Chemical Engineering - Teerthanker Mahaveer University

B.Tech (CHE) Syllabus Applicable w.e.f. Academic Session 2012-13[01112012]
3 1 0 4
Objective:
• To familiarize the basics of matrices, differential calculus, multiple integrals and vector calculus.
• To solve all problems related to matrices, calculus and vectors.
Course Contents
Unit I (Lectures 08)
Matrices: Elementary row and column transformation; Rank of matrix; Linear dependence; Consistency
of linear system of equations; Characteristic equation; Cayley-Hamilton Theorem; Eigen values and
Eigen vectors; Diagonalization; Complex and unitary matrices.
Unit II (Lectures 08)
Differential Calculus-I: Successive differentiation; Leibnitz theorem; Partial differentiation; Euler’s
theorem; Curve tracing; Change of variables; Expansion of function of several variables
Unit III (Lectures 08)
Differential Calculus–II: Jacobian; Approximation of errors; Extrema of functions of several variables;
Lagrange’s method of multipliers (Simple applications).
Unit IV (Lectures 08)
Multiple Integrals: Double and triple integral; Change of order & Change of variables; Beta and Gamma
functions; Applications to area, volume; Dirichlet integral and applications.
Unit V (Lectures 08)
Vector Calculus: Point functions; Gradient, Divergence and Curl of a vector and their physical
interpretations; Line, Surface and Volume integrals; Green’s & Stokes’ theorem; Gauss’ divergence
theorem.
Text Books
1. Grewal B.S., Higher Engineering Mathematics, Khanna Publishers.
2. Prasad C., Engineering Mathematics for Engineers, Prasad Mudralaya.
3. Dass H.K., Engineering Mathematics Vol-I, S. Chand.
Reference Books
1. Kreyszig E., Advanced Engineering Mathematics, Wiley Eastern.
2. Piskunov N, Differential & Integral Calculus, Moscow Peace Publishers.
3. Narayan Shanti, A Text book of Matrices, S. Chand.
Page 7