Syllabus (MATHEMATICS)

Course Type: ME-3

Semester: 3

Course Code: BMTMMEB23T

Course Title: Calculus, Differential Equations & Vector Calculus

(L-P-Tu): 4-0-0

Credit: 4

Practical/Theory: Theory

Course Objective: To be done.

Learning Outcome: Course Outcomes (CO): The whole course will have the following outcomes: Upon successful completion, the students will be able to CO1: differentiate successively of higher order derivatives using Leibnitz rule and can apply this to various real work probl

Syllabus:

Unit-I: Calculus [Credit: 2, 30 L]

Differential Calculus: Higher order derivatives, Leibnitz rule of successive differentiation and its applications. Taylor’s and Maclaurin’s Theorems with Lagrange’s form of remainder (Statement only), Finite Expansion with Lagrange’s form of remainder- sin(x), cos (x), exp(x), log(1+x), Basic ideas of Partial derivative (First & Second order only), Chain Rules, Homogeneous functions, Euler’s theorem on homogeneous functions of two variables and its applications.

Integral Calculus: Derivations and illustrations of simple reduction formulae, Rectification & Quadrature of simple plane curves

Unit-II: Differential Equations [Credit: 1, 15 L]

Solution of first order and first-degree differential equations: Exact differential equations, condition of exactness, Integrating Factor, Linear Equations.

Differential Equations of first order but not of first degree: Solvable for, Solvable for x, Solvable for y, Clairaut’s form.

Solution of second order linear differential equation with constant coefficients, Particular integrals for polynomial, sine, cosine & exponential functions.

Unit-III: Vector Calculus [Credit: 1, 15 L]

Differentiability of vector-valued function of one variable, Vector-valued functions of two and three variables, Gradient of scalar function, Divergence and Curl of vector valued functions

Reference Books

1. Santinarayan, Differential Calculus, S Chand
2. Ghosh & Maity, Differential Calculus, New Central Book Agency
3. Das & Mukherjee, Differential Calculus, U N Dhur
4. Ghosh & Maity, Integral Calculus, New Central Book Agency
5. Das & Mukherjee, Integral Calculus & Differential Equations, U N Dhur
6. Ghosh & Maity, Differential Equations, New Central Book Agency
7. Ghosh & Maity, Vector Calculus, New Central Book Agency
8. J.G. Chakraborty & P. R. Ghosh, Vector Analysis, U N Dhur