Unit - I Differential Calculus
1a. Solve the given simple problems based on functions.1b. Solve the given simple problems based on rules of differentiation.1c. Obtain the derivative of logarithmic, exponential functions.1d. Apply the concept of differentiation to find given equation of tangent and normal.1e. Apply the concept of differentiation to calculate maxima and minima and radius of curvature of given problem. 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
2a. Solve the given simple problem(s) based on rules of integration.2b. Obtain the given integral(s) using substitution method.2c. Integrate given simple functions using the integration by parts.2d. Evaluate the given simple integral by partial fractions. 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
3a. Solve given simple problems based on properties of definite integration.3b. Apply the concept of definite integration to find the area under the given curve(s)3c. Utilize the concept of definite integration to find area between given two curves.3d. Invoke the concept of definite integration to find the volume of revolution of given surface. 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
4a. Find the order and degree of given differential equations.4b. Form simple differential equations for simple given engineering problem(s).4c. Solve given differential equations using the method of variable separable.4d. Solve the given simple problem(s) based on linear 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 equation4.4 Application of differential equations and related engineering problems.