COURSE SUMMARY
Course Title:
Vector Calculus and Ordinary Differential Equations
Course Code:
15MAT121
Year Taught:
2015
2016
2017
2018
Semester:
2
Type:
Foundation Core
Degree:
School:
School of Engineering
Campus:
Bengaluru
Chennai
Coimbatore
Amritapuri

'Vector Calculus and Ordinary Differential Equations' is a course offered in the second semester of B. Tech. programs at School of Engineering, Amrita Vishwa Vidyapeetham.

#### SYLLABUS

Unit 1

Vector Differentiation: Vector and Scalar Functions, Derivatives, Curves, Tangents, Arc Length, Curves in Mechanics, Velocity and Acceleration, Gradient of a Scalar Field, Directional Derivative, Divergence of a Vector Field, Curl of a Vector Field. (Sections: 9.4, 9.5, 9.6, 9.9, 9.10, 9.11)

Vector Integration: Line Integral, Line Integrals Independent of Path. Green’s Theorem in the Plane (Sections: 10.1, 10.2, 10.3, 10.4).

Unit 2

Surface Integral: Surfaces for Surface Integrals, Surface Integrals, Triple Integrals – Gauss Divergence Theorem, Stoke’s Theorem. (Sections: 10.5, 10.6, 10.7, 10.9)

First Order Differential Equations: First Order ODE, Exact Differential Equations and Integrating Factors (Sections 1.1and 1.4).

Unit 3

Second Order Differential Equations: Homogeneous and non-homogeneous linear differential equations of second order (Review), Modelling: Free Oscillations,

Euler-Cauchy Equations, Solution by Undetermined Coefficients, Solution by the Method of Variation of Parameters (Sections 2.1, 2.2, 2.4, 2.5, 2.6, 2.7, 2.10).

System of Order Differential Equations: Basic Concepts and Theory, Constant Coefficient systems – Phase Plane method, Criteria for Critical Points, Stability. (Sections 4.1 – 4.4).

#### TEXTBOOK

• ‘Advanced Engineering Mathematics’, Erwin Kreyszig, John Wiley and Sons, Tenth Edition, 2015

#### REFERENCE BOOKS

• ‘Advanced Engineering Mathematics’, Dennis G. Zill and Michael R. Cullen, second edition, CBS Publishers, 2012.
• 'Calculus’, G. B. Thomas Pearson Education, 2009, Eleventh Edition.
• ‘Calculus’, Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, 3rd Edition, 2002.