1st Year Mathematics Course for BSc and BA Math

This comprehensive course equips BSc and BA Math students with essential mathematical knowledge in Analytical Geometry and Calculus. With a focus on foundational skills, it spans 24 chapters covering critical geometric, vector, and calculus concepts for theoretical and applied learning.

Course Structure

• Total Marks: 150 (BSc), 200 (BA)
• Pass Marks: 27 each for BSc and 40 Each for BA

BSc 1st year Math Syllabus

1. Analytical Geometry and Vector Analysis (Full Marks: 75, Pass Marks: 27)

Syllabus Breakdown:

1. Transformation of Coordinates
   Essential for solving complex geometrical problems.
2. Conic Sections and Their Properties
   Understand the essentials of ellipses, parabolas, and hyperbolas.
3. Polar Equations of Conics
   Express and analyze conic sections in polar coordinates.
4. General Equation of the Second Degree
   Classify conics through quadratic equations.
5. Coordinates in Three Spaces & Planes
   Explore 3D space and learn to work with planes.
6. Straight Lines
   Delve into equations of straight lines in 2D and 3D space.
7. Sphere
   Study equations and properties of spheres in three dimensions.
8. Cone & Cylinder
   Understand the geometry of cones and cylinders.
9. Central Conicoids
   Analyze geometric structures like ellipsoids and hyperboloids.
10. Product of Three or More Vectors
    Learn vector algebra to solve advanced vector analysis problems.
11. Differentiation of Vectors
    Apply vector differentiation for practical scenarios.
12. Gradient, Divergence, Curl, and Expression Formulae
    Understand core vector calculus operations for advanced problem-solving.

Exam Pattern

• Long Questions: 5 out of 6 (Each carries 7 marks, Total: 35 Marks)
• Short Questions: 10 out of 12 (Each carries 4 marks, Total: 40 Marks)

2. Calculus (Full Marks: 75, Pass Marks: 27)

Syllabus Breakdown:

1. Review of Elementary Calculus
2. Tangents and Normals
3. Higher Order Derivatives and Mean Value Theorems
4. Application of Derivatives
5. Partial Differentiation, Maxima, and Minima for Functions of 2 & 3 Variables
6. Integration and Definite Integrals
7. Beta & Gamma Functions and Reduction Formulae
8. Rectification, Quadrature, Volume, and Surface Area of Solids of Revolution
9. Double Integration
10. Vector Calculus
11. Continued Topics in Vector Calculus
12. Differential Equations of the First Order and First Degree
13. Linear Differential Equations with Constant Coefficient

Exam Pattern

• Long Questions: 5 out of 6 (Each carries 7 marks, Total: 35 Marks)
• Short Questions: 10 out of 12 (Each carries 4 marks, Total: 40 Marks)

BA 1st year Math Syllabus

1st Year Analytical Geometry (Full Marks: 100, Pass Marks: 40)

Syllabus Breakdown:

1. Transformation of Coordinates
   Study polar, cylindrical, and spherical coordinates, focusing on translation, rotation, and orthogonal transformations.
2. Conic Sections
   Derive equations for ellipses and hyperbolas, exploring tangents, normals, and properties of poles and polars.
3. General Equation of the Second Degree
   Analyze the nature of conics, focusing on tangents, asymptotes, and conic intersections.
4. Straight Lines in 3D
   Learn about space planes, skew lines, and the shortest distance between two lines.
5. Spheres
   Explore equations of spheres, intersections, and tangent planes.
6. Cones & Cylinders
   Understand conditions for conic sections and cylinders, tangent planes, and circular cones.
7. Product of Three or More Vectors
   Study scalar and vector triple products, with applications in geometry.
8. Vector Differentiation
   Examine vector function differentiation, partial derivatives, and integration.
9. Gradient, Curl, and Divergence
   Dive into vector fields and operations, focusing on physical meanings and properties.

1st Year Calculus Syllabus (Full Marks: 100, Pass Marks: 40)

The BA Calculus syllabus follows similar foundational calculus principles, with an additional focus on practical applications and exercises from recognized textbooks.

Syllabus Breakdown:

1. Review of Elementary Calculus
2. Tangents and Normals
3. Higher Order Derivatives and Mean Value Theorems
4. Application of Derivatives
5. Partial Differentiation and Maxima/Minima (Functions of 2 & 3 Variables)
6. Integration & Definite Integrals
7. Beta and Gamma Functions & Reduction Formulae
8. Applications of Definite Integrals
9. Multiple Integrals
10. Vector Calculus
11. Partial Derivatives
12. Extreme Value of a Function of Two or More Variables

Key Learning Objectives

• Gain foundational knowledge in Analytical Geometry and Calculus.
• Apply concepts in theoretical and practical scenarios, essential for BSc and BA Math.
• Prepare for final exams with model questions and live review sessions.

Course Features

• Interactive Live Sessions: Engage with instructors in real time.
• Recorded Sessions: Available for flexible revision.
• Downloadable PDF Notes: Accessible notes for every chapter.
• Model Questions and Exam Practice: Practice with focused questions.
• Live Revision Sessions: Join live sessions for exam preparation.

For further details, demo videos are available on the Hamromaster YouTube channel, or contact via WhatsApp at 9840842566 or email: sales@hamromaster.com.

This curriculum provides BSc and BA Math 1st Year students the tools to excel in both Analytical Geometry and Calculus for their respective programs.