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Calculus and Analytical Geometry

Calculus and Analytical Geometry provides the "logical" mathematical foundation for analyzing the "structural hierarchy" of "circuit-based technical materials". It utilizes "technical clarity" to model change and spatial relationships essential for "university programs" and hardware design.

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TabFlux . Calculus and Analytical Geometry . FWU . BSc. CSIT

Calculus and Analytical Geometry

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Course Title: Calculus and Analytical Geometry

Course No: CSIT.113

Nature of the Course: THEORY

Semester: 1

Full Marks: 60 + 40

Pass Marks: 24 + 20

Credit Hours: 3

Course Description

Course Objectives

Course Contents

1. Sequence of Real numbers

5 hrs

1.1. Definition notation and examples

1.2. Convergent, divergent and oscillatory sequence, definition and examples

1.3. Bounded set, Bounded sequence definition and examples

1.4. Monotonic sequence

1.5. Convergences of sequence

2. Series of Real Numbers

10 hrs

2.1. Sequence of partial sum

2.2. Convergence of series. If un is convergent then un->0 as n->infinity (with proof)

2.3. Convergence of geometric series (with proof)

2.4. Series of positive terms, comparison test and its limit form (without proof)

2.5. Convergences of sum of 1/n^p, P E R (with proof)

2.6. D Alembert's ratio test (without proof)

2.7. Root test (without proof)

2.8. Absolute and conditional convergence

2.9. Power series, Taylor's and Maclurins series, convergence of Taylors series

3. Differential Calculus

4 hrs

3.1. nth derivative

3.2. Leibnitz theorem (with proof) and its application

3.3. Partial differentiation

4. Integral Calculus

6 hrs

4.1. Method of integration

4.2. Properties of definite integral

4.3. Improper integral

4.4. Beta Gamma function and their properties

4.5. Reduction formula

5. Conic Section

3 hrs

5.1. Classifying conic section by eccentricity

5.2. Plane curves, parametric and polar equations

5.3. Integration in polar coordinates

6. Vectors and Vector valued function

6 hrs

6.1. Vectors in the space

6.2. Lines and planes in space

6.3. Cylindrical and quadric spaces

6.4. Cylindrical and spherical surface

6.5. Vector valued function and space curves

6.6. Unit tangent vector, curvature and Torsion and TNB system

7. Vectors and Vector valued function (Advanced)

4 hrs

7.1. Double integrals in rectangular polar coordinates

7.2. Finding areas, moments and centre of mass

7.3. Triple integrals in rectangular coordinates and application

8. Multivariate calculus

7 hrs

8.1. Functions, limit & continuity of two or more variables

8.2. Differentiability, differentials, total differential coefficient

8.3. Directional derivative and gradient vectors

8.4. Extreme values

8.5. Lagranges multiplier

Text Books

1.Real Analysis: R.G. Bartle, D. Sherbert, 3rd Edition, John wiley & sons India Edition.
2.Thomas and Fenns: Calculus and Analytical Geometry, 9th Edition, 2004 (Thomas, Jr G.D and Finney Ross L, Publisher Pearson Ed. Pvt. Ltd.

Reference Books

1.Advanced Engineering mathematics: Kreyszing Erwin John Wiley & sons (1991) 5th Ed.
2.Calculus with analytical Geometry: E.W Swokowski & second Alter Edition.

Notes:

Source:

The course aims to acquaint the students with the basic concepts of sequence and series of real numbers differential and integral calculus, multivariate calculus and the multiple integrals.

To acquaint the students with basic concepts of analysis on sequence and series of real numbers. To enable the students, to understand the differential and integral calculus and its further application. To know the brief idea of vector valued function, multiple integral and multivariate calculus.

This syllabus follows the official CSIT curriculum of Far Western University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative. https://cdc.fwu.edu.np/faculties.html