Want to Pass in Engineering Mathematics M1 subject with good marks? Then you have come to the right place. IIMSE have come up with the Idea to teach Mathematics M1 subject online to all those Engineering aspirants who want to score more marks.
IIMSE realize the problem faced by a number of Engineering students. If you also face difficulty to clear your Mathematics M1 backlog, then IIMSE also help you to clear this subject with good percentage. We have hired, The best Engineering Mathematics M1 faculty, Lecturer to make you master in Mathematics M1.
- To Learn and work on exact differential equations.
- A Clear understanding of types of matrices.
- How to find the rank of a Matrix?
- To learn concepts of Eigen values and Eigen vectors.
- Find extreme values of functions of 2 variables.
- To find first order differential equations is exact or not.
- Work on high order differential equations with real time examples.
- Where to apply differential equations?
- Learn partial differentiation and total derivative concepts.
No prerequisites required for this course.
Our trainers will guide you how to prepare for your upcoming End/supply examination and what topics you must focus more.
- Lectures 0
- Quizzes 0
- Duration 30 Hours
- Skill level All level
- Language English
- Students 20091
- Certificate No
- Assessments Self
Mathematics - I, M-1 Subject Course Curriculum, Syllabus.
(Linear Algebra and Differential Equations)
1.Initial Value Problems and Applications
Exact differential equations, Linear differential equations of higher order with constant coefficients.
Non homogeneous terms with RI-IS term of the type sin ax, cos ax.
Polynomials: x, e"V(x), xV(x)- Operator form of differential equation.
How to find particular integral by using inverse operator, Wronskian of functions, method of variation of parameters.
Applications: Newton's law of cooling, law of natural growth & decay, Orthogonal Trajectories and Electrical circuits.
2.Linear Systems of Equations
Topics:Types of real matrices & complex matrices, rank, echelon form, normal form, consistency and solution of linear systems (homogeneous & Non-homogeneous).
Gauss elimination, Gauss Jordon and LU decomposition methods.
Applications: How to find current in the electrical circuits?
3.Eigen values, Eigen Vectors & QuadraticForms
Topics: Eigen values, Eigen vectors and their various properties.
Cayley: Hamilton theorem (without proof), Inverse and powers of a matrix using Cayley, Hamilton theorem, Diagonalization.
Quadratic forms: Reduction of Quadratic forms into their canonical form, rank and nature of the Quadratic forms: Index and signature.
Topics:Introduction, homogeneous function, Euler's theorem, total derivative, Chain rule.
Taylor's and Mclaurin's series expansion of functions of t2 variables, functional dependence and Jacobian.
Applications: Maxima and Minima of functions of 2 variables without constraints and Lagrange's method (with constraints)
5.First Order Partial Differential Equations
Topics:Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions.
Lagranges method: to solve the first order linear equations.
Standard type methods: To solve the non linear equations.