Course Syllabus
Module 1: Vector Calculus
• Green's Theorem
• Gauss Divergence Theorem
• Stoke's Theorem
• Line Integral
• Surface Integral
• Gradient
• Divergence
• Curl
Module 2: Differential Equations
• Variables Separable Method
• Linear Differential Equations
• Homogeneous Differential Equations
• Exact Differential Equations
• Higher Order Differential Equations
• Complementary Function (CF)
• Particular Integral (PI)
Module 3: Special Functions
• Gamma Function
• Beta Function
• Applications of Gamma & Beta Functions
Module 4: Multiple Integrals
• Double Integration
• Change of Order of Integration
• Area using Double Integration
• Applications of Double Integration
Module 5: Partial Differentiation
• Partial Derivatives
• Total Derivatives
• Taylor Series for Two Variables
• Maxima and Minima of Two Variable Functions
• Jacobians
• Euler's Theorem
Module 6: Matrix Algebra
• Types of Matrices
• Matrix Operations
• Transpose of Matrix
• Minor and Cofactor
• Adjoint of Matrix
• Rank of Matrix
• Echelon Form
• Normal Form
• System of Linear Equations
• Eigenvalues
• Eigenvectors
• Diagonalization
• Cayley Hamilton Theorem
Module 7: Practice & Applications
• Solved University Questions
• Numerical Problems
• Engineering Applications
• Previous Year Questions
• Quiz and Certificate Assessment