23UMATC24 Integral Calculus Syllabus:

23UMATC24 Integral Calculus Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives of the Course

  • Knowledge on integration and its geometrical applications, double, triple integrals and improper integrals.
  • Knowledge about Beta and Gamma functions and their applications.
  • Skills to Determine Fourier series expansions.

UNIT-I:

Reduction formulae -Types, integration of product of powers of algebraic and logarithmic functions – Bernoulli’s formula,

Chapter 1: Section – 13.1 to 13.5, 13.10,15.1

UNIT-II:

Multiple Integrals – definition of double integrals – evaluation of double integrals – double integrals in polar coordinates – Change of order of integration.

Chapter  5 : Section – 1, 2.1 to 2.2, 3.1

UNIT-III:

Triple integrals –applications of multiple integrals – volumes of solids of revolution – change of variables – Jacobian.

Chapter 5: Section 4, 5.1 to 5.4

UNIT-IV:

Beta and Gamma functions – infinite integral – definitions–recurrence formula of Gamma functions – properties of Beta and Gamma functions- relation between Beta and Gamma functions – Applications.

Chapter 7: Section 2.1 to 2.3 ,3, 4, 5

UNIT-V:

Geometric and Physical Applications of Integral calculus.

Chapter 2 : Section 1.1 to 1.3, 2.1,2.2

Chapter 3 : Section  1.1 to 1.3

Recommended Text

  • S.Narayanan and T.K.Manicavachagom Pillai, Calculus Volume II, S.Viswanathan (Printers&Publishers) Pvt Limited , Chennai  (2013)

Reference Books

  • Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., 2002.
  • B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007.
  • Chatterjee, Integral Calculus and Differential Equations, Tata-McGraw Hill Publishing Company Ltd.
  • P. Dyke, An Introduction to Laplace Transforms and Fourier Series, Springer Undergraduate Mathematics Series, 2001 (second edition). Chapter 6 : Section 1.1,1.2, 2.1 to 2.4
  • UNIT-IV: Beta and Gamma functions – infinite integral – definitions–recurrence formula of Gamma functions – properties of Beta and Gamma functions- relation between Beta and Gamma functions – Applications.Chapter 7: Section 2.1 to 2.3 ,3, 4, 5