SCHEME OF EXAMINATION 
                                   AND 
                             COURSE OF STUDY 
                                    of 
                              Mathematics  
                  [Under Choice Based Credit System as proposed by UGC] 
                                      
                                   For 
                                      
                           B.Sc. (PCM &PGM) 
                           (w. e. f. Session 2018--2019) 
            
            
            
            
                                      
                                      
            
                         DEPARTMENT OF MATHEMATICS  
                  Pt. L.M.S. GOVERNMENT P.G. ( Autonomous) College 
                              Rishikesh,Dehradun 
                                      
            
                                    
                                                                                
                                                                                
                  Semester       Core Course          Ability                        Skill                              Discipline 
                                                  Enhancement                   Enhancement                              Specific 
                                                   Compulsory                      Course                                Elective 
                                                      Course                        (SEC)                                 (DSE) 
                                                      (AECC)                                                                   
                                                           
                      1         MA-DSC-111                                                                    
                                Differential 
                                Calculus 
                                 
                      2         MA-DSC-121                                                                    
                                Differential 
                                Equations 
                                 
                      3         MA-DSC-131                                   SEC 1 (choose one)               
                                Real Analysis                       MA-SEC-131(a)   Logic and Sets 
                                                                    MA-SEC-131(b)   Analytical 
                                                                    Geometry 
                                                                    MA-SEC-131(c)   Integral Calculus 
                      4         MA-DSC-141                                   SEC 2 (choose one)               
                                Algebra                             MA-SEC-141(a)   Vector Calculus 
                                                                    MA-SEC-141(b)   Mathematical 
                                                                    Finance 
                                                                    MA-SEC-141(c)   Number Theory 
                      5                            MA-GEN-151                SEC 3 (choose one)                    DSE 1A (choose one) 
                                                                    MA-SEC-151(a)   Probability and          MA-DSE-151(a)  Matrices 
                                                                    Statistics                               MA-DSE-151(b)  Mechanics 
                                                                    MA-SEC-151(b)   Theory of                MA-DSE-151(c)  Linear Algebra 
                                                                    Equations 
                                                                    MA-SEC-151(c)   Mathematical 
                                                                    Modeling 
                      6                            MA-GEN-161                SEC 4 (choose one)                    DSE 1B (choose one) 
                                                                    MA-SEC-161(a)   Boolean Algebra         MA-DSE-161(a)  Numerical 
                                                                    MA-SEC-161(b)   Transportation and  Methods   
                                                                    Game  Theory                            MA-DSE-161(b) Graph Theory   
                                                                    MA-SEC-161(c) Complex Analysis          MA-DSE-161(c)  Linear 
                                                                                                            Programming 
                         
                        Note: Each paper carries 100 marks which includes one sessional test of 30 marks and a main 
                        examination of 70 marks. 
                                                                                                                    
                           Pt.L.M.S. Govt. P.G. College, Rishikesh            
                                       (Autonomous College) 
                           NAME OF THE DEPARTMENT: MATHEMATICS  
                                                    
                    B.Sc Semester:  1st                                          Subject code : MA-DSC-111  
                   Course Title: Differential Calculus                 Credit: 6 (5L+1T) 
                   Examination Duration:3 Hours                       Max. Marks: 70 
                 
                NOTE: The question paper consists of three sections A, B and C.  Section A will consist 10 
                objective type questions (all compulsory) , each of marks 1.  Section B will  consists of 6  
                short answered questions , in which 4 to be answered ,each of marks 5.  Section C will 
                consist of 7 long answered questions , in which 4 to be answered , each of marks 10.  
                 
                Limit and Continuity (ε and δ definition), Types of discontinuities, Indeterminate forms, 
                Differentiability of functions, Rolle’s theorem, Mean Value theorems.  
                Successive differentiation, Leibnitz’s theorem, Partial differentiation, Euler’s  theorem on 
                homogeneous  functions.  Taylor’s  theorem  with  Lagrange’s  and  Cauchy’s  forms  of 
                                                                 x            m
                remainder, Taylor’s series, Maclaurin’s series of sin x, cos x, e , log(l+x), (l+x) , Maxima 
                and Minima.  
                Tangents  and  normals,  Curvature,  Asymptotes,  Singular  points.  Tracing  of  curves. 
                Parametric representation of curves and tracing of parametric curves, Polar coordinates and 
                tracing of curves in polar coordinates. 
                 
                , 
                Books Recommended 
                1.   H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., 2002. 
                2.   G.B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007. 
                 
                 
                 
                                                    
                                                    
                        Pt.L.M.S. Govt. P.G. College, Rishikesh            
                                   (Autonomous College) 
                        NAME OF THE DEPARTMENT: MATHEMATICS  
                                               
                              nd
                 B.Sc. Semester:  2                                          Subject code : MA-DSC-121 
                 Course Title: Differential Equations               Credit: 6 (5L+1T) 
                 Examination Duration: 3 Hours                       Max. Marks: 70 
               
              NOTE: The question paper consists of three sections A, B and C.  Section A will consist 10 
              objective type questions (all compulsory), each of marks 1.  Section B will consists of 6  
              short  answered questions, in which 4 to be answered, each of marks 5. Section C will 
              consist of 7 long answered questions, in which 4 to be answered, each of marks 10.  
               
              First  order  exact  differential  equations.  Integrating  factors,  rules  to  find  an  integrating 
              factor. First order higher degree equations solvable for x, y, p. Methods for solving higher-
              order differential equations. Basic theory of linear differential equations,Wronskian, and its 
              properties. Solving a differential equation by reducing its order. 
               
              Linear  homogenous  equations  with  constant  coefficients,  Linear  non-homogenous 
              equations,  The  method  of  variation  of  parameters,    The  Cauchy-Euler  equation, 
              Simultaneous differential equations, Total differential equations.  
               
              Order and degree of partial differential equations, Concept of linear and non-linear partial 
              differential equations. Formation of first order partial differential equations, Linear partial 
              differential equation of first order, Lagrange’s method, Charpit’s method  
              Classification  of  second  order  partial  differential  equations  into  elliptic,  parabolic  and 
              hyperbolic through illustrations only. 
              Books Recommended 
              1.   Shepley L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, 1984. 
              2.   Sneddon, Elements of Partial Differential Equations, McGraw-Hill, International 
                   Edition, 1967 .