Introduction Real numbers – Inequalities – Absolute value – Equation of a straight line, circle and parabola
Functions Kinds of functions – Graph of a function – Inverse function – inverse trigonometric functions – Exponential and Logarithmic functions
Limit and Continuity Limit of a function – Continuity of a function - Intermediate-Value Theorem – Limits and Continuity trigonometric, Exponential and Logarithmic functions
The Derivative The derivative function – techniques of differentiation – Implicit differentiation- differentiation of inverse function – parametric equations
Applications of the Derivative Increasing and decreasing functions – Relative extrema – Absolute extrema - Graphing of a function – Newton’s method – Rolle’s theorem – Mean value theorem
Integration The indefinite integral – the definite integral – the fundamental theorem of calculus – Average value of a function
Principles of integral evaluation Integration by parts – integration by substitution – integration of rational functions by partial fractions
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