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
Overview
Syllabus
Week 1 : Differential Calculus - Functions of One Variable
Week 2 : Partial Derivatives
Week 3 : Total Differential and Differentiability
Week 4 : Taylor's Expansion of Functions. Maxima and Minima
Week 5 : Improper Integrals
Week 6 : Double Integrals
Week 7 : Multiple Integrals & their Applications
Week 8 : System of Linear Equations - Gauss Elimination. Vector Spaces
Week 9 : Linear Transformations
Week 10 : Eigenvalues and Eigenvectors, Diagonalization
Week 11 : First Order Differential Equations
Week 12 : Higher Order Differential Equations with Constant Coefficientss
Taught by
Prof. Jitendra Kumar
