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Fundamental ideas, rates and differentials. Functions and derivatives. Differentials of algebraic functions. Use of rates and differentials in solving problems. Differentials of trigonometric functions. Velocity, acceleration and derivatives. Interpretation of functions and derivatives by means of graphs. Maximum and minimum values. Problems in maxima and minima. Differentials of logarithmic and exponential functions. Summary of differential formulas. Reversing the process of differentiation. Integral formulas. How to use integral formulas. Interpretation of integrals by means of graphs. Graphical applications of integration. Use of integrals in solving problems. The natural law of growth and the number.

The fundamental operations. Calculation with decimais. Approximate results in calculation. Factors, multiples and divisors. Fractions. Power and roots. Logarithms. Use of logarithms in arithmetic. Ratio and proportion. Series and progressions. Systems of common measures. Calculation with denominate numbers. Time, temperature and angle measure. Latitude, longitude and time. Dimensions and areas of plane figues. Dimensions, areas and volumes of solids. Graphs. Percentage. Compound interest.