Semester 1: Syllabus B.Sc. in Mathematics Honours (CBCS): Vidyasagar University

Paper Code: C1T (Credit: 6, Full Marks: 75)

Paper Name: Calculus, Geometry and Differential Equation

Syllabus – Calculus, Geometry and Differential Equation

Unit 1

  • Hyperbolic functions
  • Higher order derivatives
  • Leibnitz rule and its applications to problems of type:
    • \(\pmb{e^{ax} + b \sin x}\)
    • \(\pmb{e^{ax} + b \cos x}\)
    • \(\pmb{(ax + b)^n \sin x}\)
    • \(\pmb{(ax + b)^n \cos x}\)
  • Concavity and inflection points
  • Envelopes
  • Asymptotes
  • Curve tracing in Cartesian coordinates
  • Tracing in polar coordinates of standard curves
  • L’Hospital’s rule
  • Applications in business, economics, and life sciences

Unit 2

  • Reduction formulae
  • Derivations and illustrations of reduction formulae of the type:
    • \(\pmb{\int \sin^n x \, dx}\)
    • \(\pmb{\int \cos^n x \, dx}\)
    • \(\pmb{\int \tan^n x \, dx}\)
    • \(\pmb{\int \sec^n x \, dx}\)
    • \(\pmb{\int (\log x)^n \, dx}\)
    • \(\pmb{\int \sin^n x \sin mx \, dx}\)
  • Parametric equations
  • Parameterizing a curve
  • Arc length of a curve
  • Arc length of parametric curves
  • Area under a curve
  • Area and volume of surface of revolution
  • Techniques of sketching conics

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

Unit 4

  • Differential equations and mathematical models
  • General, particular, explicit, implicit, and singular solutions of a differential equation
  • Exact differential equations and integrating factors
  • Separable equations and equations reducible to this form
  • Linear equation and Bernoulli equations
  • Special integrating factors and transformations

Graphical Demonstration (Teaching Aid)

  • Plotting of graphs of functions:
    • \(\pmb{e^{ax} + b}\)
    • \(\pmb{\log(ax + b)}\)
    • \(\pmb{\frac{1}{ax + b}}\)
    • \(\pmb{\sin(ax + b)}\)
    • \(\pmb{\cos(ax + b)}\)
    • \(\pmb{|ax + b|}\)
  • 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)
  • Obtaining surface of revolution of curves
  • Tracing of conics in Cartesian coordinates/polar coordinates
  • Sketching:
    • Ellipsoid
    • Hyperboloid of one and two sheets
    • Elliptic cone
    • Elliptic paraboloid
    • Hyperbolic paraboloid

Suggested Books:


Syllabus – Calculus, Geometry and Differential Equation
Calculus by G.B. Thomas and R.L. Finney

Book Name: Calculus

Author: G.B. Thomas and R.L. Finney

Year: 2005

Publisher: Pearson Education, Delhi

Buy on Amazon
Differential Equations by G.F. Simmons

Book Name: Differential Equations

Author: G.F. Simmons

Year:

Publisher: Tata McGraw Hill

Buy on Amazon
Calculus by H. Anton, I. Bivens, S. Davis

Book Name: Calculus

Author: H. Anton, I. Bivens, S. Davis

Year: 2002

Publisher: John Wiley and Sons (Asia) P. Ltd., Singapore

Buy on Amazon
Calculus by M.J. Strauss, G.L. Bradley, K. J. Smith

Book Name: Calculus

Author: M.J. Strauss, G.L. Bradley, K. J. Smith

Year: 2007

Publisher: Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Delhi

Buy on Amazon
Introductory Course in Differential Equations by D. Murray

Book Name: Introductory Course in Differential Equations

Author: D. Murray

Year:

Publisher: Longmans Green and Co.

Buy on Amazon
Introduction to Calculus and Analysis (Volumes I & II) by R. Courant and F. John

Book Name: Introduction to Calculus and Analysis (Volumes I & II)

Author: R. Courant and F. John

Year: 1989

Publisher: Springer-Verlag, New York, Inc.

Buy on Amazon
Calculus and Mathematical Analysis by S. Goldberg

Book Name: Calculus and Mathematical Analysis

Author: S. Goldberg

Year:

Publisher:

Buy on Amazon
Differential Equations by S.L. Ross

Book Name: Differential Equations

Author: S.L. Ross

Year: 2004

Publisher: John Wiley and Sons, India

Buy on Amazon
Calculus by T. Apostol

Book Name: Calculus

Author: T. Apostol

Year:

Publisher:

Buy on Amazon

Share this page


FAQs – Vidyasagar University B.Sc. Honours in <a href="https://bmlabs.co.in/notes/mathematics/">Mathematics</a>

Frequently Asked Questions (FAQs)

What is the Choice Based Credit System (CBCS)?
The Choice Based Credit System (CBCS) is an educational system that offers flexibility in the choice of courses for students. It allows students to choose from a range of courses and accumulate credits based on the courses they complete. This system promotes a more comprehensive learning experience and helps students tailor their education according to their interests and career goals.
What are the core courses for the B.Sc. Honours in Mathematics at Vidyasagar University?
The core courses for the B.Sc. Honours in Mathematics are:
  • Calculus, Geometry & Differential Equation
  • Algebra
  • Real Analysis
  • Differential Equations & Vector Calculus
  • Theory of Real Functions & Introduction to Metric Space
  • Group Theory I
  • Numerical Methods
  • Riemann Integration and Series of Functions
  • Multivariate Calculus
  • Ring Theory and Linear Algebra I
  • Partial Differential Equations & Applications
  • Group Theory II
  • Metric Spaces and Complex Analysis
  • Ring Theory and Linear Algebra II
What are the Discipline Specific Electives (DSE) available?
The Discipline Specific Electives (DSE) for the B.Sc. Honours in Mathematics include:
  • Linear Programming or Point Set Topology or Theory of Equations
  • Probability & Statistics or Boolean Algebra and Automata Theory or Portfolio Optimization
  • Mechanics or Number Theory or Industrial Mathematics
  • Mathematics Modeling or Differential Geometry or Bio Mathematics
What are the Skill Enhancement Courses (SEC) offered?
The Skill Enhancement Courses (SEC) include:
  • Object Oriented Programming in C++ or Logic & Sets
  • Graph Theory or Computer Graphics or Operating System: Linux
What is the structure of the B.Sc. Honours Mathematics program?
The B.Sc. Honours Mathematics program is structured across six semesters with Core Courses, Discipline Specific Electives (DSE), Skill Enhancement Courses (SEC), and Ability Enhancement Compulsory Courses (AECC). Each semester has a mix of theoretical and practical components, and students are evaluated through Continuous Assessment (CA) and End Semester Examination (ESE).
How many total credits are required to complete the B.Sc. Honours in Mathematics?
The total number of credits required to complete the B.Sc. Honours in Mathematics is 142 credits across all six semesters.
Can I choose courses from other disciplines?
Yes, as part of the Generic Electives (GE), you can choose courses from other disciplines based on availability and departmental regulations.
What is the role of Ability Enhancement Compulsory Courses (AECC)?
Ability Enhancement Compulsory Courses (AECC) are designed to improve students’ skills and knowledge in areas such as English and Environmental Studies. These courses are mandatory and contribute to the overall credit requirement for the degree.
How are the courses evaluated in the B.Sc. Honours Mathematics program?
Courses are evaluated through a combination of Continuous Assessment (CA) and End Semester Examination (ESE). CA includes quizzes, assignments, and projects, while ESE consists of final exams at the end of each semester.
What is the duration of the B.Sc. Honours in Mathematics program?
The B.Sc. Honours in Mathematics program is designed to be completed over three years, divided into six semesters.
Can I pursue a minor or additional specialization in the program?
The program primarily focuses on Mathematics as a major. However, students can explore additional specializations or minors depending on the availability of courses and university regulations.
Are there any research opportunities in the B.Sc. Honours program?
Research opportunities are generally available through projects and assignments in higher semesters. Students interested in research should consult with their professors or academic advisors for specific opportunities.
What are the career prospects after completing the B.Sc. Honours in Mathematics?
Graduates can pursue careers in various fields such as education, finance, data analysis, actuarial science, and more. Further studies, such as a Master’s degree or professional certifications, can also enhance career prospects.
How can I access the course materials and syllabus?
Course materials and syllabus can typically be accessed through the university’s online portal or by contacting the respective department. Ensure you are enrolled and have the necessary credentials for access.
Are there any mandatory internships or projects?
While not always mandatory, internships and project work may be encouraged or required depending on specific courses or departmental guidelines. Check the course structure and departmental requirements for detailed information.
What are the benefits of studying Mathematics at the Honours level?
Studying Mathematics at the Honours level provides a deep understanding of mathematical concepts, problem-solving skills, and analytical abilities. It prepares students for advanced studies or careers in various fields where mathematics is applied.
How can I contact academic advisors or professors?
You can contact academic advisors or professors through the university’s official communication channels, such as email or the academic department office. Make sure to follow any specified procedures for scheduling meetings or consultations.
What resources are available for students in the Mathematics program?
Resources available include textbooks, online journals, library access, research papers, and departmental seminars. Students can also benefit from study groups, tutoring services, and online educational platforms.
Are there any scholarships available for Mathematics students?
Scholarships may be available based on academic performance, financial need, or other criteria. Check with the university’s financial aid office or the Mathematics department for information on available scholarships and application procedures.
What are the prerequisites for enrolling in the B.Sc. Honours in Mathematics?
Prerequisites typically include a strong background in Mathematics from secondary education. Specific requirements may vary, so it’s best to check the admission criteria outlined by the university.
How do I apply for the B.Sc. Honours in Mathematics program?
Application procedures can be found on the university’s admissions website. Follow the outlined steps, including filling out the application form, providing necessary documents, and meeting application deadlines.
Is there a placement cell for assisting with job placements?
Many universities have a placement cell that helps students with job placements and internships. Contact the university’s career services or placement office for information on available support and resources.
What is the maximum number of credits I can take in a semester?
The maximum number of credits per semester is usually defined by the university’s academic regulations. Check the specific guidelines provided by the university or consult with an academic advisor for detailed information.
Can I switch to another major or program after enrolling?
Switching majors or programs may be possible depending on university policies and availability. Consult with the academic advisor or registrar’s office to understand the procedures and requirements for changing your program.
How can I improve my chances of academic success in this program?
To improve academic success, focus on attending classes regularly, participating actively, managing your time effectively, and seeking help from professors or peers when needed. Utilize available resources and stay organized with your study materials.
Are there any extracurricular activities related to Mathematics?
Extracurricular activities may include math clubs, competitions, seminars, and workshops. Check with the Mathematics department or student organizations for opportunities to participate in activities related to your field of study.
What should I do if I need academic assistance?
If you need academic assistance, seek help from your professors, academic advisors, or tutoring services offered by the university. Additionally, participating in study groups and utilizing online resources can be beneficial.
How is the B.Sc. Honours in Mathematics different from a general B.Sc. in Mathematics?
The B.Sc. Honours program typically involves a more in-depth study of Mathematics with a focus on core and elective courses. It often requires a higher number of credits and includes more specialized courses compared to a general B.Sc. program.
What is the policy on attendance for this program?
Attendance policies are set by the university and may vary by course. Generally, regular attendance is required to meet academic standards and avoid penalties. Check the specific attendance policy for each course in the program.
How can I provide feedback about the courses or program?
Feedback can typically be provided through course evaluations, student surveys, or directly to the department or academic advisors. Your feedback helps improve the quality of the program and the educational experience.
Scroll to Top