Continuity and Differentiability: continuity and differentiability; derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions; exponential and logarithmic functions; logarithmic differentiation; derivative of functions expressed in parametric forms; second order derivatives; Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation
Applications of Derivatives: rate of change of quantities; increasing and decreasing functions; tangents and normals; use of derivatives in approximation; maxima and minima (first derivative test and second derivative test); simple problems
Integrals: integration as inverse process of differentiation; integration of a variety of functions by substitution, by partial fractions and by parts; definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof); basic properties of definite integrals and evaluation of definite integrals
Applications of the Integrals: area under simple curves — especially lines, circles, parabolas and ellipses (in standard form only); area between the two above-said curves
Differential Equations: definition, order and degree, general and particular solutions of a differential equation; formation of a differential equation whose general solution is given; solution of differential equations by the method of separation of variables; homogeneous differential equations of first order and first degree; solutions of linear differential equations