURE                                                                1

 

Chap 1           CLASSIFICATIONS OF FUNCTION                                        2

                   Classifications and terms, The nature of Algebraic expressions, Polynomials  and  fractional  functions, Partial Functions, Quadratic  equations, Solution of quadratic equations which do not factorize, Nature of roots of a quadratic equation,  Relationships between the roots and coefficients of a quadratic equation.                                                                              

 

Chap 2           TOPICS RELATED TO ALGEBRA                                          26

                   Indices, Surds, Logarithms, Exponential Equations, The Remainder Theorem, The Factor Theorem, Binomial Expressions, Pascal’s Triangle

                       

Chap 3           FUNCTIONS                                                                                  51

Mapping, Graphical Representation of functions (Curve Sketching), Domain and Range, The Quadratic Function, Inequalities, Quadratic Inequalities, Exponential functions, Rational Functions, Logarithmic functions, Simple Variations of functions, Inverse functions, The Graphs of Functions and Their Invgerses.

 

Chap 4           COORDINATE GEOMETRY                                                     82

                   Location of a Point in a Plane, Polar Coordinates, Cartesian Coordinates, Coordinate Geometry of the straight line, Gradient, The meaning of Equations, The equation of a Particular Curve, Equation of a Straight line.

 

Chap 5           DIFFERENTIATION I                                                                 120

The derivative (Slope Problem), Tangents and Normals, Gradient of a curve, Gradient Function, General Differentiation, Equations of Tangents and Normals, Stationery values, Turning Points, Investigating the Nature of Stationery Values,

 

REFERENCES                                                                                                      158

 

ANSWERS OF EXERCISES                                                                             160     

 

 

References

 

1.      FLANDERS, H. : Calculus 

         Florida, USA :W. H. Freeman and Company Publication, 1985

        

2.      DERMAN M. Z. ; ÖZKÖSELER Ö. ; ÖZTÜRK İ. ; ERGÜN M.:  Matematik

         Ankara, TR : Zafer Eğitim ve Öğretim yayını, 1997

        

3.      KOÇAK, Ş. ; ÜREYEN M. ; GÖĞÜŞ, M. ; OLGUN, Ş. ; GÖRGÜLÜ, A. :

Genel Matematik, Ünite 1-12

         Eskişehir, TR : Anadolu Üniversitesi yayını, 1997

 

4.      HACISALİHOĞLU, H. ; KAYA, R. ; ESİN, A. ; ÜREYEN, M. ; GÖRGÜLÜ, A. OLGUN, Ş. : Genel Matematik, Ünite 13-24

         Eskişehir, TR : Anadolu Üniversitesi yayını, 1997               

 

5.      SPIEGEL R. M. : Schaum’s Outline of Theory and Problems of Advanced Mathematics

         New York, USA : McGraw-Hill Book Company Publication, 1971

 

6.       FRANK, A. ; MENDELSON, E. : Schaum’s Outline of Theory and Problems of Differential and Integral Calculus

         London, UK : McGraw-Hill Book Company Publication, 1992

 

7.      GEORGE, B. T. : Calculus and Analytic Geometry, 3rd Ed.

         London, UK : Addison-Wesley Publishing Company, Inc., 1960

 

8.      GEORGE, B. T. : Calculus and Analytic Geometry, 4th Ed.

         Massachusetts, USA : Addison-Wesley Publishing Company, Inc., 1972