New online batches starting!
The Calculus course (unit) contains the following chapters:
Sets & their representation: Union, intersection & complement of sets and their algebraic properties; Power set.
Relations: Types of relations, equivalence relations
Functions: One-one, into and onto functions, composition of functions
Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions.
Limits, continuity & differentiability: Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; Derivatives of upto order two. Rolle's and Lagrange's Mean Value Theorems.
Applications of Derivatives: Rate of change of quantities, monotonic -increasing and decreasing functions, maxima and minima of functions of one variable, tangents and normals.
Integral as an anti-derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions, Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the standard types.
Integral as limit of a sum. Fundamental Theorem of Calculus, Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:
dy/dx + p(x) y = q(x)