Name: Precize Advanced Calculus 2 BA and BSc 4th Semester PU Chandigarh
Brand: Amit Book Depot
Price: 245 INR
Availability: InStock

Precize Advanced Calculus II, a comprehensive and essential book tailored specifically for BSc students in their second year at Panjab University, Chandigarh. Authored by esteemed scholars Rakesh Kumar, Dr. G.S. Sandhu, S.K. Gupta, and Mandeep Singh, this remarkable book aligns strictly with the latest syllabus, ensuring that learners engage with the most relevant and current material.

This book serves as an authoritative guide through the intricate world of advanced calculus, providing students with a deep appreciation of the subject's fundamental principles, theoretical underpinnings, and practical applications. Whether you’re tackling challenging coursework or preparing for exams, Precize Advanced Calculus II offers a structured approach to complex topics with clarity and precision.

The book begins with an exploration of sequences, allowing students to grasp the behavior of real sequences, their limits, and the essential distinctions between convergent, divergent, and oscillatory sequences. Through detailed explanations and illustrative examples, this section lays a vital foundation for understanding greater concepts in calculus.

As students progress through the text, they will encounter sequential continuity and uniform continuity—critical concepts in calculus that address the nuances of continuity in mathematical functions. Comprehensive discussions on these topics enhance the reader's understanding of limit processes and set the stage for deeper explorations of series and convergence.

Precize Advanced Calculus II is its rigorous treatment of infinite series. The authors meticulously dissect the characteristics and behaviors of series, equipping students with a robust set of convergence tests including the Ratio Test and Cauchy's Integral Test. This discussion doesn’t just provide theoretical knowledge; it empowers learners to effectively analyze and interpret series, a skill crucial for higher-level studies and real-world applications in fields such as engineering, physics, and computer science.

Moreover, the book offers a focus on alternating series and the principles of absolute and conditional convergence, helping students develop a nuanced understanding of series' properties. The structured review sections at the end of each topic reinforce learning and encourage a proactive approach to studying, allowing students to self-assess their comprehension and mastery of the material.

Have Doubts Regarding This Product ? Ask Your Question

Q1

What topics are covered in this book?

A1

The book covers essential topics such as sequences, continuity (sequential and uniform), infinite series, convergence tests, and alternating series. Detailed explanations and examples guide students through these concepts.
Q2

How does this book align with the latest syllabus of Panjab University?

A2

The content of Precize Advanced Calculus II is designed to strictly adhere to the latest syllabus set by Panjab University, ensuring that students study the most relevant and current material.
Q3

Who are the authors of this book?

A3

The book is authored by esteemed scholars Rakesh Kumar, Dr. G.S. Sandhu, S.K. Gupta, and Mandeep Singh.
Q4

Does the book include practice problems?

A4

Yes, the book features well-illustrated examples and practice problems to reinforce learning and help students self-assess their understanding of the material.
Q5

What is the teaching approach of the book?

A5

The authors adopt a student-friendly approach that emphasizes clarity and precision in explanations, encouraging deep engagement with each topic and fostering critical thinking.
Q6

How can this book help with exam preparation?

A6

The structured approach, comprehensive explanations, and practice problems included in the book make it an effective resource for preparing for exams and tackling challenging coursework.
Q7

Can this book be used for self-study?

A7

Absolutely! The clear explanations, examples, and review questions make it an excellent choice for students looking to study independently.
Q8

Is there a focus on real-world applications in the book?

A8

Yes, the book discusses the practical applications of advanced calculus concepts in fields such as engineering, physics, and computer science.
Q9

Can this book be beneficial for competitive exams or further studies?

A9

Yes, the rigorous treatment of advanced calculus topics and practice problems make this book a useful resource for students preparing for competitive exams and further studies in mathematics or related fields.
Q10

Are there illustrations or visual aids included in the book?

A10

Yes, the book is well-illustrated with examples and visual aids designed to enhance comprehension and make complex concepts more accessible.

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1. Sequence

1 Real Sequences

2.Bounds of Sequence

3.Convergent, Divergent and Oscillatory Sequences

4.Algebra of Limits

5.Monotonic Sequences

6.Cauchy's Theorems on Limits

7.Subsequences

8.Cauchy's Convergence Criterion

Review of the Chapter

2.Sequential Continuity and Uniform Continuity

1.Continuity

2.Sequential Continuity

3.Uniform Continuity

Review of the Chapter

3.Infinite Series

1.Infinite Series

2.Behaviour of an Infinite Series

3.Series of Non-negative Terms

4.Comparison Tests

5.Cauchy's Integral Test

6.Cauchy's Root Test

7.Ratio Test

7.1.Kummer’s Test

7.2.D’Alembert’s Ratio Test

7.3.Raabe’s Test

7.4.De Morgan’s and Bertrand’s Test

7.5.Gauss’ Test

7.6.Logarithmic Test

8.Alternating series

9.Absolute and conditional Convergence

10.Rearrangement of Terms

Review of the Chapter

Paper I: ADVANCED CALCULUS II

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.

Unit-I

Definition of a sequence, Bounds of a sequence, Convergent, divergent and oscillatory sequences,

Algebra of limits, Monotonic Sequences, Cauchy’s theorems on limits, Subsequences, Bolzano-Weierstrass

Theorem, Cauchy’s convergence criterion.

Sequential continuity and Uniform continuity of functions of single variable.

Unit-II

Series of non-negative terms. P-Test. Comparison tests. Cauchy’s integral test. Cauchy’s Root

test. Ratio tests : Kummer’s Test, D’Alembert’s test, Raabe’s test, De Morgan and Bertrand’s test, Gauss

Test, Logarithmic test. Alternating series. Leibnitz’s theorem. Absolute and conditional convergence,

Rearrangement of absolutely convergent series, Riemann’s rearrangement theorem.

1. Sequence

1 Real Sequences

2.Bounds of Sequence

3.Convergent, Divergent and Oscillatory Sequences

4.Algebra of Limits

5.Monotonic Sequences

6.Cauchy's Theorems on Limits

7.Subsequences

8.Cauchy's Convergence Criterion

Review of the Chapter

2.Sequential Continuity and Uniform Continuity

1.Continuity

2.Sequential Continuity

3.Uniform Continuity

Review of the Chapter

3.Infinite Series

1.Infinite Series

2.Behaviour of an Infinite Series

3.Series of Non-negative Terms

4.Comparison Tests

5.Cauchy's Integral Test

6.Cauchy's Root Test

7.Ratio Test

7.1.Kummer’s Test

7.2.D’Alembert’s Ratio Test

7.3.Raabe’s Test

7.4.De Morgan’s and Bertrand’s Test

7.5.Gauss’ Test

7.6.Logarithmic Test

8.Alternating series

9.Absolute and conditional Convergence

10.Rearrangement of Terms

Review of the Chapter

Have Doubts Regarding This Product ? Ask Your Question

Q1

What topics are covered in this book?

A1

The book covers essential topics such as sequences, continuity (sequential and uniform), infinite series, convergence tests, and alternating series. Detailed explanations and examples guide students through these concepts.
Q2

How does this book align with the latest syllabus of Panjab University?

A2

The content of Precize Advanced Calculus II is designed to strictly adhere to the latest syllabus set by Panjab University, ensuring that students study the most relevant and current material.
Q3

Who are the authors of this book?

A3

The book is authored by esteemed scholars Rakesh Kumar, Dr. G.S. Sandhu, S.K. Gupta, and Mandeep Singh.
Q4

Does the book include practice problems?

A4

Yes, the book features well-illustrated examples and practice problems to reinforce learning and help students self-assess their understanding of the material.
Q5

What is the teaching approach of the book?

A5

The authors adopt a student-friendly approach that emphasizes clarity and precision in explanations, encouraging deep engagement with each topic and fostering critical thinking.
Q6

How can this book help with exam preparation?

A6

The structured approach, comprehensive explanations, and practice problems included in the book make it an effective resource for preparing for exams and tackling challenging coursework.
Q7

Can this book be used for self-study?

A7

Absolutely! The clear explanations, examples, and review questions make it an excellent choice for students looking to study independently.
Q8

Is there a focus on real-world applications in the book?

A8

Yes, the book discusses the practical applications of advanced calculus concepts in fields such as engineering, physics, and computer science.
Q9

Can this book be beneficial for competitive exams or further studies?

A9

Yes, the rigorous treatment of advanced calculus topics and practice problems make this book a useful resource for students preparing for competitive exams and further studies in mathematics or related fields.
Q10

Are there illustrations or visual aids included in the book?

A10

Yes, the book is well-illustrated with examples and visual aids designed to enhance comprehension and make complex concepts more accessible.

Paper I: ADVANCED CALCULUS II

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.

Unit-I

Definition of a sequence, Bounds of a sequence, Convergent, divergent and oscillatory sequences,

Algebra of limits, Monotonic Sequences, Cauchy’s theorems on limits, Subsequences, Bolzano-Weierstrass

Theorem, Cauchy’s convergence criterion.

Sequential continuity and Uniform continuity of functions of single variable.

Unit-II

Series of non-negative terms. P-Test. Comparison tests. Cauchy’s integral test. Cauchy’s Root

test. Ratio tests : Kummer’s Test, D’Alembert’s test, Raabe’s test, De Morgan and Bertrand’s test, Gauss

Test, Logarithmic test. Alternating series. Leibnitz’s theorem. Absolute and conditional convergence,

Rearrangement of absolutely convergent series, Riemann’s rearrangement theorem.

0.00

0 Overall Rating

5

0
4

0
3

0
2

0
1

0

Try this product & share your review & thoughts