CertifiedTEACHING MODE: Online (Skype)
Syllabus:
UNIT-I: Matrices Matrices: Types of Matrices, Symmetric; Hermitian; Skew-symmetric; Skew-Hermitian; orthogonal matrices; Unitary Matrices; rank of a matrix by Echelon form and Normal form, Inverse of Non-singular matrices by Gauss-Jordan method; System of linear equations; solving system of Homogeneous and Non-Homogeneous equations. Gauss elimination method; Gauss Seidel Iteration Method.
UNIT-II: Eigen values and Eigen vectors Linear Transformation and Orthogonal Transformation: Eigen values and Eigenvectors and their properties: Diagonalization of a matrix; Cayley-Hamilton Theorem (without proof); finding inverse and power of a matrix by Cayley-Hamilton Theorem; Quadratic forms andNature of the Quadratic Forms; Reduction of Quadratic form to canonical forms by Orthogonal Transformation
UNIT-III: Sequences & Series Sequence: Definition of a Sequence, limit; Convergent, Divergent and Oscillatory sequences. Series: Convergent, Divergent and Oscillatory Series; Series of positive terms; Comparison test, p-test, D-Alembert’s ratio test; Raabe’s test; Cauchy’s Integral test; Cauchy’s root test; logarithmic test. Alternating series: Leibnitz test; Alternating Convergent series: Absolute and Conditionally Convergence.
UNIT-IV: Calculus Mean value theorems: Rolle’s theorem, Lagrange’s Mean value theorem with their Geometrical Interpretation and applications, Cauchy’s Mean value Theorem. Taylor’s Series. Applications of definite integrals to evaluate surface areas and volumes of revolutions of curves (Only in Cartesian coordinates), Definition of Improper Integral: Beta and Gamma functions and their applications.
UNIT-V: Multivariable calculus (Partial Differentiation and applications) Definitions of Limit and continuity. Partial Differentiation; Euler’s Theorem; Total derivative; Jacobian; Functional dependence & independence, Maxima and minima of functions of two variables and three variables using method of Lagrange multipliers.
WHO CAN ATTEND?? ( Failed or Regular Students )
Students those who are have degree maths backlog or students those who are trying for best marks can attend this class. The classes will be separate for supply students and regular students.
STUDENTS CAN LEARN FROM THIS:
- a) Basics and Formulas
- b) Detailed explanation about every topic ( Subject Knowledge )
- c) Weekly Tests ( Proficiency in subject )
- d) Daily Assignments ( For more and more practice )
STUDENT HAS TO COME WITH:
Students has to come for this class with note book and pen only.
SUMMARY:
Finally students who wants get good marks as well as subject knowledge can join in this class. Students can get 100% best result and it will be helpful in future also.
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