Unit - I Differential Calculus 1.1 Functions and Limits : a) Concept of function and simple examples. b) Concept of limits without examples. 1.2 Derivatives : a) Rules of derivatives such as sum, product, quotient of functions. b) Derivative of composite functions (chain Rule), implicit and parametric functions. c) Derivatives of inverse, logarithmic and exponential functions. 1.3 Applications of derivative : a) Second order derivative without examples. b) Equation of tangent and normal. c) Maxima and minima. d) Radius of curvature. Unit - II Integral Calculus 2.1 Simple integration : Rules of integration and integration of standard functions. 2.2 Methods of Integration : a) Integration by substitution b) Integration by parts c) Integration by partial fractions. Unit - III Applications of Definite Integration 3.1 Definite Integration : a) Simple examples b) Properties of definite integral (without proof) and simple examples. 3.2 Applications of Integration : a) Area under the curve. b) Area between two curves. c) Volume of revolution. Unit - IV First Order First Degree Differential Equations 4.1 Concept of differential equation. 4.2 Order, degree and formation of differential equation. 4.3 Solution of differential equation. a) Variable separable form b) Linear differential equation 4.4 Application of differential equations and related engineering problems. Unit - V Probability Distribution 5.1 Probability distribution. a) Discrete probability distribution. b) Continuous probability distribution. 5.2 Binomial distribution. 5.3 Poisson's distribution. 5.4 Normal distribution.
