Differential calculus: Functions of real variable and their plots, limit. Continuity and derivatives, physical meaning of derivative of a function. Successive derivatives: Leibniz Theorem; Roll’s theorem, new value theorem, and Taylor’s theorem. Taylor’s and Maclaurin’s series and expansion inunctions. Maximum and minimum values of function: Functions of two or three variables partial and total derivatives. Euler’s theorem. Tangent and normal. Subtangent and subnormal in Cartesian and polar coordinates. Curvature, asymptotes and curve tracing. Integral Calculus: Different techniques of integration. Definite integral as the limit of a sum and as an area. Definition of remain integral, fundamental theorem of integral calculus and its applications to definite integrals, reduction formulae, Walli’s formulae. Improper integrals. Improper integrals: Beta and gamma functions.
Course Catalogue
Differential Calculus:
Functional Analysis and Graphical Information: function, properties of functions, graphs of functions, new function from old, lines and family of functions, Limit: Limits( an informal view), one sided limits, the relation between one sided and two sided limits, computing limits, Continuity: continuity and discontinuity, some properties of continuity, the intermediated value theorem, Derivatives: slop and rate of change, tangent and normal, derivative of a function, physical meaning of derivative of a function, techniques of differentiation, chain rule, successive derivatives, Derivative in graphing and applications: analysis of functions, maximum and minimum, Expansion functions: Taylor’s series, Maclaurian’s series, Leibniz; Rolle’s and Mean Value theorems, Partials and total derivatives of a function of two or three variables.
Integral Calculus:
Different technique of integration: integration, fundamental integrals, methods of substitutions, integration of rational functions, integration by parts, integrals of special trigonometric functions, reduction formulae for trigonometric functions, Definite integrals: general properties of definite integral, definite integral as the limit of sum and as an area, definition of Riemann integral, Fundamental theorem of integral calculus and its applications to definite integrals, determination of arc length, Improper integrals, Double integrals, Evaluation of Areas and Volumes.
Differential Calculus:
Functional Analysis and Graphical Information: function, properties of functions, graphs of functions, new function from old, lines and family of functions, Limit: Limits( an informal view), one sided limits, the relation between one sided and two sided limits, computing limits, Continuity: continuity and discontinuity, some properties of continuity, the intermediated value theorem, Derivatives: slop and rate of change, tangent and normal, derivative of a function, physical meaning of derivative of a function, techniques of differentiation, chain rule, successive derivatives, Derivative in graphing and applications: analysis of functions, maximum and minimum, Expansion functions: Taylor’s series, Maclaurian’s series, Leibniz; Rolle’s and Mean Value theorems, Partials and total derivatives of a function of two or three variables.
Integral Calculus:
Different technique of integration: integration, fundamental integrals, methods of substitutions, integration of rational functions, integration by parts, integrals of special trigonometric functions, reduction formulae for trigonometric functions, Definite integrals: general properties of definite integral, definite integral as the limit of sum and as an area, definition of Riemann integral, Fundamental theorem of integral calculus and its applications to definite integrals, determination of arc length, Improper integrals, Double integrals, Evaluation of Areas and Volumes.