Course Detail

 Course Name Vector Calculus and Ordinary Differential Equations Course Code 15 MAT 121 Program B. Tech. (Bachelor of Technology) in Electrical and Electronics Engineering, B. Tech. in Civil Engineering, B. Tech. (Bachelor of Technology) in Aerospace Engineering, B. Tech. in Chemical Engineering, B. Tech. (Bachelor of Technology) in Mechanical Engineering, B. Tech. (Bachelor of Technology) in Computer Science and Engineering Semester Two Year Taught 2019

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).

Text Books

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

Resources

• ‘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.

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