Engineering Mathematics - I

ABOUT THE COURSE:This course is about the basic mathematics that is fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in differential calculus,integral calculus, linear algebra and differential equations with applications to various engineering problems. This course will cover the following main topics: Mean Value Theorems; Indeterminate Forms; Taylor's and Maclaurin's Theorems. Partial Derivatives; Differentiability; Taylor's Expansion of Functions of Several Variables. Maxima and Minima. Improper Integrals. Differentiation under Integral Sign (Leibnitz rule).Multiple Integrals and their Properties. Applications of Multiple Integrals. System of Linear Equations. Vector Spaces; Basis and Dimension of a Vector Space. Rank of a Matrix and its Properties. Linear Transformation. Eigenvalues and Eigen vectors. Diagonalization . First Order Differential Equations. Higher Order Differential Equations with Constant Coefficients. Cauchy-Euler Equations.INTENDED AUDIENCE : All branches of science and engineering

Week 1 : Differential Calculus - Functions of One VariableWeek 2 : Partial DerivativesWeek 3 : Total Differential and DifferentiabilityWeek 4 : Taylor's Expansion of Functions. Maxima and MinimaWeek 5 : Improper IntegralsWeek 6 : Double IntegralsWeek 7 : Multiple Integrals & their ApplicationsWeek 8 : System of Linear Equations - Gauss Elimination. Vector SpacesWeek 9 : Linear TransformationsWeek 10 : Eigenvalues and Eigenvectors, DiagonalizationWeek 11 : First Order Differential EquationsWeek 12 : Higher Order Differential Equations with Constant Coefficientss