Topics and Syllabus - BE Civil Engineering Applied Mathematics 2 Semester 2 (FE First Year) University of Mumbai

1 Beta and Gamma Functions, Differentiation Under Integral Sign and Exact Differential Equation

1.01 Beta and Gamma Functions and Its Properties

1.02 Rectification of Plane Curves

1.03 Differential Equation of First Order and First Degree

2 Differential Calculus

2.01 Linear Differential Equations(Review), Equation Reduciable to Linear Form, Bernoulli’S Equation

2.02 Linear Differential Eqaution with Constant Coeffiecient

2.03 Cauchy’S Homogeneous Linear Differential Equation and Legendre’S Differential Equation, Method of Variation of Parameters

2.04 Simple Application of Differential Equation of First Order and Second Order to Electrical and Mechanical Engineering Problem

3 Numerical Solution of Ordinary Differential Equations of First Order and First Degree and Multiple Integrals

3.01 Taylor’S Series Method,Euler’S Method,Modified Euler Method,Runga‐Kutta Fourth Order Formula

3.02 Multiple Integrals‐Double Integration

4 Multiple Integrals with Application and Numerical Integration

4.01 Triple Integration

4.02 Application to Double Integrals to Compute Area, Mass, Volume. Application of Triple Integral to Compute Volume

4.03 Numerical Integration