Applied Mathematics-I
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See all →- Complex Numbers Notes FE Sem 1 Applied Maths-I | Mumbai Univ MU FE Sem 1 Applied Mathematics-I Module 1: De Moivre's theorem, expansions of sin nθ, cos nθ, powers and roots of complex numbers, solved e...
- Hyperbolic Functions Notes FE Sem 1 Applied Maths-I | Mumbai Univ MU FE Sem 1 Applied Maths-I Module 2: hyperbolic and inverse functions, separating real and imaginary parts, logarithm of complex numbers.
- Partial Differentiation Notes FE Sem 1 Maths-I | Mumbai Univ MU FE Sem 1 Applied Maths-I Module 3: partial derivatives, composite functions, Euler's theorem on homogeneous functions with proof and dedu...
- Maxima Minima & Leibnitz Notes FE Sem 1 Maths-I | Mumbai Univ MU FE Sem 1 Applied Maths-I Module 4: maxima and minima of two-variable functions, nth derivatives of standard functions and Leibnitz's theo...
- Matrices Notes FE Sem 1 Applied Maths-I | Mumbai University MU FE Sem 1 Applied Maths-I Module 5: Hermitian, unitary, orthogonal matrices, rank by echelon and normal form, PAQ, consistency of linear e...
- Numerical Methods Notes FE Sem 1 Applied Maths-I | Mumbai Univ MU FE Sem 1 Applied Maths-I Module 6: Newton-Raphson, Regula Falsi, Gauss-Jacobi and Gauss-Seidel iteration methods with fully worked exampl...
Top questions
See all →- What is a Jacobian of two or three variables and how do I calculate it? In one line The Jacobian J=∂(u,v)/∂(x,y) is the determinant of all first partial derivatives of u,v with respect to x,y ; it measures how a... 1
- What is Lagrange's method of undetermined multipliers for finding maxima and minima with a constraint? In one line To optimise f(x,y,z) subject to φ(x,y,z)=0 , form F=f+λφ and solve F_x=F_y=F_z=0 together with φ=0 . Explained simply Suppose yo... 1
- What are symmetric and skew-symmetric matrices, and how is any square matrix written as their sum? In one line A square matrix is symmetric if A^T=A and skew-symmetric if A^T=-A ; every square matrix equals 1/2(A+A^T)+1/2(A-A^T) , a symmet... 1
- How do I find the inverse of a 3×3 matrix using the adjoint method? In one line If |A|≠0 , then A⁻¹=1/|A| adj A , where adj A is the transpose of the matrix of cofactors. Explained simply The inverse of a num... 1
- What are Hermitian and skew-Hermitian matrices and what properties do they have? In one line A complex square matrix is Hermitian if it equals its conjugate transpose ( A^θ=A ) and skew-Hermitian if A^θ=-A ; they are the... 1
- What are orthogonal and unitary matrices and how do I check whether a matrix is one? In one line A real matrix is orthogonal if AA^T=I (so A⁻¹=A^T ); a complex matrix is unitary if AA^θ=I (so A⁻¹=A^θ ). Explained simply Rotat... 1