Page 68 - CatalogNEP-PS

*TUTORIAL (15 Hours (1 Hour per week))

SUGGUESTED READINGS:

1. Anton, Howard, Bivens, Irl, & Davis, Stephen (2013). Calculus (10th ed.). John Wiley &
Sons Singapore Pvt. Ltd. Reprint (2016) by Wiley India Pvt. Ltd. Delhi.
2. Prasad, Gorakh (2016). Differential Calculus (19th ed.). Pothishala Pvt. Ltd. Allahabad.
3. Ross, Kenneth A. (2013). Elementary Analysis: The Theory of Calculus (2nd ed.).
Undergraduate Texts in Mathematics, Springer. Indian reprint.
4. Apostol, T. M. (2007). Calculus: One-Variable Calculus with an Introduction to Linear
Algebra (2nd ed.). Vol. 1. Wiley India Pvt. Ltd.
5. Ghorpade, Sudhir R. & Limaye, B. V. (2006). A Course in Calculus and Real Analysis.
Undergraduate Texts in Mathematics, Springer (SIE). Indian reprint.
6. Shanti Narayan ―Differential Calculus‖ Shyam Lal Charitable Trust, Ram Nagar, New
Delhi.
7. Spectrum- Differential Calculus, Sharma Publications, Jalandhar
8. A Text Book of Calculus, S. Dinesh & Co, Jalandhar

Maths.121 Differential Equations 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:
 Ordinary and partial differential equations.
 Basic theory of higher order linear differential equations, Wronskian and its properties.
 Various techniques to find the solutions of above differential equations which provide a
basis to model complex real-world situations.

LEARNING OUTCOMES:

This course will enable the students to:
 Solve the exact, linear, Bernoulli equations, find orthogonal trajectories and solve rate
16. problems.
 Apply the method of undetermined coefficients and variation of parameters to solve linear
differential equations.
 Solve Cauchy-Euler equations and system of linear differential equations.
 Formulate and solve various types of first and second order partial differential equations.

THEORY (45 Hours)

UNIT- 1 Ordinary Differential Equations (15 Hours)

First order ordinary differential equations: Basic concepts and ideas, First order Exact differential
equations, integrating factors and rules to find integrating factors, Linear equations and Bernoulli
equations, Initial value problems, Applications of first order differential equations: Orthogonal
trajectories and Rate problems; Basic theory of higher order linear differential equations,
Wronskian and its properties.
UNIT- 2 Explicit Methods of Solving Higher-Order Linear Differential Equations(12 Hours)

Linear homogeneous equations with constant coefficients, Linear non-homogeneous equations,
Method of undetermined coefficients, Method of variation of parameters, Cauchy-Euler equations,
System of linear differential equations.

UNIT – 3 First and Second Order Partial Differential Equations (18 Hours)

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