Advanced course covering integration techniques, applications of integrals, sequences and series, and parametric equations. Key topics include:

• Integration methods (by parts, partial fractions, trigonometric substitution)
• Arc length and surface area calculations
• Convergence tests for infinite series
• Taylor and Fourier series expansions

Comprehensive study of ordinary and partial differential equations with engineering applications:

• First-order linear and nonlinear equations
• Laplace transforms and phase plane analysis
• Stability theory and bifurcations
• Numerical methods (Euler, Runge-Kutta)
• Applications in heat transfer and oscillations

Fundamental concepts in vector spaces and matrix theory:

• Vector spaces and linear transformations
• Eigenvalues and diagonalization
• QR decomposition and singular value decomposition
• Applications in computer graphics and machine learning
• Numerical linear algebra techniques

Supervision of final year projects combining mathematical theory with practical applications:

• Machine learning algorithms and optimization
• Control systems and robotics applications
• Computational fluid dynamics simulations
• Mathematical modeling of real-world systems
• Signal processing and time-series analysis

Projects typically involve Python/R/MATLAB programming and collaboration with industry partners.