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 MATHEMATICS I

BEG101SH

Year :I Semester :1

Teaching Schedule Hours/week

Examination Scheme

Total Marks

Remarks

Final

Internal Assessments

Theory

Practical

Theory Marks

Practical Marks

L

P

T

Duration

Marks

Duration

Marks

3

2

3

80

--

--

20

--

100

 

Objective: The basic objective of the course is to provide a sound knowledge of calculus and other related topics.

 

1. Limits and continuity of a function: Limit of a function with examples, infinity as a limit, continuity of a function, simple properties of a continuous function. 3

 

1. Derivatives: Review of derivatives (Derivatives of Implicit, Parametric equation, hyperbolic and inverse hyperbolic functions), Higher order derivatives, successive derivatives and Leibnitz theorem, Functions of two or more variables, Partial derivatives, total differential coefficients. 6

 

1. Applications of derivatives: Extrema of function of two or three variables, mean value theorems, Taylor and Maclaurin’s infinite series, Indeterminate forms and L’Hospital’s rule, Tangent and normal, curvature, Assymptotes and curve tracing. 8

 

1. Integration: Basic integration formulas, Integration methods, Standard Integrals, Definite Integral and its properties, Definite integral as the limit of a sum, Fundamental theorem of integral calculus, Improper integrals, Reduction formulae for integrals, Beta and Gamma functions. 8

 

1. Applications of Integral Calculus: Determination of area, Lengths, Volumes and surface areas of solid of revolution, multiple integrals, change of order of integration. 5

 

1. Plane Analytic Geometry: Translation and rotation of axes, circles, conic sections, parabolas, ellipses, hyperbolas and central conics. 8

 

1. Vector Algebra: Vector components, zero vector, unit vector, addition, equality, Direction cosines, space co-ordinates (Cartesian, cylindrical and spherical co-ordinates), equation relating these co-ordinates, scalar and vector, product of two vectors, product of three vectors or more vectors, lines and planes. 7

 

Recommended Books:

 

1. Differential Calculus – M.B. Singh and B.C. Bajracharya, 

  Sukunda Pustak Bhawan, Kathmandu.

1. Calculus and Analytic Geometry – Thomas and Finney

  Narosa Publishing House, India.

1. Basic Mathematics (Vol. I and II) – D. R. Bajracharya

  National Book Center, Kathmandu.

1. A text book of vector Analysis - M.B. Singh and B.C. Bajracharya, 

  Sukunda Pustak Bhawan, Kathmandu.

 

1. Integral Calculus and Differential Equations – G. D. Pant & G. S. Sth 

Sunila Prakashan, Kathmandu.

1. Higher Coordinate Geometry – Lalji Prasad

Paramount Publications, Patna, India.

1. Two-dimensional Geometry – M.R. Joshi.