Unit 1

Trigonometry: Expansions of sin n(θ), cos n(θ), tan n(θ) in powers of Sin θ, Cos θ, Tan θ. Expansion of Sin n(θ), Cos n(θ), Sin m(θ), Cos m(θ) in terms of Sines and Cosines of Multiplies of θ – Power series for Sin θ, Cos θ, Tan θ – Hyperbolic Functions – Inverse Hyperbolic Functions – Logarithm of complex numbers – Summation of Trigonometric Series – Gregory Series – Euler Series.

Unit 2

Differentiation: Applications of Derivative: Mean Value theory – Concavity and Curve Sketching – Maxima and Minima.

Unit 3

Differential Equations of First Order: Formation of Differential Equations. Solutions of Differential Equations (Variable Separable, Homogeneous Equations and Equations reducible to Homogeneous Form, Linear and Equations reducible to Linear Form, Exact Differential Equations and Equations reducible to Exact form). Differential Equations not of the first degree (solvable for ‘p’, solvable for ‘y’, solvable for ‘x’, Clairaut’s Equation). Applications.

Unit 4

Differential Equations of Higher Order: Homogeneous Linear Differential Equations with Constant Coefficient and Euler- Cauchy Differential Equations, Basis of Solutions and Wronskian. Non-Homogeneous Equations – Method of Undetermined Coefficients and Method of Variation of Parameters.

Unit 5

Boundary Value Problems for Second Order Equations: Green’s function, Sturm Comparison Theorems and Oscillations, Eigenvalue Problems. Applications.

1. George B. Thomas, Maurice D. Weir, Joel R. Hass, ‘Calculus’, Pearson Education, 2009, 11th Ed.
2. E. Kreyszig ‘Advanced Engineering Mathematics’, John Wiley and Sons, 2002, 8th Ed.
3. P. K. Mittal ‘Mathematics for Degree students’, S. Chand & Co, 2011, New Delhi.
4. P. Kandasamy and K. Thilagavathi, “Mathematics for B.Sc.”, Branch I Vol. I, Vol. II, S. Chand & Co.