Mathematical Concepts Of Engineering - Emat-1

A brief introduction to the mathematical concepts needed for engineering stream students.

What you'll learn
Matrices Functions of several variables
Differential equations
Geometrical applications of differential calculus and sequences and series.
Requirements
Basic knowledge of Matrices
Basic knowledge of Differential Equations
Basic knowledge of Geometrical Appplications of differential calculus and sequences and series.
Description
Are you an Engineering student finding it difficult to understanding Mathematical concepts, problems, etc. Then this course is for you.This course is designed to give a brief introduction to the mathematical concepts needed for engineering stream students.It is designed for the course EMAT-1 (first semester). Topics including Eigen values and Eigen vectors of a real matrixProperties of Eigen valuesCayley – Hamilton theoremReduction of a symmetric matrix to diagonal formOrthogonal matricesReduction of quadratic form to canonical form by orthogonal transformationsEuler's TheoremTotal differentiationTaylor’s expansion - IntroductionMaxima and Minima of functions of two variablesJacobiansLinear equations of second order with constant and variable coefficientsHomogeneous equation of Euler's typeThese topics provide the fundamental basis of applying the concepts of engineering into motion.The concepts are presented in a progressive detail-oriented scheme, explaining the basics and ending with the applications of the concepts. With mastering these basics concepts under the guidance of a teacher, the student can easily manipulate and grasp the engineering concepts in no time.

Overview

Section 1: Introduction

Lecture 1 Introduction Characteristic equation of a matrix- Eigen values and Eigen

Lecture 2 Characteristic equation of a matrix- Eigen values and Eigen Part1

Lecture 3 Characteristic equation of a matrix- Eigen values and Eigen Part2

Section 2: Eigen values and Eigen vectors of a real matrix

Lecture 4 Eigen values and Eigen vectors of a real matrix Part1

Lecture 5 Eigen values and Eigen vectors of a real matrix Part 2

Lecture 6 Eigen values and Eigen vectors of a real matrix Part 3

Lecture 7 Eigen values and Eigen vectors of a real matrix Part 4

Section 3: Properties of Eigen values

Lecture 8 Properties of Eigen values

Section 4: Cayley – Hamilton theorem

Lecture 9 Cayley – Hamilton theorem

Section 5: Reduction of a symmetric matrix to diagonal form

Lecture 10 Rreduction of a symmetric matrix to diagonal form Part1

Lecture 11 Rreduction of a symmetric matrix to diagonal form Part2

Section 6: Orthogonal matrices

Lecture 12 Orthogonal matrices

Section 7: Reduction of quadratic form to canonical form by orthogonal transformations

Lecture 13 Reduction of quadratic form to canonical

Lecture 14 Reduction of quadratic form to canonical form by orthogonal transformations

Section 8: Euler;s Theorem

Lecture 15 Euler;s Theorem

Lecture 16 Function of two variables – Partial derivatives - Euler’s theorem

Section 9: Total differentiation

Lecture 17 Total differentiation Part1

Lecture 18 Total differentiation Part2

Section 10: Taylor’s expansion - Introduction

Lecture 19 Taylor’s expansion Part 1

Lecture 20 Taylor’s expansion Part 2

Lecture 21 Taylor’s expansion Part 3

Lecture 22 Taylor’s expansion Part4

Section 11: Maxima and Minima of functions of two variables

Lecture 23 Maxima and Minima of functions of two variables: -Introduction

Lecture 24 Maxima and Minima of functions of two variables:

Lecture 25 Constrained Maxima and Minima by Lagrangian Multiplier method Part 1

Lecture 26 Constrained Maxima and Minima by Lagrangian Multiplier method Part 2

Section 12: Jacobians

Lecture 27 Jacobians Part1

Lecture 28 Jacobians Part2

Section 13: Linear equations of second order with constant and variable coefficients

Lecture 29 Linear equations of second order with constant and variable coefficients Part1

Lecture 30 Linear equations of second order with constant and variable coefficients PART 2

Lecture 31 Linear equations of second order with constant and variable coefficients PART 3

Lecture 32 Linear equations of second order with constant and variable coefficients PART 4

Lecture 33 Linear equations of second order with constant and variable coefficients PART 5

Section 14: Homogeneous equation of Euler's type

Lecture 34 Homogeneous equation of Euler's type

Lecture 35 Equations reduced to homogeneous equation (Legentre's type)

Section 15: Simutaneous linear differential equation with constant coefficients

Lecture 36 Simutaneous linear differential equation with constant coefficients P1

Lecture 37 Simutaneous linear differential equation with constant coefficients P2

Section 16: Method of variation of parameter

Lecture 38 Method of variation of parameter P1

Lecture 39 Method of variation of parameter P2

Section 17: Curvature

Lecture 40 Geometrical Application of Differential calculus-Curvature

Section 18: Curvature of Cartesian and polar coordinates

Lecture 41 Curvature of Cartesian and polar coordinates P1

Lecture 42 Curvature of Cartesian and polar coordinates P2

Section 19: Last Section

Lecture 43 Bonus Lecture

Students pursuing Engineering Degree first year