CALCULUS AND LINEAR ALGEBRA
Semester :I CIE
Marks” : 40
Course Code : 18MAT11 SEE Marks: 60
Teaching Hours/week (L:T:P) =: 3:2:0
Exam Hours’: 03 Credits : 04
Course Learning Objectives:
This course
Calculus and Linear Algebra (18MAT11) will enable students:
¢ To familiarize the important tools of calculus and
differential equations that are essential in all branches of engineering.
MODULE-I
Differential
Calculus-1: Review of elementary differential calculus, Polar curves -
angle between the radius vector and tangent, angle between two curves, pedal
equation. Curvature and radius of curvature- Cartesian and polar forms; Centre
and circle of curvature (All without proof-formulae only) —applications to
evolutes and involutes. (RBT Levels: L1 & L2)
MODULE-II
Differential
Calculus-2: Taylor’s and Maclaurin’s series expansions for one variable
(statements only), indeterminate forms - L’Hospital’s rule. Partial
differentiation; Total derivatives-differentiation of composite functions.
Maxima and minima for a function of two variables; Method of Lagrange
multipliers with one subsidiary condition. Applications of maxima and minima
with illustrative examples. Jacobians-simple problems.(RBT Levels: L1 & L2)
Click here to download module-2
MODULE-III
Integral
Calculus: Review of elementary integral calculus.
Multiple
integrals: Evaluation of double and triple integrals. Evaluation of
double integrals- change of order of integration and changing into polar co-
ordinates. Applications to find area volume and centre of gravity Beta and
Gamma functions: Definitions, Relation between beta and gamma functions and
simple problems.
(RBT Levels: L1 & L2)
Click here to download Module-3
MODULE-IV
Ordinary
differential equations (ODE’s) of first order: Exact and reducible to
exact differential equations. Bernoulli’s equation. Applications of
ODE’s-orthogonal trajectories, Newton’s law of cooling and L- Rcircuits.
Nonlinear differential equations: Introduction to general and singular
solutions ; Solvable for p only; Clairaut’s and reducible to Clairaut’s
equations only. (RBT Levels: L1, L2 & L3)
Click here to download Module-4
MODULE-V
Linear Algebra: Rank of a
matrix-echelon form. Solution of system of linear equations — consistency.
Gauss-elimination method, Gauss —Jordan method and Approximate solution by
Gauss-Seidel method. Eigen values and eigenvectors- Rayleigh’s power method.
Diagonalization ofa square matrix of order two. (RBT Levels : L1, L2 & L3)
Click here to download Module-5
Web links and Video
Lectures:
2.
http://www.class-central.com/subject/math(MOOCs)
4.
VTUEDUSAT
PROGRAMME - 20
Course Outcomes:
On completion of
this course, students are able to:
CO1 : Apply the knowledge of calculus to solve problems
related to polar curves and its applications in determining the bentness ofa
curve.
CO2 : Learn the notion of partial differentiation to
calculate rates of change of multivariate functions and solve problems related
to composite functions and Jacobians.
GD CO3 : Apply the concept of change of order of
integration and variables to
evaluate multiple integrals and their usage in computing
the area and volumes.
CO4 : Solve first order linear/nonlinear differential
equation analytically using
standard methods
CO5 : Make use of matrix theory for solving system of
linear equations and
compute eigenvalues and eigenvectors required for matrix
diagonalization process.
Question Paper
Pattern:
The SEE question paper will be set for 100 marks and the
marks scored will be proportionately reduced to 60.
The question paper will have ten full questions carrying
equal marks. Each full question carries 20 marks.
There will be two full questions (with a maximum of four
sub questions) from each module.
Each full question will have sub questions covering all
the topics under a module.
The students will have to answer five full questions,
selecting one full question from each module.
Click Here For Imp question
Click here to download Previous year question paper-1
Textbooks:
1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015.
2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed.(Reprint), 2016.
Reference books:
1. C.Ray Wylie, Louis C.Barrett : “Advanced Engineering Mathematics", 6th Edition, 2. McGraw-Hill Book Co., New York, 1995.
2. James Stewart : “Calculus —Early Transcendentals”, Cengage Learning India Private Ltd., 2017.
3. B.V.Ramana: "Higher Engineering Mathematics" 11th Edition, Tata McGraw-Hill, 2010.
4. Srimanta Pal & Subobh C Bhunia: “Engineering Mathematics”, Oxford University Press, 3rd Reprint, 2016.
5. Gupta C.B., Singh S.R. and Mukesh Kumar: “Engineering Mathematics for Semester I & II”, Mc-Graw Hill Education (India) Pvt.Ltd., 2015.
Softcopy Textbook Links:
1. ADVANCED ENGINEERING MATHEMATICS 10th ed Download Link
2. CALCULUS EARLY TRANSCENDENTALS Download Link
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