Name: Krishna Concise Course Differential Equations 2 BA and BSc 4th Semester PU
Brand: Amit Book Depot
Price: 225 INR
Availability: InStock

Differential Equations-1, authored by Sanjay Gupta and published by Krishna Brothers, serves as an essential book for BA/BSc 2nd Year students enrolled in their 3rd semester at Panjab University, Chandigarh. This comprehensive guide delves into the essential principles and applications of differential equations, making it an indispensable resource for students seeking to excel in this critical area of mathematics.

The book meticulously explores various types of differential equations, catering to the diverse academic needs of learners. Understanding these mathematical concepts is essential for students pursuing degrees in mathematics, physics, engineering, and various related disciplines. Differential Equations-1 not only aligns with the curriculum for BA/BSc 2nd Year, Semester 3 but also prepares students for advanced studies and real-world applications.

The first chapter focuses on exact differential equations, presenting a clear and thorough explanation of the theory and providing numerous examples to reinforce understanding. This section lays the groundwork for more complex topics, enabling students to grasp the foundational concepts that will be essential for their future learning.

In the subsequent chapters, readers will explore differential equations of first order and higher degree, delving into the intricacies of these equations and their solutions. The book discusses concepts like singular solutions and orthogonal solutions, enhancing students' comprehension of the varied types of problem-solving techniques involved.

Sanjay Gupta's approach to complex subjects is accessible and engaging. He meticulously details linear equations with constant coefficients and linear equations with variable coefficients, ensuring that students gain a robust understanding of the methodologies and applications relevant to these equations. The chapter on linear equations of second order builds on earlier concepts, making it easy for students to transition from one topic to another while reinforcing their learning through organized presentation.

Additionally, the examination of simultaneous differential equations prepares students for real-world applications, illustrating how systems of equations can be solved simultaneously. This is particularly beneficial for students aspiring to careers in fields that require analytical and mathematical proficiency.

Have Doubts Regarding This Product ? Ask Your Question

Q1

What topics are covered in this book?

A1

The book covers a range of topics including exact differential equations, differential equations of first order and higher degree, singular solutions, linear equations (both constant and variable coefficients), and simultaneous differential equations.
Q2

What is the educational approach of the author?

A2

Sanjay Gupta employs a clear and engaging writing style that breaks down complex concepts, making them accessible for students.
Q3

Are there practical examples included in the book?

A3

Yes, the book includes numerous practical examples and illustrative problems to enhance understanding and application of the concepts covered.
Q4

Does the book include practice problems for students?

A4

Yes, each chapter is equipped with practice problems and conceptual questions to reinforce learning and facilitate self-assessment.
Q5

How is the content structured in "Differential Equations-1"?

A5

The book is organized into distinct chapters that sequentially build on one another, reinforcing foundational knowledge before introducing more complex topics.
Q6

What is the significance of studying differential equations for students?

A6

Understanding differential equations is crucial for students in mathematics, physics, engineering, and related fields, as they are widely used in modeling real-world phenomena.
Q7

How does this book prepare students for advanced studies?

A7

The comprehensive coverage of topics equips students with the necessary foundational knowledge needed for higher-level courses in mathematics and applied fields.
Q8

Can this book help in exam preparation?

A8

Yes, the structured content, along with practice problems and clear explanations, makes it a valuable resource for exam preparation.
Q9

Is this book suitable for self-study?

A9

Yes, the clear explanations and structured approach make this book an excellent choice for self-study for students seeking to master differential equations.
Q10

What are some key features of the book?

A10

Key features include clear explanations, numerous examples, structured content, and practice problems that facilitate student engagement and comprehension.

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1.Exact differential equations

2.Differential equations of first order and higher degree

3.Singular solution

4.Orthogonal solution

5.Linear equations with constant coefficients

6.Linear equations with variable coefficients

7.Linear equations of second order

8.Simultaneous differential equations

DIFFERENTIAL EQUATIONS- II

Max. Marks: 30

Time: 3 Hours

Int. Assessment: 3 Marks

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 the first and second kind. Legendre function. Generating function. Recurrence

relation and orthogonality of Bessel and Legendre functions.

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

Division by .