MLR Institute of Technology
ADVANCED CALCULUS
I B. TECH- II SEMESTER
Course Code Category Hours / Week Credits Maximum Marks
L T P C CIE SEE Total
A4BS04 BSC
3 1 - 4 30 70 100
COURSE OBJECTIVES:
To learn
1. Evaluation of length, areas& volumes of different curves of revolution.
2. The partial derivatives of several variable functions.
3. Concept and application of Laplace transforms.
4. Fourier series for periodic functions.
5. Classification of second order partial differential equations.
COURSE OUTCOMES:
Upon successful completion of the course, the student is able to
1. Evaluate the improper integrals using beta and gamma functions.
2. Find the Maxima and Minima of several variable functions.
3. Solve the differential equations using Laplace transform techniques.
4. Find the Fourier series of the periodic functions.
5. Solve one dimensional heat equation, wave equation using method of separation of
variables.
BETA GAMMA FUNCTIONS AND APPLICATIONS OF DEFINITE
UNIT-I Classes: 11
INTEGTALS
Beta- Gamma Functions and their Properties-Relation between them- Evaluation of improper
integrals using Gamma and Beta functions.
Application of definite integrals: Lengths, evaluate surface areas and volumes of revolution of
curves (only in Cartesian co-ordinates).
UNIT-II CALCULUS OF SEVERAL VARIABLES Classes: 11
Limit, Continuity - Partial derivative- Partial derivatives of higher order -Total derivative - Chain rule,
Jacobians -functional dependence & independence. Applications: Maxima and Minima of functions of
UNIT-III LAPLACE TRANSFORMS Classes: 12
Laplace transforms of elementary functions- First shifting theorem - Change of scale property
n
Multiplication by t - Division by t Laplace transforms of derivatives and integrals Unit step function
Second shifting theorem Periodic function Evaluation of integrals by Laplace transforms
Inverse Laplace transforms- Method of partial fractions Other methods of finding inverse transforms
Convolution theorem Applications of Laplace transforms to ordinary differential equations.
UNIT-IV FOURIER SERIES Classes:10
Periodic function-Determination of Fourier Coefficients-Fourier Series-Even and Odd functions-
Fourier series in arbitrary interval-Even Odd periodic continuation-Half range Fourier sine and cosine
expansions.
PARTIAL DIFFERENTIAL EQUATIONS OF SECOND ORDER AND
UNIT-V Classes: 08
APPLICATIONS
Method of separation of variables. Classification of second order partial differential equations.
Applications of Partial differential equations- one dimensional wave equation, Heat equation.
TEXT BOOKS:
th
1. Ervin Kreyszig, Advanced Engineering Mathematics, 9 Edition, John Wiley & Sons, 2006.
2. B.S.Grewal, Higher Engineering Mathematics, Khanna publishers, 36th Edition, 2010.
REFERENCE BOOKS:
1. G.B.Thomas, calculus and analytical geometry,9th Edition, Pearson Reprint 2006.
2. N.P Bali and Manish Goyal ,A Text of Engineering Mathematics,Laxmi publications,2008.
3. E.L.Ince, Ordinary differential Equations,Dover publications,1958.
WEB REFERENCES:
B.Tech- CSE Academic Regulations & Syllabus MLR18 Page 44
MLR Institute of Technology
1. https://www.efunda.com/math/math_home/math.cfm
2. https://www.ocw.mit.edu/resources/#Mathematics
3. https://www.sosmath.com/
4. https://www.mathworld.wolfram.com/
E -TEXT BOOKS:
1.https://www.e-booksdirectory.com/details.php?ebook=10166
2.https://www.e-booksdirectory.com/details.php?ebook=10166
MOOCS COURSE:
1. https://swayam.gov.in/
2. https://onlinecourses.nptel.ac.in/
B.Tech- CSE Academic Regulations & Syllabus MLR18 Page 45
