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The Course of Calculus:

1. Differential Calculus:

Bounds, Limits and continuity, properties of continuous functions, Derivatives, Leibniz'sTheorem,Rolles Theorem Lagrange's Mean Value Theorem, Cauchy's Mean Value Theorem, Generalized Mean value theorem, indeterminate forms, Taylor's and Maclaurin's series.

2. Intergral Calculus:

Antiderivatives Techniques of Intergration, Riemann Integral, Properties of definite Integrals, Mean value theorem, Reduction formulae Improper Integrals, Beta and Gamma Integrals.

3. Fourier Series:

Periodic function, periodic extensions, even and odd functions, Fourier coefficients. Expansion of functions in Fourier series. Functions with arbitrary periods. Fourier sine and cosine series.

4. Differential Equations: I. Differential equations, formation and solutions, equations of first order, Initial and boundary value problems. Various methods for solving first order differential equations. Orthogonal trajectories. Non-linear first order differential equations, Envelopes and singular solutions.

5. Differential Equations: II. Higher order differential equations with constant coefficients, Superposition of solution. Cauchy-Euler's equations System of two first order linear homogenous equations. Non-Linear equation discussed with the help of population growth.