MA115 Calculus

Program: B.Sc. First Semester Credits: 06

Functions of a real variable: Functions and their graphs, Inverse functions and logarithm, Limit of a function and Limit Laws, Precise definition of a limit (δ-ϵ), One sided limits, Continuity at a point, Limit involving infinity, Tangents and derivatives at a point, Derivative as a function, derivative as rate of change, chain rule, Linearization and Differentials, Monotonic functions and first derivative test, Concavity, Points of inflexion, Differentiability of Functions, Rolle’s Theorem, Mean Value theorems, Successive Differentiation, Leibnitz’s Theorem, Maclaurin series, Taylor’s Theorem with Lagrange’s and Cauchy’s forms of remainder,Tangents, Normal, Curvature, Asymptotes, Singular Points, Tracing of Curves,Evaluating Definite Integral, Fundamental theorem of calculus.

Functions of several real variables: Functions of two and three variables, Limits for functions of two variables, Continuity, Partial derivatives, Partial derivatives and continuity, Total differential and Differentiability, Directional derivatives and gradient vectors, Tangent planes and differentials, Extreme values and saddle points, Euler’ theorem, Lagrange’s Multiplier Method, Taylor’s series, Jacobians, Double Integrals, Double Integrals in Polar Form, Triple Integrals in Rectangular Coordinates, Triple Integrals in Cylindrical & Spherical Coordinates, Change of variable in Multiple Integrals, Change of order in multiple integral, applications of multiple integrals.

Books Recommended: