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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 y t i l To apply the concepts of radius of curvature, i ) ) h b ) CLR-4 c % a m k r e % ( o n r evolute, envelope in problems of Science and a c i ( t e o o e a n l t n g : s a t y n B e W e d s c n e ( e Engineering e i g R u l m n g e F n m e p r S m g a i s w , i i n s a o u n c n i o l n s i i CLR-5 Application of Sequences and Series in all problems & e t r n U a & n g e k f y l i l a T o t v . o n u l i s K a e i t t r e t e o t C n h L : involving Science and Engineering n g & g A P a o D D e A T c n l T i g i & M d d , a r m n & n f 1 2 3 s e e e i n u m n u o o y t t t s r e e d c s n o - - - t L c c l Course Learning At the end of this course, learners will i l e y m c r n e g e l i e e i v i b i j e i d i e a s O O O g v c h m v p p o o o d f e n r r o S S S e x x n n t o i 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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