Calculus - I
Calculus Contents A
     Introduction to Functions
      Function definition, notation and terminology
         Domain, range and codomain
         Evaluating a function
         Composition of functions (a function of a function)
         Inverse function
     The graph of a function
      Function's behavior, properties and characteristic points of the graph
         Domain and range
         Roots or zero function values, x-intercepts, y-intercepts
         Increasing/decreasing intervals
         The instantaneous rate of change or the derivative
         Continuity and discontinuity
         Vertical, horizontal and oblique or slant asymptotes
         Stationary points and/or critical points
         Turning points (extremes, local or relative maximums or minimums)
         Inflection points and intervals of concavity
         Symmetry of a function, parity - odd and even functions
      Transformations of original or source function
         How some changes of a function's notation affect the graph of the function
         Translations of the graph of a function
         Reflections of the graph of a function
      Types of functions - basic classification
         Algebraic functions and Transcendental functions
      Algebraic functions
         The polynomial function
         Rational functions
         Reciprocal function
      Transcendental functions
         Exponential and logarithmic functions, inverse functions
         Trigonometric (cyclometric) functions and inverse trigonometric functions (arc-functions)
     The graphs of the elementary functions
         The graphs of algebraic and transcendental functions
      The graphs of algebraic functions
      The graphs of the polynomial functions
         The source or original polynomial function
         Translating (parallel shifting) of the polynomial function
         Coordinates of translations and their role in the polynomial expression
      The graph of the linear function
      The graph of the quadratic function
      The graphs of the cubic function
         The graphs of the source cubic functions
         The graphs of the translated cubic functions
      The graphs of the quartic function
         The graphs of the quartic functions types 1 and 2
         The graphs of the quartic functions types 3/1 and 3/2
         The graphs of the quartic functions types  4/1 . . . 4/6
      Sigma notation of the polynomial
          Coefficients of the source polynomial in the form of a recursive formula
          Coefficients of the source polynomial function are related to its derivative at x0
      Translated power function
         Translated sextic function example
      Graphs of rational functions
         Basic properties of rational functions
         Vertical asymptotes of rational functions
         Horizontal asymptote of rational functions
         The oblique or slant asymptote of rational functions
         The graph of the reciprocal function, equilateral or rectangular hyperbola
         Translation of the reciprocal function, linear rational function
         Graphs of rational functions examples
      The graphs of transcendental functions
      Exponential and logarithmic functions are mutually inverse functions
         The graph of the exponential function
         The graph of the logarithmic function
      Trigonometric (cyclometric) functions and inverse trigonometric functions (arc functions)
         The graphs of the trigonometric functions and inverse trigonometric functions or arc-functions
         The graph of the sine function
         The graph of the cosine function
         The graph of the arc-sine function and the arc-cosine function
         The graph of the tangent function and the cotangent function
         The graph of the arc-tangent function and the arc-cotangent function
         The graph of the cosecant function
         The graph of the secant function
         The graph of the arc-cosecant and the arc-secant function
 
 
 
 
 
 
 
 
 
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