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Mathematics I

This course provides the "logical" foundation for "instructional materials" by covering calculus of one variable, including limits, differentiation, and integration. It focuses on the "technical clarity" needed to formulate real-world problems into mathematical statements and demonstrate solutions numerically or graphically.

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TabFlux . Engineering Mathematics I . TU . BCT-NEW

Engineering Mathematics I

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Course Title: Engineering Mathematics I

Course No: ENSH 101

Nature of the Course: THEORY

Semester: 1

Full Marks: 40 + 60

Pass Marks: 16 + 24

Credit Hours: 3

Course Description

Course Objectives

Course Contents

1. Derivatives and its Applications

10 hrs

1.1. Review of derivative and differentiability, mean value theorems with interpretations

1.2. Indeterminate forms, types and their real life examples, L-Hospital's rule

1.3. Power series of single valued functions

Taylor's series

Maclaurin's series

1.4. Asymptotes to Cartesian and Polar curves

1.5. Pedal equation to Cartesian and Polar curves

1.6. Curvature and radius of curvature for Cartesian curves

2. Antiderivatives and its Applications

11 hrs

2.1. Review of definite and indefinite integrals

2.2. Differentiation under integral sign

2.3. Improper integrals

2.4. Application of Beta and Gamma functions

2.5. Area, arc length, volume and surface of revolution in plane for Cartesian curves

2.6. Centroid and moment of inertia under area of curve

3. Ordinary Differential Equations and its Applications

10 hrs

3.1. Review of order, degree, solution of first order first degree differential equations by variable separation method and solution of homogeneous equations

3.2. Linear differential equation and equations reducible to linear differential equation of first order Bernoulli's equation, modeling electric circuit

3.3. First order and higher degree differential equations; Clairaut's form

3.4. Linear second order differential equations with constant coefficient and variable coefficients reducible to constant coefficients, Cauchy's equations and modeling mass spring system

3.5. Application in physical sciences and engineering

4. Plane Analytic Geometry

4 hrs

4.1. Transformation of coordinates: Translation and rotation

4.2. Equation of conic in Cartesian and Polar form, identification of conics

5. Three dimensional geometry

10 hrs

5.1. The straight line: Symmetrical and general form

5.2. Coplanar lines

5.3. Shortest distance

5.4. Sphere: General equation, plane section by planes, tangent planes

5.5. Introduction to right circular cone and right circular cylinder

Reference Books

1.Jeffery, A., (2001), Advanced Engineering Mathematics. Academic Press.
2.O'Neill, P.V., (2003), Advanced Engineering Mathematics. Thomson Learning.
3.Kreyszig , A. (1993), Advanced engineering Mathematics (Latest Edition). John Wiley & Sons.
4.Sastry, S.S. (2008), Engineering Mathematics Volume I and II. PHI India.
5.Wylie, C., Barrett, L.(1995), Advanced Engineering Mathematics (Latest Edition), McGraw-Hill College.
6.Thomas, T., Finny, R. (1984), Calculus and Analytic Geometry (Latest Edition.), Addison-Wesley.

Notes:

Source:

This course develops essential mathematical concepts, skills, and techniques required for engineering and technical fields. It focuses on applying mathematical methods to analyze, model, and solve engineering problems effectively.

To equip the students with the essential mathematical skills and techniques that are relevant to the engineering fields and enable them to solve engineering problems using mathematical methods.

This syllabus follows the official BCT 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/computer-engineering-curriculum-structure-2635