The continuum of numbers -- The concept of function -- The elementary functions -- Sequences -- Mathematical

induction -- The limited of a sequence -- Further discussion of the concept of limit -- The concept of limit

for functions of a continous variable -- Limits and the number concept -- Theorems on continuous functions --

Polar coordinates -- Remarks on complex numbers -- The fundamental ideas of the integral and differential

calculus -- The integral -- Elementary examples of integration -- Fundamental rules of integration -- The

integral as a function of the upper limit (Indifinite integral) -- Logarithm defined by an integral --

Exponiental function and powers -- The integral of an arbitrary power of x --The derivative -- The integral,

the primitive function, and the fundamental theorems of the calculus -- The techniques of calculus --

Differentiation and integration of the elementary functions -- The simplest rules for differentiation and

their applications -- The derivative of the inverse function -- Differentiation of composite functions -- Some

applications of the exponential function -- The hyperbolic functions -- Maxima and minima -- The order of

magnitude of functions -- Techniques of integration -- Table of elementary integrals -- The method of

substitution -- Further examples of the substitution method -- Integration by parts -- Integration of rational

functions -- Integration of some other claseses of functions -- Integrals of elementary functions -- Extension

of the concept of integral -- The differential equations of the trigonometric functions -- Applications in

Physics and Geometry -- Theory of plane curves -- Vectors in two dimensions -- Motion of a particle under

given forces -- Free fall of a body resisted by air -- The simplest type of elstic vibration -- Motion on a

given curve -- Motion in a gravitational field -- Work and energy -- Taylor´s expansion -- Expansion of the

Logarithm and the inverse tangent -- Taylor´s theorem -- Expression and estimates for the remainder --

Expansions of the elementary functions -- Numerical meethods -- Computation of integrals -- Other examples of

numerical methods -- Numerical solution of equations -- Infinite sums and products -- The concepts of

convergence and divergence -- Sequences of functions -- Expasion of given functions in power series. Method of

undetermined coefficient -- Trigonometric series -- Periodic functions -- Superposition of harmonic vibrations

-- Fourier series -- Further discussion of convergence -- Aproximation by Trigonometric and rational

polynomials -- Differential equations for the simplest types of vibration -- Vibration problems of mechanics

and physics -- Solution of the homogeneous equation. Free oscillations -- The nonhomogeneous equation. Forced

oscillations --