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#### Overview

• Videos 128
• Duration 16:50:04
• Branch B.E/B.Tech
• Language English
##### Course Description

This 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 the student from a necessary base to develop analytic and design concepts.

B.Tech 1st Year

JNTUH

##### Learning Outcomes
• Types of matrices and their properties.
• The concept of rank of a matrix and applying the same to understand the consistency solving the linear systems.
• The concepts of eigen values and eigen vectors and reducing the quadratic forms into their canonical forms.
• Evaluation of integrals using Beta and Gamma Functions.
• Evaluation of multiple integrals and applying them to compute the volume and areas of regions.
• Determine Laplace transform and Inverse Laplace transform of various functions and use Laplace transforms to determine general solution to linear ODE

#### Curriculum

• UNIT 1 Theory of 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 Non-Singular matrices by Gauss-Jordan Method, Solution of system of Linear Equations, Solution of system of Homogeneous Linear Equations, Consistency and solution of linear systems(Homogeneous and Non-Homogeneous) Part 1, Consistency and solution of linear systems(Homogeneous and Non-Homogeneous) Part 2, Gauss Seidel iteration method, Gauss Elimination and Seidel iteration method Part 1, Gauss Elimination and Seidel iteration method Part 2, Cayley-Hamilton Theorem(Without Proof), Cayley-Hamilton Theorem Problem, Finding Inverse and power of a matrix by Cayley-Hamilton Theorem, Eigen Values and Eigen Vectors of a matrix, 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 matrix by Orthogonal Reduction, Diagonalization of matrix (Problem 1), Diagonalization of matrix (Problem 2), 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 part-1, Reduction of Quadratic form to canonical form by orthogonal transformation part-2
5:23:58
• UNIT 2 Differential calculus methods: 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, Functional Dependence and Independence, Jacobian Determinant, Jacobian Problem 1, Jacobian Problem 2, 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
1:38:57
• UNIT 3 Improper integration, Multiple integration & applications: Gamma Function, Gamma Function Part 1, Beta Function, Properties, Relation between Beta and Gamma functions, Relation between Beta and Gamma functions - Part 1, Relation between Beta and Gamma functions - Part 2, Multiple Integrals Introduction, Double Integrals, Triple Integrals, Triple Integrals Part 1, Change of variables, Change of order of integration, Applications to find Areas, Applications to find Areas Part 1, Moment of Inertia and volumes, Moment of Inertia and volumes Part 1
2:39:38
• UNIT 4 Differential equations and applications: Exact differential equations, Reducible to exact Part 1, Reducible to exact Part 2, Linear differential equations of higher order with constant coefficients - PART 1, Linear differential equations of higher order with constant coefficients - PART 2, Linear differential equations of higher order with constant coefficients - PART 3, Non homogeneous terms with RHS term of the type ax e , sin ax, cos ax 01, Non homogeneous terms with RHS term of the type ax e , sin ax, cos ax,02, Higher order differentional equations Problem 1, Higher order differentional equations Problem 2, Higher order differentional equations Problem 3, Higher order differentional equations Problem 4, Higher order differentional equations Problem 5, Higher order differentional equations Problem 6, Higher order differentional equations Problem 7, Higher order differentional equations Problem 8, Higher order differentional equations Problem 9, Higher order differentional equations Problem 10, Operator form of the differential equation, Finding particular integral using inverse operator, Method of variation of parameters, Method of variation of parameters Part1, Applications : Newton?s law of cooling and natural growth and decay, Problems on Newton?s law of cooling, Problems on natural growth and decay, Orthogonal trajectories, Problems on Orthogonal Trajectories Part 1, Problems on Orthogonal Trajectories Part 2, Problems on EDE, EDE Polar Form, Electrical Circuits Applications
3:43:55
• UNIT 5 Laplace transform and its applications to Ordinary differential equations: Introduction, Transforms of elementary functions, Transforms of elementary functions-PART 01, Transforms of elementary functions Problems, Transforms of elementary functions Problems Part 1, First Shifting theorem, Problems on First Shifting theorem, Properties of laplace transforms, Properties of laplace transforms Part 1, Transform of Derivatives & Integrals, Problems transforms of derivatives, Transforms of integrals, Multiplication by t power n& Division by t, Multiplication by t power n, Division by t .(statements only), Inverse Transforms, Introduction, Basic Formulas of Inverse Laplace Transform, Problems on Inverse Laplace Transform, Method of Partial fraction, Method of Partial fraction Part 1, First Shifting theorem (Table), Problem on First Shifting theorem, Second Shifting Theorem, Inverse Laplace Transform of Derivatives,Integrals, Multiplication & Division by S, IT Convolution theorem, Convolution theorem (without proof), , ,
2:10:31

#### 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.