Mathematics-I Syllabus
Calculus of single and several variables — limits, integration, sequences and series, partial derivatives and vector calculus.
Syllabus — 8 Units
- 1
Limits & Continuity
Review of limits, continuity and differentiability.
- 2
Mean Value Theorems
Mean value theorem, Taylor's theorem, maxima and minima.
- 3
Integration
Riemann integrals, Fundamental Theorem of Calculus, improper integrals, applications to area and volume.
- 4
Sequences & Series
Convergence of sequences and series, power series.
- 5
Partial Derivatives
Gradient and directional derivatives, chain rule, maxima and minima, Lagrange multipliers.
- 6
Multiple Integration
Double and triple integration, Jacobians and change of variables formula.
- 7
Vector Calculus
Parametrization of curves and surfaces, vector fields, line and surface integrals.
- 8
Integral Theorems
Divergence and curl; theorems of Green, Gauss and Stokes.