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.

Calculus I

Course Title: Calculus I

Course No: BDS105

Nature of the Course: THEORY

Semester: 1

Full Marks: 45 + 30

Pass Marks: 18 + 12

Credit Hours: 3

Course Description

This course includes limits, continuity, differentiation and integration of algebraic and transcendental functions, and their applications.

Course Objectives

After successful completion of this course, student will be able to

Solve the problems of limit, continuity, differentiation and integration
Apply the techniques of calculus to solve real life problems

Course Contents

1. Limits and Continuity

8 hrs

1.1. Limit of a function

1.2. Calculating limits using the limit laws

1.3. Computing limits of algebraic functions by definition

1.4. Limits at infinity

1.5. Asymptotes: horizontal, vertical and oblique

1.6. Continuity at a point

2. Derivatives

7 hrs

2.1. Derivatives and their rules

2.2. Linear approximations and differentials

2.3. Indeterminate forms and L’Hospital’s rule

2.4. Higher order derivatives

3. Application of Derivative

10 hrs

3.1. Rolle’s Theorem and Mean value theorem

3.2. Monotonic functions

3.3. Optimization problems

3.4. Marginal analysis

3.5. Sketching curve using calculus

3.6. Newton’s method

4. Integrals

13 hrs

4.1. Definite integral

4.2. Fundamental theorems of calculus

4.3. Indefinite integrals and their properties

4.4. Properties of definite integrals

4.5. Reduction formulae

4.6. Improper integrals

4.7. Beta and Gamma functions

4.8. Numerical methods of integration

5. Application of Integration

10 hrs

5.1. Areas between curves

5.2. Volumes

5.3. Volumes by cylindrical shells

5.4. Average value of a function

5.5. Arc length

5.6. Area of a surface of revolution

5.7. Applications in economics

Reference Books

1.Stewart J., Calculus: Early Transcendental Functions, 7th edition, Thomson Brooks/Cole
2.Larson, et al, Calculus: Early Transcendental Functions, Houghton Mifflin, 2011
3.Robert A. Adams, Christopher Essex, Calculus: a complete course, Pearson, 2010

Notes:

This syllabus follows the official BDS curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.

Calculus and Analytical Geometry

Calculus and Analytical Geometry

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TabFlux . Calculus I . TU . BDS

Calculus I

Course Description

Course Objectives

Course Contents

Reference Books

Notes: