Topics and Syllabus - BE Electronics Engineering Applied Mathematics 1 Semester 1 (FE First Year) University of Mumbai

Solution of system of linear algebraic equations, by

• Gauss Elimination Method (Review)
• Guass Jordan Method
• Crouts Method (LU)
• Gauss Seidal Method    and
• Jacobi iteration (Scilab programming for above methods is to be taught  during lecture hours)

• Types of Matrices (symmetric, skew‐ symmetric, Hermitian, Skew Hermitian,Unitary, Orthogonal Matrices and properties of Matrices).
• Rank of a Matrix using Echelon forms, reduction to normal form, PAQ forms, system of homogeneous and non –homogeneous equations, their consistency and solutions. Linear dependent and independent vectors.  

• Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof).
• Deductions from Euler’S Theorem

• Partial derivatives of first and higher order, total differentials, differentiation of composite and implicit functions.

• nth derivative of standard functions.
• Leibnitz’s Thoerem (without proof) and problems.

• Regression Analysis (to be introduced for estimation only) (Scilab programming related to fitting of curves is to be taught during lecture hours)

• Lagrange’s method of undetermined multipliers with one constraint.
• Jacobian, Jacobian of implicit function.
• Partial derivative of implicit function using jacobian.

• Taylor’s Theorem (Statement only) and Taylor’s series, Maclaurin’s series (Statement only).
• Expansion of ex , sinx, cosx, tanx, sinhx, coshx, tanhx, log(1+x), sin‐1 x, cos1 x, Binomial series.
• Indeterminate forms, L‐ Hospital Rule, problems involving series also.

Concepts :
• Successive Differentiation  question (1)
• nth derivative of standard functions  question (4)
• Leibnitz’S Theorem (Without Proof) and Problems  question (3)

Concepts :
• Logarithmic Functions  question (6)
• Separation of Real and Imaginary Parts of Logarithmic Functions  question (7)