Semester 1: Syllabus: B.Sc. in 4 years Mathematics Honours / Honours with Research (NEP): Vidyasagar University
Table of Contents
Semester-1
MJ-1: Calculus, Geometry and Ordinary Differential Equation
Unit 1
- Hyperbolic functions
- Higher order derivatives
- Leibnitz rule and its applications
- Concavity and inflection points
- Curvature
- Envelopes
- Asymptotes
- Curve tracing in cartesian coordinates
- Curve tracing in polar coordinates of standard curves
- L’Hospital’s rule
- Applications in business, economics and life sciences
Unit 2
Unit 3
- Reflection properties of conics
- Rotation of axes and second degree equations
- Classification of conics using the discriminant
- Polar equations of conics
- Spheres
- Cylindrical surfaces
- Central conicoids
- Paraboloids
- Plane sections of conicoids
- Generating lines
- Classification of quadrics
- Illustrations of graphing standard quadric surfaces like cone, ellipsoid
SEC 1: MATLAB-1
Unit 1
Unit 2
- Find the sum, product, max, min of a list of numbers in an array, in a sub-array without library functions
- Find a sub-matrix of the given matrix
- Find the column sum, product, max, min of the given matrix without library functions
- Find the row sum, product, max, min of the given matrix without library functions
- Define any transcendental function and then find and show the table of its functional values
- Plotting of graph of functions \( e^{ax+b} \), \( \log(ax + b) \), \( \log \frac{1}{ax + b} \), \( \sin(ax + b) \), \( \cos(ax + b) \), \( |ax + b| \) and to illustrate the effect of a and b on the graph
- Plotting the graphs of polynomial of degree 4 and 5, the derivative graph, the second derivative graph and comparing them
- Sketching parametric curves (e.g., trochoid, cycloid, epicycloids, hypocycloid)
- Tracing of conics in Cartesian coordinates/polar coordinates
- Sketching ellipsoid, hyperboloid of one and two sheets, elliptic cone, elliptic paraboloid, and hyperbolic paraboloid using Cartesian coordinates
MI-1: Calculus, Geometry and Ordinary Differential Equation
Unit 1
- Hyperbolic functions
- Higher order derivatives
- Leibnitz rule and its applications
- Concavity and inflection points
- Curvature
- Envelopes
- Asymptotes
- Curve tracing in cartesian coordinates
- Curve tracing in polar coordinates of standard curves
- L’Hospital’s rule
- Applications in business, economics and life sciences
Unit 2
Unit 3
- Reflection properties of conics
- Rotation of axes and second degree equations
- Classification of conics using the discriminant
- Polar equations of conics
- Spheres
- Cylindrical surfaces
- Central conicoids
- Paraboloids
- Plane sections of conicoids
- Generating lines
- Classification of quadrics
- Illustrations of graphing standard quadric surfaces like cone, ellipsoid
VAC-01: ENVS- Environmental Studies
Unit-I: Introduction to Environmental Studies
Unit-II: Ecosystems
Unit-III: Natural Resources: Renewable and Non-renewable Resources
- Land resources and land use change
- Land degradation, soil erosion and desertification
- Deforestation: Causes and impacts due to mining, dam building on environment, forests, biodiversity and tribal populations
- Joint forest management
- Water: Use and over-exploitation of surface and ground water, floods, droughts, conflicts over water (international & interstate)
- Energy resources: Renewable and non-renewable energy sources, use of alternate energy sources, growing energy needs, case studies
Unit-IV: Biodiversity and Conservation
- Levels of biological diversity: genetic, species and ecosystem diversity
- Bio-geographic zones of India
- Biodiversity patterns and global biodiversity hot spots
- India as a mega-biodiversity nation
- Endangered and endemic species of India
- Threats to biodiversity: Habitat loss, poaching of wildlife, man-wildlife conflicts, biological invasions
- Conservation of biodiversity: In-situ and Ex-situ conservation of biodiversity
- Ecosystem and biodiversity services: Ecological, economic, social, ethical, aesthetic and informational value
Unit-V: Environmental Pollution
Unit-VI: Environmental Policies & Practices
- Climate change, global warming, ozone layer depletion, acid rain and impacts on human communities and agriculture
- Environment Laws: Environment Protection Act; Air (Prevention & Control of Pollution) Act; Water (Prevention and control of Pollution) Act; Wildlife Protection Act; Forest Conservation Act
- International agreements: Montreal and Kyoto protocols and Convention on Biological Diversity (CBD)
- Nature reserves, tribal populations and rights, and human-wildlife conflicts in Indian context
- Environmental policy and gender issues
Unit-VII: Human Communities and the Environment
- Human population growth: Impacts on environment, human health and welfare
- Resettlement and rehabilitation of project affected persons; case studies
- Disaster management: floods, earthquake, cyclones and landslides
- Environmental movements: Chipko, Silent Valley, Bishnois of Rajasthan
- Environmental ethics: Role of Indian and other religions and cultures in environmental conservation
- Environmental communication and public awareness, case studies (e.g. CNG vehicles in Delhi)
Unit-VIII: Field Work
- Visit to an area to document environmental assets: river/ forest/ flora/fauna, etc.
- Visit to a local polluted site–Urban/Rural/Industrial/Agricultural
- Study of common plants, insects, birds and basic principles of identification
- Study of simple ecosystems–pond, river, Delhi Ridge, etc.
- Disaster management
- Coastal ecosystem
AEC-1T: Communicative English-01
1. Communication Skills
2. Listening Skills
3. Speaking Skills
4. Reading Skills
(Option-1) MDC-01T: Indian Constitution
Unit-I
Unit-II
Unit-III
(Option-2) MDC-01T: Social Value and Ethics
Unit-I
Unit-II
Unit-III
- Mind Culture
- Life and Mind
- Bio-Magnetism
- Universal Magnetism (God-Realization and Self-Realization)
- Genetic Centre
- Thought Action
- Short-Term Memory
- Expansiveness
- Thought Waves
- Channelizing the Mind
- Meditation
- Spiritual Value
- Structure of the Body
- The Three Forces of the Body
- Life-Body Relation
- Natural Causes and Unnatural Causes for Diseases
- Methods in Curing Diseases
(Option-3) MDC-01T: Sports and fitness
Unit-1
Unit-2
Unit-3
(Option-4) MDC-01T: Basics of information technology (IT)
Unit-I
Unit-II
- Role of I/O Devices in a Computer System
- Input Units: Keyboard, Terminals and Its Types
- Pointing Devices, Scanners and Its Types
- Voice Recognition Systems, Vision Input System
- Touch Screen
- Output Units: Monitors and Its Types
- Printers: Impact Printers and Its Types, Non-Impact Printers and Its Types
- Plotters: Types of Plotters
- Sound Cards, Speakers
Unit-III
- Software and Its Needs
- Types of Software
- System Software: Operating System, Utility Programs
- Programming Language: Machine Language, Assembly Language, High Level Language – Their Advantages & Disadvantages
- Application Software and Its Types: Word Processing, Spread Sheets, Presentation, Graphics, DBMS Software
Unit-IV
Unit-VI
Unit-VII
(Option-5) MDC-01T: Basics of Accounting
Unit-I
- Meaning, Importance, and Objectives of Accounting
- Concepts and Convention of Accounting
- Meaning, Users, Sources of Accounting Information
- Some Basic Terms: Transaction, Account, Asset, Liability, Capital, Expenditure, Income, Revenue, Profit, Loss
- Concept of Revenue and Capital Transactions
- Accounting Year, Financial Year
- Features of Recordable Transactions and Events
- Recording of Transactions
- Types of Accounts: Personal Account, Real Account, Nominal Account
- Golden Rules and American Approach of Accounting: Rules for Debit and Credit
- Double Entry System, Accounting Equation
- Process of Accounting: Business Transactions, Journal Entries, Ledger Posting, Trial Balance
Unit-II
Unit-III
Unit-IV
Unit-V
(Option-6) MDC-01T: NGO and its Operations
Unit 1
Unit 3
Unit 4
Unit 5
(Option-7) MDC-01T: Business Organisation
Unit–I
Unit–II
Unit–III
Unit-IV
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