Syllabus Engineering Mathematics - I (BSC-101-BES) Credit Examination Scheme : 03 CCE : 30 Marks 01 End-Semester : 70 Marks Term Work : 25 Marks 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 range Fourier series, Harmonic analysis, Applications to problems in Engineering. (Chapters - 1, 2, 3, 4) 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. (Chapter - 5) 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. (Chapter - 6) 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. (Chapters - 7, 8) 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. (Chapter - 9)
