Syllabus Mathematics - 1 Total Credits L+T+ (PR/2) Assessment Pattern and Marks Total Marks C Theory Tutorial / Practical ESE (E) PA / CA (M) PA/CA (I) ESE (V) 4 70 30 0 0 100 Unit 1 Module 1 : Basic Calculus : Evaluation of improper integrals of Type-I and Type-II, Beta and Gamma functions and their properties; Applications of definite integrals to evaluate surface areas and volumes of revolutions. (Chapters - 1, 2) Unit 2 Module 2 : Single-variable Calculus (Differentiation) : Taylor’s and Maclaurin’s theorem for a function of one variable, Taylor’s and Maclaurin’s series of a function using statement of the theorems; Extreme values of functions; Indeterminate forms and L' Hospital's rule. (Chapters - 3, 4) Unit 3 Module 3 : Sequences and Series : Sequence of numbers and its convergence, Infinite series; Tests for convergence (Telescoping series, Geometric series test, Integral test, p-test, comparison test, D’ Alembert’s ratio test, Cauchy’s root test), Alternating series test; Power series, Radius and interval of convergence, Conditional and Absolute convergence of a power series. (Chapter - 5) Unit 4 Module 4 : Multivariable Calculus (Differentiation) : Limit, Continuity and Differentiation for function of two or more variables, total derivative, gradient, directional derivatives; Tangent plane and Normal line to the surface 𝑓(𝑥, 𝑦, 𝑧) = 𝑐; Extreme values for function of two variables (Maxima, minima and saddle points); Method of Lagrange multipliers. (Chapter - 6) Unit 5 Module 5 : Multivariable Calculus (Integration) : Multiple Integration : Double integrals (Cartesian, Polar), change of order of integration in double integrals, Change of variables (Cartesian to polar), Applications : areas and volumes, Center of mass and Gravity (constant and variable densities); Triple integrals (Cartesian, Cylindrical, Spherical). (Chapter - 7)
