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                                                                       MATHEMATICS 
                                
                               Year-1          Semester-1 
                                 Teaching Schedule hours/Week                                 Examination Scheme 
                                   L P T Internal Assessment  Final  Total 
                                   3                                        Theory      Practical*    Theory Practical**               
                                                 - 2                                                                                100 
                                                                              20                         80  
                                 
                                
                               Objectives:- 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. 
                                
                               2. 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 variable, Partial derivatives total differential coefficients. 
                                
                               3. 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. 
                                
                               4. Integration: Basic integration formulas, Integration methods, standard integrals, Definite Integrals  
                                   and its properties. Definite integral as the limit of a sum, Fundamental theorem of integral calculus,  
                                   Improper integrals, Reduction formulate for integrals, Beta and Gamma functions. 
                                
                               5. Applications of Integral Calculus: Determination of area. Lengths, Volumes and surface areas of  
                                   solid of revolution, multiple integrals, change of order of integration. 
                                
                               6. Plane Analytic Geometry: Translation and rotation of axes, circles, conic sections, parabolas,  
                                   ellipses, hyperbolas and central conic. 
                                
                               7. 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. 
                                
                               Recommended Books:-
                                                         
                                
                               1.Differential Calculus- M.B.Singh and B.C.Bajracharya, Sukunda pustak bhawan Kathmandu. 
                                
                               2. Calculus and Analytic Geometry- Thomas and Finny, Narosa pub. house India. 
                                
                               3. Basic Mathematics (Vol-I & Vol-II)- D.R.Bajracharya, National book center , Kathmandu 
                                
                               4. A text book of vector Analysis- MB. Singh and B.C. Bajrachrya. Sukunda pustak Bhawan,  
                                  Kathmadu 
                                
                               5. Integral Calculus and Differential Equation- G.D. Pant & G.S. 8th Sunila Prakashyan, Kathmandu 
                                
                               6. Higher Coordinate Geometry: Lalji Prasad, Paramount Publications, Patna,India 
                                
                               7. Two-dimensional Geometry- M.R. Joshi 
                                
                                
                                
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