Course: MAT 122 2.0 Calculus (Compulsory)
Course content:
Real Sequences: Sequences and Subsequences, Monotonic and bounded sequences, Limit of a Sequence, Convergent and Divergent sequences, Limit Laws, Limits of Some important Sequences; Series: Infinite Series, Necessary condition for convergent, Series with positive terms, Convergence of the series, Comparison Tests, Alternating Series, Absolute convergence and Conditionally convergence, Ratio Test and Root Test, Rearrangement of Series, Other tests; Piecewise Continuous Functions and Discontinuities: Limits involving infinity, Piecewise Continuous Functions and the nature of discontinuities ( removable, infinite, jump and oscillatory discontinuities), Asymptotes; The Derivative: Derivatives, Differentiation Formulae, Higher derivatives, Indeterminate Forms and L’Hopital’s Rule; The Mean Value theorem and curve sketching: Maximum and minimum values, The Mean Value Theorem, Monotonic Functions and the First Derivative Test, Concavity and Points of Infection, Curve Sketching; Power Series: Representation of Functions as Power Series, Taylor’s and Maclaurin’s Series, The Binomial Series
Recommended Readings:
Set Theory and Related Topics – Schaum Series, Calculus – James Stewart