PRECIZE Differential Equations – I

₹295.00

The present book is strictly in accordance with the latest syllabus implemented by Panjab University, Chandigarh as per NEP 2020. It is the culmination of honest and sincere efforts on the part of the authors to meet the requirements of students who opt for mathematics at the Graduation level. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned exercises have been given in each chapter to provide the students with an opportunity of exhaustive practice. At the end of the each chapter, REVIEW OF THE CHAPTER has been introduced so that the students can revise the chapter at a glance.

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Limit and continuity of functions of two and three variables. Partial differentiation up to second order. Total differential, differentiation of composite and implicit functions. Euler’s Theorem on homogeneous functions, differentiability of real-valued functions of two and three variables. Schwarz and Young’s theorems (without proof).

Exact differential equations; Necessary and sufficient condition for a differential equation of the type M(x, y) dx + N(x ,y) dy = 0 to be exact. Integrating factor of a D.E. and methods to find it. First order and higher degree differential equations solvable for x, y, p = . Clairaut’s form and equations reducible to Clairaut’s form. Singular solution as an envelope of general solution.

Geometrical meaning of a differential equation, orthogonal trajectories. Homogeneous linear differential equations with constant coefficients and its solutions.

Theorems for finding particular integralsr. Non-homogeneous linear differential equations with constant coefficients and its solutions.

Solution of Homogenous and non Homogeneous Linear differential equations with variable coefficients – Cauchy and Legendre Equations. Exactness of Linear differential equations of nth order and solution of linear differential equations that can be made exact using integrating factor.

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