Mathematics - III

Definition: Mathematics - III covers advanced mathematical tools like Laplace transforms, Fourier series, and partial differential equations essential for engineering analysis.

Unit 1: Laplace Transforms

• Laplace transform of elementary functions.
• Properties of Laplace transform.
• Inverse Laplace transform.
• Applications to differential equations.

Unit 2: Fourier Series and Transforms

• Fourier series expansion.
• Half-range series.
• Fourier integrals and transforms.

Unit 3: Partial Differential Equations

• Formation of PDEs.
• Lagrange’s method.
• Wave equation, Heat equation, Laplace equation.

Unit 4: Functions of Complex Variables

• Analytic functions, Cauchy-Riemann equations.
• Complex integration, Cauchy’s theorem.
• Residues and contour integration.

Unit 5: Statistics and Probability

• Measures of central tendency and dispersion.
• Correlation and regression.
• Probability distributions – Binomial, Poisson, Normal.

Unit 6: Numerical Methods

• Solution of algebraic and transcendental equations.
• Interpolation, Numerical integration.
• Solution of ordinary differential equations.