Engineering Mathematics-I
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Course Objectives
To familiarize the students with concepts and techniques in Calculus, Fourier series and Linear Algebra. 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
After successful completion of the course, learner will be able to:
CO1: Apply mean value theorems and its generalizations leading to Taylors and Maclaurin’s series useful in the analysis of engineering problems. Determine the Fourier series representation and harmonic analysis of periodic functions in engineering applications.
CO2: Evaluate derivative functions of several variables that are essential in various engineering problems.
CO3: Apply the concept of Jacobian to find partial derivatives of implicit function and functional dependence. Use of partial derivatives in estimating errors & approximations and finding extreme values of the function.
CO4: Apply the essential tool of matrices and linear algebra in a comprehensive manner for analysis of system of linear equations, Linear dependence & Independence, finding linear and orthogonal transformations.
CO5: Determine Eigen values & Eigen vectors. Use it to diagonalize matrix and to reduce quadratic form to canonical form, applicable to engineering problems.
Unit-I: Single Variable Calculus
Rolle’s Theorem, Mean Value Theorems, Taylor's and Maclaurin's Series, Indeterminate Forms and L' Hospital's Rule. Fourier series: Full range and Half rage Fourier series, Harmonic analysis, Applications to problems in Engineering
Unit-II: Multivariable Calculus – Partial Differentiation
Introduction to functions of several variables, Limit, Continuity and Partial Derivatives. Euler's Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative and Change of Independent variables.
Unit-III: 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 and Applications to problems in Engineering
Unit-IV: Linear Algebra – Matrices and 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.
Unit-V: Linear Algebra - Eigen Values, Eigen Vectors and Diagonalization
Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonalization of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations. Application to problems in Engineering
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