UNIT : 1 The real number system as a complete ordered filed neighborhood open and closed sets limit points of sets.
UNIT : 2 Limits and Continuity: Definition of Limit, Algebra of Limits, Right hand and Left hand Limits, Definition of Continuity, Types of Discontinuity and algebra of Continuous functions.
UNIT : 3 Infinite Series: Convergent series, Divergent series Oscillatory series, Leibnitz test(Alternating Series test), Positive term series test, p-series test, Comparison test, D’Almberts ratio test, Cauchy’s nth root test and Rabbe’s test.
UNIT : 4 Mean Value Theorems : Rolle’s Theorem, Lagrange’s Mean Value theorem, Cauchy’s Mean Value theorem and Maclaurin series for Sin x, Cos x, Tan x, log(1-x), log(1+x)m, ex etc, Indeterminate forms, maxima and minima(Application of maxima or minima to simple problems).
UNIT : 5 Sequence : Sequence, Subsequence, Bounded Sequence, Convergent Sequence, Divergent Sequence, Monotonic Sequence, Cauchy Sequence.
Suggested Readings
- 1. E. Kreyzing Engineering Mathematics
- 2. Gorakha Prasad Differential Calculus
- 3. Shanti Narayan Differential Calculus
- 4. Prof. P.N. Chatterji Infinite Series