This is the first mathematics course you will be studying in the Bachelor’s Degree Programme. The aim of this course is to develop an understanding of basic mathematical concepts and techniques that you will require for studying other mathematics courses of the programme, as well as any further study and work you undertake in mathematics. Calculus is divided into two broad areas, differential calculus and integral calculus. Broadly speaking, differential calculus is the study of change and integral calculus is about adding up the parts. Differential calculus helps you to find, for example, the effect of changing conditions on a system being investigated, and hence to gain control over the system. The process of this mathematical investigation uses the powerful technique of modelling the phenomena concerned. The models usually involve differential equations. Differential calculus is useful in formulating models and integral calculus is used to solve the differential equations associated with the model. Apart from well known applications in physics, mathematical models based on calculus are used for the study of population ecology, cybernetics, management practices, economics and medicine.
In this course on differential equations, we shall be dealing with both ordinary as well as partial differential equations. For a better understanding of the concepts in the course a good knowledge of calculus is essential. The knowledge of our calculus course BMTC-131 will more or less fulfill your this requirement. Since BMTC-131only deals with a function of one variable, to fill up the gaps, we have added contents on functions of two and more variables in this course. Accordingly, we have divided the material in this course into four blocks.
Real Analysis is the branch of mathematics that studies the structure of real numbers and the behavior of functions defined on the set of real numbers. You already have some idea of the structure of the set of real numbers, and of functions defined on it, from the 1st semester course, Calculus. In that course you were introduced to many concepts such as limit, continuity, differentiability and integrability for real-valued functions, though more from an algorithmic and computational aspect. However, when you apply the algorithms, it is important to know the logic behind them. The study of analysis provides the reasons behind these computation rules. The study will also help you to develop “analytical thinking” and the ability to apply mathematics more precisely and confidently.
Algebra is a word that you are familiar with. You may also know that it is derived from the Arabic word ‘Al-jabr’. Classically, algebra was concerned with obtaining solutions of equations. Then came ‘modern algebra’, a term used to describe detailed investigations within classical algebra. In Block 1 of the course, Calculus, you have studied some of the concepts of modern algebra – sets and operations on them, functions, a binary operation on a set, an algebraic way of studying plane geometry, properties of complex numbers, what a polynomial over R is, and solutions of some polynomial equations. In this course, we shall build on this learning, and take you much further. In this course, we will focus on ‘abstract algebra’, a generalisation of modern algebra. In abstract algebra we study algebraic systems that are defined by axioms alone. These axioms normally evolve from concrete situations. In this course, comprising four blocks, you will study three basic algebraic systems, namely, groups, rings and fields.
Linear algebra is a fundamental area in mathematics, focusing on the efficient solution of systems of linear equations. The course material introduces matrices, vector spaces, subspaces, basis and dimension, linear transformations, eigenvalues, and inner product spaces. Linear algebra deals with solving systems of linear equations, which is essential in various fields such as optimization and statistics. The concept of linearity is also crucial in differential equations, difference equations, and geometric transformations
This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods.
BHIC-131: History of India from the Earliest Times upto c. 300 CE
Course Title:
History of India from the Earliest Times upto c. 300 CE
Course Code:
BHIC-131
Coordinator:
Course Type (Credit):
null (6 Credits)
Course Introduction:
The discipline of history is a changed filed today. The historians have gone beyond studying and writing about kings, their kingdoms and personal achivements. They are moving towards new areas of enquiry and inveestigation and raising questions pertaining to various aspects and dimensions of society like how did it evolve and what changes took place ? A large amount of new data has come to light in the past three decades, leading to fresh interpretations snd prespectives in many cases. An attempet has been made in the present Course BHIC 131 : History of India from the Earliest Times up to c. 300ce to incorporate such aspects whil retaining the earlier arguments wherever valid . tThe chronological span of this Course closes before the Gupta period.
BUDC-131: Urdu Adab Mein Nasri-o-Sheri Asnaf Ka Mutala
Course Title:
Urdu Adab Mein Nasri-o-Sheri Asnaf Ka Mutala
Course Code:
BUDC-131
Coordinator:
Course Type (Credit):
Theory (6 Credits)
Course Introduction:
This course is an important component of the undergraduate curriculum, offering a comprehensive and scholarly study of the major prose and poetic genres of Urdu literature. Through it, learners not only gain familiarity with the rich prose and poetic traditions of Urdu but also develop a deeper understanding of their intellectual, artistic, and cultural dimensions. The course provides students with insightful knowledge of the historical evolution, intellectual trends, and literary diversity that define the grandeur and depth of Urdu literature.
This undergraduate-level course offers an in-depth study of classical Urdu ghazal. Through this course, learners are introduced to the art of the ghazal—its origin, development, intellectual aspects, artistic features, and linguistic beauty. It includes the study of selected ghazals by eminent classical poets such as Wali, Siraj, Mir, and Dard, who endowed Urdu ghazal with intellectual depth, artistic refinement, and emotional subtlety. The course helps students understand the structure, themes, style, and symbolic dimensions of the ghazal, while also acquainting them with its literary, cultural, and intellectual significance. Through this study, learners gain a profound understanding of the classical tradition of Urdu literature and develop a deeper appreciation of the aesthetic and intellectual continuity of the Urdu ghazal.
This undergraduate-level course offers a detailed study of the life and literary contributions of Mirza Asadullah Khan Ghalib, one of the greatest poets of Urdu literature. Through this course, learners are introduced to Ghalib’s poetic and prose writings, including his ghazals, letters, and other literary forms. The course enables students to comprehend his intellectual perspectives and creative genius.
It explores the themes, style, symbolism, imagery, and intellectual depth of Ghalib’s poetry, helping learners appreciate the philosophical reflections, mystic insights, and universal human experiences embodied in his works. This course acquaints students with the intellectual and cultural spirit of the golden age of Urdu literature, in which Ghalib’s poetry emerged as a symbol of new literary consciousness and intellectual revolution.
Chronologically, this is in continuation to the Course BHIC-131: History of India from the Earliest Times up to c. 300 CE. It gives a historical overview of major polities that emerged and made their mark during this period both in the northern and southern India: the Guptas, the Pushyabhutis followed by the Pallavas, the Pandyas, the Kalachuris, the Kadambas, the Chalukyas, the Cholas, the Hoysalas, the Rajputs, the Rashtrakutas, the Arabs, and the invasions of Mahmud Ghazni and Mohammad Ghouri. It also encapsulates economic, social and cultural history that this period exhibits, demonstrates and reflects. This applies to land holdings, revenue systems, agrarian relations, social structure, gender relations, growth and development of art, language and literature, coming up of religion and the ensuing religious trends etc. Hence, it offers an in-depth insight into the significant transition from the early historic to the early medieval period of Indian history. We need to understand and study this shift as students of Indian history. This Course covers 16 Units arranged and ordered both thematically and sequentially.
BHIE-145: Some aspects of European History: C. 1789 – 1945
Individual and Society examines the relationship between personal identity and social structures through literature. It explores how writers portray social norms, conflicts, and the individual’s role within society.
Media and Communication Skills introduces learners to the fundamentals of mass communication and media. It develops writing, presentation, and analytical skills for print, electronic, and digital media contexts.
From Language to Literature explores the transition from basic language skills to literary appreciation. It helps learners understand how language shapes meaning, style, and creativity in literary texts.
Language and Linguistics explores the scientific study of language, its structure, and use. It helps learners understand how languages function, evolve, and shape human communication.
English in Daily Life helps learners develop effective communication skills for professional settings. It focuses on writing, speaking, and interpersonal skills needed in modern workplaces.
English at the Workplace equips learners with practical language skills for professional communication. It emphasizes effective writing, speaking, and etiquette required in office and organizational settings..
The course covers the art and craft of creative writing, including modes of creative writing, writing for the media, and preparing for publication. It aims to develop students' creative and literary skills through practical exercises and critical appreciation of various writing genres.
यह पाठ्यक्रम शिक्षार्थियों को संस्कृत नाट्य साहित्य के इतिहास और नाट्यशास्त्रीय पद्धतियों तथा अभिज्ञानशाकुन्तलम् एवं प्रतिमानाटक से परिचय कराने के उद्देश्य से तैयार किया गया है।
यह पाठ्यक्रम टोडरमल के ग्रंथ “वास्तुसौख्यम्” और वास्तुशास्त्र के मूल सिद्धांतों से परिचित कराने के लिए तैयार किया गया है। यह पाठ्यक्रम वास्तुशास्त्र का परिचय, प्रमुख ग्रंथ, वास्तुपुरुष का स्वरूप, भूमि परीक्षण, दिक् साधन, निवास हेतु स्थान-निर्वाचन, गृह पर्यावरण, वृक्षारोपण, शिलान्यास विधि, पंचविध गृह, द्वार और स्तम्भ प्रमाण, मर्मस्थान और वास्तुचक्र से संबंधित महत्वपूर्ण विषयों का अध्ययन कराता है।
यह पाठ्यक्रम संस्कृत के नीति-साहित्य की प्रमुख कृतियों — हितोपदेश और चाणक्यनीति — के साथ-साथ संस्कृत गद्य और नीतिकाव्य की ऐतिहासिक परंपरा का परिचय कराता है। इसमें नीति, नैतिकता, व्यवहार-कौशल तथा शासन-संबंधी आदर्शों का अध्ययन कराया जाता है। इस पाठ्यक्रम का उद्देश्य विद्यार्थियों को संस्कृत गद्य की अभिव्यक्ति-शैली, नीति-साहित्य की शिक्षाप्रद परंपरा और उसके ऐतिहासिक विकास से अवगत कराना है।
यह पाठ्यक्रम संस्कृत भाषा की व्याकरणिक संरचना, शब्दरचना, रूपविज्ञान और वाक्यविन्यास के मूल सिद्धांतों का अध्ययन कराता है। इसमें संधि, समास, कारक, धातु, प्रत्यय आदि के नियमों का व्यवस्थित परिचय दिया गया है। इसका उद्देश्य विद्यार्थियों को संस्कृत भाषा के शुद्ध, सुबोध और व्याकरणसम्मत प्रयोग में दक्ष बनाना है।
यह पाठ्यक्रम भारतीय साहित्य में निहित राष्ट्रीय चेतना, स्वतंत्रता-भावना और सांस्कृतिक एकता के विविध रूपों का अध्ययन कराता है। इसमें यह बताया गया है कि किस प्रकार भारतीय साहित्य ने राष्ट्रीय जागरण, स्वाभिमान और सामाजिक पुनर्जागरण में महत्वपूर्ण भूमिका निभाई। इसका उद्देश्य विद्यार्थियों को साहित्य में प्रकट राष्ट्रभाव, देशप्रेम और भारतीय सांस्कृतिक मूल्यों की समझ प्रदान करना है।
यह पाठ्यक्रम मौखिक (भाषा) और अशाब्दिक (शारीरिक भाषा) संचार सहित मानव संचार के मूल सिद्धांतों से परिचित कराता है, और यह भी बताता है कि विचारों और भावनाओं के आदान-प्रदान में इनका उपयोग कैसे किया जाता है।
यह पाठ्यक्रम छात्रों को दैनिक जीवन, व्यावसायिक संचार और रचनात्मक क्षेत्रों सहित विभिन्न संदर्भों में हिंदी भाषा के विविध अनुप्रयोगों और कार्यात्मक उपयोगों की व्यापक समझ प्रदान करता है ।
