Overview
 Units 5
 Duration 10:28:55
 Branch B.E/B.Tech
 Language English
Course Description
The course is designed to equip the students with the necessary mathematical skills and techniques that are essential for an engineering course. The skills derived from the course will help students form a necessary base to develop analytic and design concepts. Apart from video lectures, we provide 10 hours of tuition before 2 weeks of the examination.
Recommended For
B.Tech 1st Year JNTU
University
JNTUH
Learning Outcomes
 After going through this course, a student will be able to confidently appear for the M1 examination with learning in the following areas.
 Write a matrix representation of a set of linear equations and solutions.
 The concepts of eigen values, eigen vectors, and reducing the quadratic forms into their canonical forms.
 Analyze the nature of the sequence series.
 Solve the applications on mean value theorems.
 Find extreme values of functions of two variables with or without constraints.
 Each student will undergo video tutorials for two weeks before the exam for one hour/day.
Curriculum


UNIT 1 Matrices: Types of real matrices and complex matrices, Types of real matrices and complex matrices Part 1, Types of real matrices and complex matrices Part 2, Types of real matrices and complex matrices Part 3, Rank Of Matrix, Rank Of Matrix Problem, Echelonform Problem Part 1, Echelonform Problem Part 2, Normal Form Or Canonical Form, Normalform (or) Canonical form problem, Inverse of NonSingular matrices by GaussJordan Method, Solution of system of Linear Equations, Solution of system of Homogeneous Linear Equations, Consistency and solution of linear systems(Homogeneous and NonHomogeneous) Part 1, Consistency and solution of linear systems(Homogeneous and NonHomogeneous) Part 2, Gauss Seidel iteration method, Gauss Elimination and Seidel iteration method Part 1, Gauss Elimination and Seidel iteration method Part 22:43:20



UNIT 2 Eigen Values and Eigen Vectors (Linear Transformation and Orthogonal transformation): Eigen Values and Eigen Vectors, Eigen Values and Eigen Vectors and their properties Theorem, Eigen Values and Eigen Vectors and their properties Theorem Part 1, Eigen Values and Eigen Vectors Problems Part 1, Eigen Values and Eigen Vectors Problems Part 2, Eigen Values and Eigen Vectors Problems Part 3, Diagonalization of matrix, Diagonalization of a matric by Othogonal Reduction, Diagonalization of matrix (Problem 1), Diagonalization of matrix (Problem 2), CayleyHamilton Theorem(Without Proof), CayleyHamilton Theorem Problem, Finding Inverse and power of a matrix by CayleyHamilton Theorem, Quadratic Forms and Nature Of The Quadratic Form, Quadratic Forms and Nature of the Quadratic forms part 1, Quadratic Forms and Nature of the Quadratic forms part 2, Reduction of Quadratic Form To Canonical Form, Reduction of Quadratic form to canonical form by orthogonal transformation part1, Reduction of Quadratic form to canonical form by orthogonal transformation part22:40:38



UNIT 3 Sequences and Series: Definition of Sequence,Limit,Convergent,Divergent and Oscillatory sequences, Convergent,Divergent and Oscillatory series Part 1, Convergent,Divergent and Oscillatory series Part 2, Limit Comparison Test, Limit Comparison Test Problem 1, Limit Comparison Test Problem 2, Limit Comparison Test Problem 3, ptest,DAlembert's ratio test, Raabe's test, Cauchy's nth Root Test & Cauchy's Integral Test, Cauchy's Integral test and Cauchy's root test Problem 1, Cauchy's Integral test and Cauchy's root test Problem 2, Cauchy's Integral test and Cauchy's root test Problem 3, Logarithmic test, Alternating series : Leibnitz test, Alternating series : Leibnitz test Problem, Alternating Convergent series : Absolute and Conditionally convergence1:19:16



UNIT 4 Calculus: Rolle's Theorem, Geometrical Interpretation Of Rolle's Theorem, Mean Value Theorems:Rolle's Theorem Part 1, Mean Value Theorems:Rolle's Theorem Part 2, Mean Value Theorems:Rolle's Theorem Part 3, Lagrange's Mean Value Theorem, Geometrical Interpretation Of Lagrange's Mean Value Theorem, Lagrange's Mean value theorem and applications Part 1, Lagrange's Mean value theorem and applications Part 2, Cauchy's Mean Value Theorem, Taylor's Series, Surface areas and volumes of solid of revolution, Applications of definite integrals to evaluate surface areas and volumes of revolution of curves, Definition of improper integral, Beta Gamma Function and applications Part 1, Beta Gamma Function and applications Part 2, Beta Gamma Function and applications Part 3, Beta Gamma Function and applications Part 4, Beta Gamma Function and applications Part 5, Beta Gamma Function and applications Part 61:40:40



UNIT 5 Multivariable Calculus(Partial Differentiation and Applications): Euler's Theorem, Euler's Theorem Problem 1, Euler's Theorem Problem 2, Total Derivative, Chain Rule of Partial Derivation, Chain Rule of Partial Derivation Problem 1, Chain Rule of Partial Derivation Problem 2, Chain Rule of Partial Derivation Problem 3, Jacobian Determinant, Jacobian Problem 1, Jacobian Problem 2, Functional Dependence and Independence, Maxima and minima of functions of 1 & 2 variables, Lagranges Method, Max and min of functions of 2 & 3 variables using method of Lagrange Multipliers Part 1, Max and min of functions of 2 & 3 variables using method of Lagrange Multipliers Part 2, Max and min of functions of 2 & 3 variables using method of Lagrange Multipliers Part 3, Taylor's Series and Maclaurin's Series, Taylor's Series and Maclaurin's Series Part 1, Taylor's Series and Maclaurin's Series Part 22:05:01

Instructor
Mr C Srinivas MSc ,BEd (Osmania)
Mr. Srinivas has mastered teaching Mathematics subjects at various engineering colleges with over 17+ years of quality experience in teaching at several prestigious engineering colleges. He has won several awards like 'Best Faculty/Best Trainer'. Here at VirtuLearn, he explains clearly how to easily solve the complicated problems in the M1 subject and many practice problems with solutions.