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File: Differential Calculus Book Pdf 172093 | Calculus And Linear Algebra
template 6 course learning syllabus course learning syllabus includes learning outcomes learning plan assessment plan l t p c course 18mab101 course course bs basic sciences calculus and linear algebra ...

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           Template 6 :  Course Learning Syllabus 
            
           Course Learning Syllabus ( // includes Learning Outcomes  & Learning Plan & Assessment Plan ) 
                                                                                                                                                          L  T  P  C 
            Course  18MAB101 Course                                                                               Course 
                                                                                                                             BS      Basic Sciences 
                                                     CALCULUS AND LINEAR ALGEBRA 
             Code                      Name                                                                     Category                                 3  1  0  4 
                            T 
            
               Pre-                                              Co-
                                                                                                                     Progressiv
             requisite  Nil                                   requisite  NIl                                                      Nil 
                                                                                                                     e Courses 
              Courses                                          Courses 
           Course Offering                                                           Data Book / 
                                           Mathematics                                                               nil 
           Department                                                                Codes/Standards 
            
           Course Learning                The purpose of learning this course is 
                                                                                                       
                                                                                          Learning                   Program Learning Outcomes (PLO) 
                                          to: 
           Rationale (CLR): 
           CLR-1  Application of Matrices in problems of  Science  
                                                                                           1   2   3        1   2   3   4    5   6    7    8   9   10  11  12  13   14  15 
           :        and  Engineering  
                    To apply the concept of Taylor series, Maxima 
           CLR-2 
                                                                                                       
                    minima, composite function  and Jacobian in 
           :  
                    problems of science and  Engineering 
           CLR-3 To Apply the concept  of Differential Equations in 
                                                                                                       
           :        problems of Science and Engineering  
                                                                                                                                        
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                    To apply the concepts of radius of curvature,                                                          
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                    evolute, envelope in problems of Science and                                                          a
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           CLR-5 Application of Sequences and Series in all problems                                                                                     &
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           :        involving Science and Engineering 
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           Course Learning                At the end of this course, learners will                                                              i
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                                          be able to: 
           Outcomes (CLO):   
                                                                                                                                                n
                                                                                            L   E   E        E   P   D    A   M   S    E    E   I   C    P   L   P   P    P
                    Apply the Knowledge of Matrices, Eigenvalues and 
           CLO-1 
                                                                                         2    85  80      L        L                          M            H            
                    Eigen Vectors Reduce to Quadratics form in problems 
           : 
                    involving Science and Engineering 
                    Gain familiarity in the knowledge of Maxima and 
           CLO-2 
                                                                                         2    85  80      L            M  M                                             
                    Minima, Jacobian, and Taylor series and apply them tn 
           : 
                    the problems involving Science and Engineering 
           CLO-3 Gain knowledge in solution of  Differential Equations 
                                                                                         2    85  80           M                              M            H            
           :        and Its applications in engineering problems  
                    To gain the knowledge of Radius, Centre, envelopre  
           CLO-
                                                                                         2    85  80      L  M         M                      M            H            
                    and Circle of of curvature and apply them in the 
           4 : 
                    problems involving Science and Engineering  
                                                                                                       
                    Gain the knowledge of convergence and divergence of 
           CLO-5 
                                                                                         2    85  80           M  L                           M            H            
                    series using different test and apply sequences and 
                                                                                                       
           : 
                    Series in the problems involving Science and Engineering 
            
            
            
            
            
            
            
            
            
            
            
            
            
            
            
            
                             Learning Unit /         Learning Unit / Module          Learning Unit /             Learning Unit /             Learning Unit / 
                  
                                 Module 1                         2                      Module 3                    Module 4                    Module 5 
             Duration 
                                     12                          12                          12                          12                          12 
              (hour) 
                                                                                 Linear equations of 
                                                     Function of two             second order with  Radius of Curvature Series of Five terms 
                  SLO- Characteristic 
                                                     variables – Partial         constant                   – Cartesian                 – Test of 
                    1 
                         equation  
                                                     derivatives                 coefficients when          coordinates                 Convergence-  
                                                                                 PI=0 or exponential 
            S-1 
                                                                                 Linear equations of 
                                                                                 second order with  Radius of Curvature 
                  SLO- Eigen values of a                                                                                                Comparison test – 
                                                     Total differential          constant                   – Cartesian 
                    2 
                         real matrix                                                                                                    Integral test-  
                                                                                 coefficients when          coordinates 
                                                                                 PI=sinax or cosax 
                                                                                 Linear equations of 
                                                                                 second order with 
                  SLO- Eigen vectors of a                                                                   Radius of Curvature Comparison test – 
                                                     Total differential          constant 
                    1 
                         real matrix                                                                        – Polar coordinates  Integral test-  
                                                                                 coefficients when 
                                                                                 PI=polynomial  
            S-2 
                                                                                 Linear equations of 
                                                     Taylor’s expansion          second order with 
                  SLO- Eigen vectors of a            with two variables          constant                   Radius of Curvature Comparison test – 
                    2 
                         real matrix                 up to second order  coefficients when                  – Polar coordinates  Integral test-. 
                                                     terms                       PI=exponential with 
                                                                                 sinax or Cosax 
                                                                                 Linear equations of 
                                                     Taylor’s expansion          second order with 
                  SLO- Properties of Eigen  with two variables                   constant                                               D’Alemberts Ratio 
                                                                                                            Circle of curvature 
                    1 
                         values                      up to third order           coefficients when                                      test, 
                                                     terms                       PI= exponential 
                                                                                 with polynomial 
            S-3 
                                                                                 Linear equations of 
                                                                                 second order with 
                  SLO- Cayley – Hamilton                                         constant                                               D’Alemberts Ratio 
                                                     Maxima and Minima                                      Circle of curvature 
                    2 
                         theorem                                                 coefficients when                                      test, 
                                                                                 PI=polynomial with 
                                                                                 sinhax or coshax 
                         Problem solving             Problem solving             Problem solving            Problem solving             Problem solving 
                  SLO-
                         using tutorial sheet  using tutorial sheet  using tutorial sheet using tutorial sheet  using tutorial sheet 
                    1 
                         1                           4                           6                          11                          14 
            S-4 
                         Problem solving             Problem solving             Problem solving            Applications of             Problem solving 
                  SLO-
                         using tutorial sheet  using tutorial sheet  using tutorial sheet Radius of curvature  using tutorial sheet 
                    2 
                         1                           4                           6                          in engineering              14 
            S-5  SLO-
                         Finding A inverse           Maxima and Minima  Linear equations of  Centre of curvature Raabe’s root test. 
                1 
                   using Cayley –                              second order 
                   Hamilton theorem                            variable coefficients 
                   Finging higher 
                                                               Linear equations of 
              SLO- powers of A using 
                                         Maxima and Minima  second order            Centre of curvature Raabe’s root test. 
               2 
                   Cayley – Hamilton 
                                                               variable coefficients 
                   theorem 
                   orthogonal reduction 
                                                               Homogeneous 
              SLO- of a symmetric                                                                        Covergent of 
                                         Maxima and Minima  equation of Euler       Centre of curvature 
                1 
                   matrix to diagonal                                                                    Exponential Series  
                                                               type 
                   form 
         S-6 
                   orthogonal reduction Constrained Maxima 
                                                               Homogeneous 
              SLO- of a symmetric        and Minima by                              Evolute of  a 
                                                               equation of                               Cauchy’s Root test 
               2 
                   matrix to diagonal  Lagrangian Multiplier                        parabola  
                                                               Legendre’s Type 
                   form                  method 
                   orthogonal reduction Constrained Maxima 
                                                               Homogeneous 
              SLO- of a symmetric        and Minima by 
                                                               equation of          Evolute of an ellipse Log test 
                1 
                   matrix to diagonal  Lagrangian Multiplier 
                                                               Legendre’s Type 
                   form                  method 
         S-7 
                   orthogonal reduction Constrained Maxima                          Envelope of 
                                                               Equations reducible 
              SLO- of a symmetric        and Minima by                              standard curves 
                                                               to homogeneous                            Log test 
               2 
                   matrix to diagonal  Lagrangian Multiplier 
                                                               form 
                   form                  method 
                   Problem solving       Problem solving       Problem solving      Problem solving      Problem solving 
              SLO-
                   using tutorial sheet  using tutorial sheet  using tutorial sheet using tutorial sheet  using tutorial sheet 
                1 
                   2                     5                     9                    12                   15 
         S-8 
                   Problem solving       Problem solving       Problem solving      Applications of      Problem solving 
              SLO-
                   using tutorial sheet  using tutorial sheet  using tutorial sheet Curvature in         using tutorial sheet 
               2 
                   2                     5                     9                    engineering          15 
                   Reduction of                                Equations reducible 
              SLO-                       Jacobians of two                           Beta Gamma           Alternating Series: 
                   Quadratic form to                           to homogeneous 
                1 
                                         Variables                                  Functions            Leibnitz test 
                   canonical                                   form 
         S-9 
                   Quadratic form to 
                                                                                    Beta Gamma 
              SLO- canonical form by     Jacobians of Three  Variation of                                Alternating Series: 
                                                                                    Functions and Their 
               2 
                   orthogonal            variables             parameters                                Leibnitz test 
                                                                                    Properties  
                   transformations 
                   Quadratic form to  Jacobians problems                            Sequences – 
              SLO- canonical form by                           Variation of         Definition and       Series of positive 
                1 
                   orthogonal                                  parameters           Examples             and Negative terms. 
         S-10 
                   transformations                                                   
                                         Jacobians Problems  Simultaneous first 
              SLO-                                                                  Series – Types of    Series of positive 
                   Orthogonal matrices                         order with constant 
               2 
                                                                                    Convergence          and Negative terms. 
                                                               co-efficient. 
              SLO- Reduction of          Properties of         Simultaneous first  Series of Five terms Absolute 
         S-11 
                1 
                   quadratic form to     Jacobians and         order with constant – Test of             Convergence 
                             canonical form                    Problems                          co-efficient.                    Convergence-  
                             Reduction of                      Properties of                     Simultaneous first 
                     SLO-                                                                                                         Comparison test –  Conditional 
                             quadratic form to                 Jacobians and                     order with constant 
                        2 
                                                                                                                                  Integral test-                   Convergence 
                             canonical form                    problems                          co-efficient. 
                                                               Application of                    Problem solving                                                   Problem solving 
                             Problem solving                   Taylor’s series                   using tutorial sheet Problem solving                              using tutorial sheet 
                     SLO-
                             using tutorial sheet  Maxima Minima                                 10                               using tutorial sheet  13 
                        1 
                             3                                 Jacobians in                                                       13 
                                                               Engineering 
             S-12 
                                                               Application of                    Applications of                                                   Applications 
                             Applications of                   Taylor’s series                   Differential                     Problem solving                  Convergence of 
                     SLO-
                             Matrices in                       Maxima Minima                     Equation in                      using tutorial sheet  series in engineering  
                        2 
                             Engineering                       Jacobians in                      engineering                      13 
                                                               Engineering 
                              
                                                                                                                                                                    
                                   1.    Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons,2006. 
                                   2.    B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010. 
                                   3.  Veerarajan T., Engineering Mathematics for first year, Tata McGraw-Hill, New Delhi,2008 
                                                                                                                                                                               th
                                   4.  Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11  Reprint,       
             Learning                    2010 
             Resources             5.  G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson,Reprint, 
                                         2002 
                                   6.  N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, 
                                         Reprint, 2008 
                                    
                                    
              
                         Level of                                                 Continuous Assessment 
                                                                                                                                                               Final Examination (40%) 
                         Thinking               CA – 1 (20%)                           CA – 2 (20%)                          CA – 3 (20%) # 
                       Remember 
             Level 
                                                       40 %                                   30 %                                    30 %                                   30 % 
                       Understand 
             1 
                       Apply 
             Level 
                                                       40 %                                   40 %                                    40 %                                   40 % 
                       Analyze 
             2 
                       Evaluate 
             Level 
                                                       20 %                                   30 %                                    30 %                                   30 % 
                       Create 
             3 
              # CA – 3 can be from any combination of these: Assignments, Seminars, Tech Talks, Mini-Projects, Case-Studies, Self-Study, MOOCs, 
             Certifications, Conf. Paper etc., 
             SLO – Session Learning Outcome 
              
              
              
              
              
              
              
              
              
              
              
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...Template course learning syllabus includes outcomes plan assessment l t p c mab bs basic sciences calculus and linear algebra code name category pre co progressiv requisite nil e courses offering data book mathematics department codes standards the purpose of this is program plo to rationale clr application matrices in problems science engineering apply concept taylor series maxima minima composite function jacobian differential equations y i concepts radius curvature h b a m k r o n evolute envelope g s...

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