Name: Brilliant Differential Equations 2 BA and BSc 4th Semester PU Chandigarh
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Price: 550 INR
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Brilliant Differential Equations 2 BA and BSc 4th Semester PU Chandigarh

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Brilliant Differential Equations II by D.R. Sharma is an essential book tailored for B.Sc. 2nd-year students at Panjab University, Chandigarh. Published by Sharma Publications, this book aligns with the latest syllabus and offers a clear and concise exploration of key concepts in differential equations. With a focus on practical applications, it covers topics such as series solutions, Bessel and Legendre functions, and Laplace transforms, providing students with the necessary tools to solve complex problems.

Brilliant Differential Equations II, a meticulously crafted book by D.R. Sharma, published by Sharma Publications. Specifically designed for B.Sc. 2nd year students at Panjab University, Chandigarh, this essential resource aligns perfectly with the latest syllabus, ensuring that learners acquire the most up-to-date knowledge in this crucial area of mathematics.

This engaging and comprehensive text opens with a section on Preliminaries, providing students with the foundational concepts required to tackle more complex topics. The book progresses logically, making it suitable for both novice learners and those looking to deepen their understanding of differential equations.

Solution of Differential Equations in Series, lays the groundwork for understanding various methods to solve differential equations. With clear explanations and numerous examples, readers will gain valuable insights into series solutions, exploring the convergence and applications of power series in solving differential equations.Bessel’s Equation, Functions, and their Properties, This chapter delves into Bessel functions, which play a pivotal role in many scientific fields, including physics and engineering. D.R. Sharma elucidates the properties and applications of these functions, equipping students with practical tools for solving real-world problems.

Legendre’s Functions and their Properties, introducing readers to another set of orthogonal functions that are instrumental in mathematical physics. Concepts such as Legendre polynomials, their derivation, and applications are elaborated in a structured format, ensuring students can follow along and grasp the material effectively.Partial Differential Equations of First Order, Here, the author presents methods for solving these equations, emphasizing the importance of understanding both theory and application. This chapter serves as a bridge to even more advanced topics, making it an essential part of the curriculum.

Laplace Transforms, This section introduces the Laplace transform as a powerful technique for simplifying the process of solving linear differential equations. The author provides step-by-step instructions and illustrative examples to clarify concepts, making sure students are well-prepared to apply Laplace transforms in various scenarios.Inverse Laplace Transforms and the Convolution Theorem, topics that are critical for understanding the relationship between the time and frequency domains. D.R. Sharma presents these advanced concepts with clarity, ensuring that students can effectively grasp their significance and utility. Applications of Laplace Transforms to Solve Integral and Differential Equations, This chapter not only reinforces prior learning but also demonstrates the practicality of differential equations in various fields, making it an invaluable resource for students preparing for their careers.

Have Doubts Regarding This Product ? Ask Your Question

Q1

What is "Brilliant Differential Equations II"?

A1

"Brilliant Differential Equations II" is a book authored by D.R. Sharma, specifically designed for B.Sc. 2nd year students at Panjab University, Chandigarh. It comprehensively covers key topics in differential equations that align with the latest syllabus.
Q2

Does the book align with the current syllabus of Panjab University?

A2

Yes, the book is specifically tailored to match the syllabus requirements for B.Sc. 2nd year students at Panjab University, ensuring that learners receive up-to-date knowledge.
Q3

What teaching methods are used in the book?

A3

The book employs clear explanations, numerous examples, and step-by-step instructions to facilitate learning. It also uses structured formats to present concepts, making it suitable for both novice learners and those seeking deeper insights.
Q4

Are there practice problems included in the book?

A4

Yes, the book includes numerous examples and problems to reinforce understanding and encourage practice, allowing students to apply what they have learned.
Q5

Is there a section for revision or summary?

A5

Each chapter typically concludes with summaries or important points, enabling students to review key concepts effectively.
Q6

Is this book suitable for self-study?

A6

Yes, the structured approach and clear explanations make it suitable for self-study, provided the learner has a foundational understanding of calculus and basic differential equations.
Q7

Is this book useful for competitive examinations?

A7

Yes, the book covers foundational topics that are often included in various competitive exams, making it a valuable resource for students preparing for such assessments.
Q8

What is the quality of the illustrations and diagrams in the book?

A8

The illustrations and diagrams in the book are designed to enhance understanding of complex concepts, and they are presented clearly and in context with the related material.
Q9

Are there sections that summarize key points or formulas?

A9

Yes, each chapter typically concludes with key points, formulas, and summaries that help reinforce learning and make revision easier
Q10

Is this book beginner-friendly?

A10

Yes, the book is structured to accommodate beginners, providing foundational concepts in the preliminaries section before diving into more complex topics. Each chapter builds on the previous one, facilitating gradual learning.

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0. Preliminaries

1. Solution of Differential Equations in Series

2. Bessel’s Equation, Functions, and their Properties

3. Legendre’s Functions and their Properties

4. Partial Differential Equations of First Order

5. Laplace Transforms

6. Inverse Laplace Transforms and Convolution Theorem

7. Applications of Laplace Transforms to Solve Integral and Differential Equations

Paper II : DIFFERENTIAL EQUATIONS- II

Max. Marks : 30

Time : 3 Hours

Note: 1. The syllabus has been split into two Units: Unit-I and Unit-II. Four questions will be set

from each Unit.

2. A student will be asked to attempt five questions selecting at least two questions from each

Unit. Each question will carry 6 marks.

3. The teaching time shall be five periods (45 minutes each) per paper per week including

tutorial.

4. If internal assessment is to be conducted in the form of written examinations, then there will

be only one written examination in a Semester.

Unit-I

Series solution of differential equations-Power Series method, Bessel and Legendre equations.

Bessel functions of First and Second kind. Legendre function. Generating function. Recurrence

relation and orthogonality of Bessel and Legendre function.

Partial Differential Equations: Origin of first order Partial Differential Equations, Linear Equation of

first order, Integral surfaces passing through a given curve, surfaces orthogonal to a given system of surfaces.

Unit-II

Inverse Laplace transforms- Linearity property, Shifting properties, Change of Scale Property.

Inverse Laplace transforms of derivatives and integrals, Convolution theorem.

Applications of Laplace Transforms - Solution of differential equations with constant coefficients,

Solution of differential equations with variable coefficients, Solution of simultaneous differential equations.

Laplace Transformation-Linearity of the Laplace transformation. Existence theorem for Laplace

transformations, Shifting Theorems, Laplace transforms of derivatives and integrals, Multiplication of t ,

Division by t.