Engineering Mathematics-I

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• Overview

  Prerequisites

  • Differentiation, Integration, Maxima and Minima, Determinants and Matrices

  Course Objectives

  To make the students familiarize with concepts and techniques in Calculus, Fourier series and Matrices. The aim is to equip them with the techniques to understand advanced level mathematics and its applications that would enhance analytical thinking power, useful in their disciplines.
  

  Course Outcomes

  • Mean value theorems and its generalizations leading to Taylors and Maclaurin’s series useful in the analysis of engineering problems. 
  • The Fourier series representation and harmonic analysis for design and analysis of periodic continuous and discrete systems. 
  • To deal withderivative of functions of several variables that are essential in various branches of Engineering. 
  • To apply the concept of Jacobian to find partial derivative of implicit function and functional dependence. Use of partial derivatives in estimating error and approximation and finding extreme values of the function. 
  • The essential tool of matrices and linear algebra in a comprehensive manner for analysis of system of linear equations, finding linear and orthogonal transformations, Eigen values and Eigen vectors applicable to engineering problems

• Syllabus and Notes

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  Unit 1

  

  Unit 2

  

  Unit 3

  

  Unit 4

  

  Unit 5

  

  Unit 6

  Unit 1

  ×

  Differential Calculus

  Rolle’s Theorem, Mean Value Theorems, Taylor's Series and Maclaurin's Series, Expansion of functions using standard expansions, Indeterminate Forms, L' Hospital's Rule, Evaluation of Limits and Applications.
  

  Close

  Unit 2

  ×

  Fourier Series

  Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series, Harmonic analysis, Parseval’s identity and Applications to problems in Engineering.
  

  Close

  Unit 3

  ×

  Partial Differentiation

  Introduction to functions of several variables, Partial Derivatives, Euler's Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of Independent variables.
  

  Close

  Unit 4

  ×

  Applications of Partial Differentiation

  Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of two variables, Lagrange's method of undetermined multipliers.
  

  Close

  Unit 5

  ×

  Linear Algebra-Matrices, System of Linear Equations

  Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations, Application to problems in Engineering.
  

  Close

  Unit 6

  ×

  Linear Algebra-Eigen Values and Eigen Vectors, Diagonaliztion

  Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.
  

  Close
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