ENGINEERING MATHEMATICS -I (2017-18)

Course Code: / MA102 / Title: / Engineering Mathematics – I

Course Objective:

The student will study calculus of applied mathematics

Course Outcomes:

Having studied this course, he will be able to

PO1 / PO2 / PO3
CO1 / Partially differentiate and finds the Jacobian of a function and solves problems on Taylor series for function of single variable. / 3 / 2 / 1
CO2 / Expand the function in terms of Taylor series for function of two variables, finds extreme values and apply the same for engineering problems. / 2 / 2 / 1
CO3 / Determine the pedal equation for a polar curve, plot the curve/geometry of a function and estimate area, volume through line integrals. / 3 / 2
CO4 / Evaluate improper integrals using beta, gamma functions, multiple integralsand apply the concept of multiple integrals to engineering applications (area, volume etc). / 3 / 1
CO5 / Solve problems on gradient, divergence, curl and apply this to problems on dynamics so as to extract the physics. / 3 / 2
Mode / 3 / 2 / 1

ENGINEERING MATHEMATICS – I (2017-18)

(Common to all branches of engineering)

Exam hours: 3 Sub. Code MA102

Hours / week: 4 LTPC:4-0-0-4

Total hours: 52

COURSE CONTENTS

Unit 1 / Differential Calculus – I
Definition of average growth rate and its illustrative examples. Definition of differentiability. Statement of Taylor’s theorem, Taylor series and Maclaurin series for function of a single variable. Illustrative examples.
Partial Differentiation: Definition of Partial derivative, Physical and geometrical interpretation of partial Differentiation, Application oriented problems on the partial derivatives from engineering field, total derivative rule and partial differentiation of composite functions and problems. Jacobian and its Illustrative examples. / (7 Hours)
Unit 2 / Differential Calculus – II
Statement of Taylor theorem for a function of two variables and illustrative examples on Taylor and Maclaurin series. Maxima & Minima for a function of two variable, Finding extreme values of the function using Lagrange’s multipliers method. Illustrative examples from engineering field. / (7 hours)
PART B
Unit 3 / Differential Calculus – III
Polar curves:Angle between radius vector and tangent, Angle between two polar curves, Orthogonality of polar curves, Pedal equation of polar curves.
Derivative of an arc length, Radius of curvature in Cartesian, polar & Pedal forms, Illustrative examples. / (6 hours)
Unit 4 / Integral Calculus-I
Evaluation of indefinite and definite integrals using standard reduction formulae. Tracing of curves in Cartesian and Polar form (Cissoids, Strophoid, Folium of Descartes, Lemniscates of Bernoulli and cycloid). / (6 hours)
PART C
Unit 5 / Integral Calculus-II
Improper integrals: Beta and Gamma functions, Relation between Beta and Gamma functions, Illustrative Examples. Differentiation under integral sign using Leibnitz’s rule with constant coefficients, illustrative examples. / (7 hours)
Unit 6 / Integral Calculus-III
Applications of Line Integrals: Finding area of a planar region, length of a planar curve, surface of revolution, volume of revolution and illustrative examples (Cissoids, Strophoid, folium of Descartes, Lemniscates of Bernoulli and cycloid). / (6 hours)
PART D
Unit 7 / Multiple Integrals: Evaluation of double integrals in Cartesian & Polar form, Evaluation by changing to polar form, Evaluation of triple integrals, Application to find area, volume and mass. / (7 hours)
Unit 8 / Vector Differentiation: Velocity & acceleration of a vector point function, Gradient, divergence & curl. Physical & Geometrical Interpretation of Gradient, divergence & curl. Solenoidalirrotational vectors, vector identities, illustrative examples from engineering field – moment of a force, velocity of a rotating body, rotation of a rigid body. / (6 hours)
Note - Theorems and properties without proof. Applicable to all the units.
Text books:
  1. Dr. B. S. Grewal, Higher Engineering Mathematics, Khanna Publications, 44th edition, 2016.
  2. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley India Pvt. Ltd. 8th Edition(Wiley student edition) 2004.

Reference books:
  1. Tom M Apostol, Calculus, Volume 1 and 2, Wiley India (Delhi) Publication, 2nd Edition, 2014.
  2. R K Jain and S R K Iyengar, Advanced Engineering mathematics by Narosa publishers, 2nd edition,2005.
  3. Thomas Finney,Calculus, 9th edition, Pearson education, 2002.