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Mathematics II

Centering on the "structural hierarchy" of linear algebra, this course covers systems of linear equations, vector spaces, and eigenvalues. It equips students with the "technical" skills to solve matrix equations using the Gauss-Jordan method and understand algebraic structures like groups, rings, and fields.

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TabFlux . Engineering Mathematics II . TU . BEI-NEW

Engineering Mathematics II

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Course Title: Engineering Mathematics II

Course No: ENSH 151

Nature of the Course: THEORY

Semester: 2

Full Marks: 40 + 60

Pass Marks: 16 + 24

Credit Hours: 3

Course Description

Course Objectives

Course Contents

1. Calculus of Two and More Variables

6 hrs8 marks

1.1. Partial differentiation

Partial derivatives of first and higher order

Homogeneous function: Euler's theorem for two and three variables

Total derivatives and differentials, differentiation of composite and implicit functions

Jacobians and their properties

1.2. Extreme values of two and three variables. Lagrange's multiplier

1.3. Application in optimization of function of two variables in one constraint

2. Multiple Integrals

7 hrs8 marks

2.1. Double integrals in Cartesian and Polar form, change of order of integration

2.2. Triple integrals in Cartesian, cylindrical and spherical coordinates

2.3. Area, volume, moment of inertia, mass and centroid by double and triple integrals

3. Vector Calculus

12 hrs18 marks

3.1. Review of scalar and vector products, scalar and vector triple product, scalar and vector product of four vectors

3.2. Vector differentiation and integration, their geometrical meaning, velocity and acceleration

3.3. Vector differential operators: Gradient, directional derivatives, divergence and curl

3.4. Line integrals, independent of path, conservative and irrotational vector fields, scalar potential

3.5. Introduction to Green's theorem and its application

3.6. Surface integrals, calculation of flux

3.7. Volume integrals, Gauss divergence theorem (Without proof) and its application in evaluation of surface integrals

3.8. Introduction to Stoke's theorem and its application

4. Laplace Transform

7 hrs8 marks

4.1. Definition of Laplace transform, condition for existence, Laplace transforms of some elementary functions, properties of Laplace transform, shifting and change of scale properties

4.2. Inverse Laplace transform, uniqueness of inverse Laplace transform, properties of inverse Laplace transform

4.3. Laplace transform of derivatives and integral, multiplication and division by t^n, the convolution theorem

4.4. Laplace transform of Heaviside's unit function, Dirac-delta function and periodic functions

4.5. Application of Laplace transform to ordinary differential equations

8 hrs12 marks

5.1. Review of algebra of real and complex matrices

5.2. Rank of matrices and its application in system of linear equations

5.3. Vector space, linear dependence and independence

5.4. Eigen values: Cayley Hamilton theorem and its applications

5.5. Eigen vectors, diagonalization of matrices

5.6. Reduction of quadratic forms into canonical forms (Three variables only)

6. Solution of Differential Equation in Series and Special Functions

5 hrs6 marks

6.1. Power series method

6.2. Bessel's functions: Introduction, properties and application

6.3. Legendre's function: Introduction, properties and application

Laboratory Works

Reference Books

1.Kreyszig, E. (2011). Advanced engineering mathematics. John Wiley & Sons.
2.Jeffrey, A. (2002). Advanced engineering mathematics. Academic Press.
3.O'Neil, P.V. (2011). Advanced engineering mathematics. Cengage Learning.
4.Sastry, S.S. (2008). Engineering mathematics (Vols. I–II). PHI Learning.
5.Wylie, C.R, Barrett, L.C. (1995). Advanced engineering mathematics (Latest Edition). McGraw-Hill.
6.Dutta, D. (2006). Textbook of engineering mathematics (Vols. I–II). New Age International.

Notes:

Source:

Engineering Mathematics II covers advanced mathematical topics including calculus of two and more variables, multiple integrals, vector calculus, Laplace transforms, matrices, and solution of differential equations in series and special functions. These concepts are applied in the study of electronics engineering.

After completion of the course students will be able to apply knowledge of partial differentiation, multiple integrals, vector calculus, optimization, matrices and infinite series in their corresponding study area.

This syllabus follows the official BEI curriculum of Tribhuwan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative. https://ioe.tu.edu.np/pages/electronics-engineering-curriculum-structure-2660