UNIT : 1 BASIC CONCEPTS:
Definition of Sets, Number systems, Relations Functions.
LIMIT CONTINUITY: Definition of limit, Limit of a function, Right and Left hand Limits, Algebra of limits, General principle for existence of limit, limit of inequalities, Method of finding limits, Continuity of functions, Cauchy’s definition, graphical meaning of continuity, Kinds of discontinuities.
DIFFERENTIAL CALCULUS: Successive differentiation, Leibnitz theorem, Partial differentiation, Euler's Theorem, change of variables, Jacobian theorem.
UNIT : 2 INTEGRAL CALCULUS:
Integration of rational and Irrational functions, Reduction Formulae, Definite Integral, Rectification; Quadrature, volumes and surfaces of Revolution, Simple applications of integration & simple problems of double and triple integrals.
UNIT : 3 DIFFERENTIAL EQUATION:
Differential equations of first order, Differential equations of 2nd order, Differential of 2nd order with constant coefficients.
UNIT : 4 VECTOR CALCULUS AND ALGEBRA:
Vectors, Differentiation and partial differentiation of vector functions, derivative of sum, Dot product and cross product of two vectors, gradient, divergence and curl.
UNIT : 5 COORDINATE GEOMETRY:
Straight lines, Circles and the system of circles; standard equations and properties of Parabola. Ellipse and Hyperbolas, General equation of second degree in two variables, tracing of simple conic section.
Suggested Readings :
- 1. E. Kreyzig, "Engineering Mathematics".
- 2. B.S. Grewal, "Higher Engineering Mathematics"
- 3. Shanti Narayan, "Differential Calculus"
- 4. K.P. Gupta. “Vector Calculus”