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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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Engineering
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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):
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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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