Analytical Geometry - BSc and BA 1st year Math Course with Free Notes
in 1st Year
Created by
Hamromaster
What you will learn?
Live Interactive Classes
Recorded Sessions
Chapter-wise PDF Notes
Model Question Papers
Past Question Papers
Solution Manuals
Live Revision Classes
Chapter Assignments
Discussion Groups
About this course
The Analytical Geometry and Vector Analysis course is a foundational subject for both BSc and BA students, designed to build strong mathematical skills and provide deep insights into the geometric and vector aspects of mathematics. Whether you're in the Physical Science stream (BSc) or pursuing Arts (BA), this course equips you with the knowledge needed to tackle both theoretical and applied problems in 2D and 3D geometry and vector calculus.
With each class, you'll have access to:
- Interactive live sessions to engage directly with instructors and clear doubts in real-time.
- Recorded sessions are available anytime, allowing you to revise Quickly
- Downloadable PDF notes for each chapter, providing a comprehensive understanding of the Topic.
- Model questions and past question papers to practice exam-relevant problems
Syllabus Breakdown:
BSc Syllabus (Full Marks: 75, Pass Marks: 27)
This course covers 12 critical chapters from the TU syllabus, including:
1. Transformation of Coordinates
Master coordinate transformations to solve complex geometrical problems.
2. Conic Sections & Their Properties
Understanding ellipses, parabolas, and hyperbolas, is essential for Analytical Geometry.
3. Polar Equations of Conics
Learn to express conic sections in polar coordinates.
4. General Equation of the Second Degree
Study quadratic equations and classify conics.
5. Coordinates in Three Spaces & Planes
Explore three-dimensional space and learn to work with planes and lines.
6. Straight Lines
Delve into equations of straight lines in 2D and 3D space.
7. Sphere
Learn the equations and properties of spheres in three-dimensional geometry.
8. Cone & Cylinder
Understand the geometry of cones and cylinders.
9. Central Conicoids
Analyze ellipsoids, paraboloids, and hyperboloids.
10. Product of Three or More Vectors
Dive into advanced vector algebra to solve vector analysis problems.
11. Differentiation of Vectors
Master vector differentiation for practical applications in physics and engineering.
12. Gradient, Divergence, Curl & Expression Formulae
Understand these core vector calculus operations for advanced problem-solving.
Question Pattern for BSc 1st Year Math (Analytical Geometry)
In the final exam, students will be required to attempt Long Questions and Short Questions following this pattern:
- Total Marks: 75
- Passing Marks: 27
Question Breakdown:
- 6 Long Questions (Each carries 7 marks)
- Attempt 5 out of 6 Long Questions
- Total marks from Long Questions: 5 x 7 = 35 Marks
- 12 Short Questions (Each carries 4 marks)
- Attempt 10 out of 12 Short Questions
- Total marks from Short Questions: 10 x 4 = 40 Marks
Overall Attempt:
You must attempt a total of 5 Long Questions and 10 Short Questions for a combined total of 75 marks.
BA Syllabus (Full Marks: 100, Pass Marks: 40)
The course syllabus includes 10 units:
- Transformation of Coordinates: Study polar, cylindrical, and spherical coordinates, and learn about translation, rotation, and orthogonal transformations.
- Conic Sections: Derive equations for ellipses and hyperbolas, and explore tangents, normals, and properties of poles and polars.
- General Equations of Second Degree: Understand the nature of conics, tangents, asymptotes, and intersections of conic sections.
- Straight Lines in 3D: Review space planes and line equations, including skew lines and the shortest distance between two lines.
- Spheres: Explore the equations of spheres, intersections, and tangent planes.
- Cones & Cylinders: Understand conditions for conic sections and cylinders, tangent planes, and circular cones.
- Product of Three or More Vectors: Learn about scalar and vector triple products and applications in geometry.
- Vector Differentiation: Study differentiation of vector functions, partial derivatives, and vector integration.
- Gradient, Curl, and Divergence: Dive into vector fields and operations, along with their physical meanings and properties.
Why Choose This Course?
- Live Classes: Engage with instructors and ask questions in real-time.
- Recorded Sessions: Revisit any session at your convenience.
- PDF Notes: Access downloadable notes for each chapter, structured to the BSc & BA 1st Year Math syllabus.
- Exam-Oriented Preparation: Practice with model and past question papers, focused on key topics like Analytical Geometry and Vector Analysis.
- Live Revision Sessions: Revise with live review classes before your exams.
This course caters to students who are aiming for excellent performance in their exams, offering everything from conceptual understanding to exam-focused revision. Whether you're tackling Analytical Geometry or advancing through Vector Analysis, you will be fully equipped to excel in both BSc and BA programs. You can Watch Demo Videos from the Course Curriculum or the Hamromaster YouTube channel for Further Details Whatsapp at 9840842566 or mail sales@hamromaster.com.
Requirements
Basic Mathematical Knowledge
Access to a Stable Internet Connection
A Computer or Mobile Device
Willingness to Practice Regularly
Interest in Geometry and Vector Analysis
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FAQ
What topics are covered in the BSc 1st Year Math (Analytical Geometry) syllabus?
This course covers 12 key chapters, including Transformation of Coordinates, Conic Sections, Polar Equations of Conics, General Equations of the Second Degree, and Vector Analysis topics such as Vector Differentiation, Gradient, Divergence, and Curl.
Are the classes live, and can I access recorded sessions?
Yes! The course includes live interactive classes, and all sessions are recorded so you can access them anytime for revision or if you miss a live session.
Will I get chapter-wise notes and question papers?
Absolutely! The course provides chapter-wise PDF notes, model questions, and past exam papers for you to practice and prepare for your final exams.
How can I join the course and access study materials?
You can join the course by contacting us through WhatsApp or email. Once enrolled, you'll get access to live classes, recorded sessions, PDF notes, and model question papers.
How does this course help me prepare for my exams?
The course is designed to follow the Tribhuvan University syllabus and focuses on exam-relevant topics. With detailed live sessions, revision classes, and practice papers, you'll be fully prepared to handle both long and short questions in your final exam.
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New Class Recordings (082 Batch)
42 Parts
Day 1 - Intro & Syllabus
489.88 MB
Day 2 - Plane
435.01 MB
Day 3 - Plane Part 2
451.09 MB
Day 4
418.81 MB
Day 5
415.81 MB
Day-6- Straight lines- Transformation of equation of line from general form to symmetrical form (1)
415.81 MB
Day-7- Straight line- angle between line and plane+ condition for a line to lie on a plane
423.19 MB
Day 8
376.43 MB
Day 9
409.34 MB
Day 10
439.01 MB
Day 11
406.02 MB
Day 12
426.37 MB
Day 13
383.87 MB
Day 14
398.67 MB
Day 15
391.39 MB
Day 16
409.87 MB
Day 17
492.73 MB
Day-18- Cone and Cylinder- Equation of line in which plane cuts the cone
437.79 MB
Day 19
384.17 MB
Day-20
437.07 MB
Day-21- Cone and Cylinder- Enveloping cone+ right circular cone
413.64 MB
Day-22
386.06 MB
Day-23- Cone and Cylinder- Central Conicoid- condition of tangency+ equation of normal+ six normal from a point
407.89 MB
Day-24
409.71 MB
Day-25- Product of three or four vector- Scalar Triple product- Introduction+ Geometrical interpretation of scalar triple product
394.2 MB
Day-26- Product of three or four vector- Vector triple product and its geometrical interpretation
395.5 MB
Day 27
377.86 MB
Day-28- Product of three or four vectors- Vector Product of four vectors
431.1 MB
Day-29- Vector Product of three or four vector- Reciprocal system of vectors
384.7 MB
Day 30
394.61 MB
Day-31- Differentiation and integration of vectors- Necessary and sufficient condition theorem
420.11 MB
Day-32
376.3 MB
Day-33- Gradient,Divergence and Curl- Definition + geometrical interpretation of gradient,curl and Divergence
379.41 MB
Day-34- Gradient, Divergence and Curl- Use of vector differential operator for product function
413.83 MB
Day-35- Gradient, Divergence and Curl- Second order differential operator
406.42 MB
Day-36- Gradient, Divergence and Curl- Examples of it
379.62 MB
Day-37- Gradient, Divergence and Curl of a vectors- Examples on it+ directional derivative
388.83 MB
Day-38- Transformation of coordinates- examples on translation and rotation
393.76 MB
Day-39- Transformation of coordinates- examples on translation and rotation
393.76 MB
Day-40- Transformation of coordinates- Invariant
360.85 MB
Day-41- The ellipse- Standard form of ellipse+ Auxilary circle
386.8 MB
Day 42
339.72 MB
The Ellipse - Conic Sections & Their Properties (2D)
6 Parts
Day-4- The ellipse-Introduction+ formula+Auxiliary circle+Eccentricity
448.97 MB
Day-5- The ellipse- Important question of solved example
381.78 MB
Day-6- The ellipse- Condition to be tangent+ equation of tangent+point of contact
382.71 MB
Day -7- The ellipse- Equation of normal+ Director circle and their example
380.77 MB
Day -8- The ellipse- Some important examples of ellipse
294.04 MB
Day -9- The ellipse-joint equation of tangent+ chord of contact+ pole and polar+ diameter+ conjugate diameter
462.79 MB
Hyperbola - Conic Section and Their Properties (2D)
3 Parts
Day-10- The hyperbola- introduction to it and formula
410.95 MB
Day -11-The hyperbola- Important examples
416.64 MB
Day-12-The hyperbola- Asymptotes of hyperbola + example
365.09 MB
Transformation of Coordinates (2D)
3 Parts
Day-1- Transformation of coordinates- introduction +examples of translation
413.45 MB
Day-2- Transformation of coordinates- proof and examples of rotation+ invariants
428.63 MB
Day-3- Transformation of coordinates- Transformation where linear term missing
291.38 MB
Polar Equation of a Conic (2D)
3 Parts
Day -13- Polar equation of a conic- equation of polar conic, directrix, tangents
422.4 MB
Day -14- polar equation of a conic- Examples of it of one kind
421.58 MB
Day -15- polar equation of a conic- important examples of it
413.05 MB
General Equation of 2nd Degree (2D)
5 Parts
Day -16- General equation of second degree- conditions for general equation of second degree to represent conic section
348.36 MB
Day -17- General equation of second degree- Find nature and position ( parabola)
509.48 MB
Day -19- General equation of second degree- Tracing curve of ellipse and hyperbola
458.22 MB
Day -20- General equation of second degree- Equation of tangent of a conic+ condition to be tangent
437.36 MB
Day-21- General equation of second degree- equation of a normal+ polar+chord of contact+ mid point of chord of a conic
408.55 MB
Coordinates in 3 Space and Plane (3D)
3 Parts
Day 22 - Coordinated in 3 Space and Plane Introduction
441.32 MB
Day 23 - Angle Between Planes & Their Examples
430.74 MB
Day 24 - Intersection of Line Between 2 Planes & Angle Between Bisecting Planes and its Examples
387.73 MB
Straight Line (3D)
6 Parts
Straight line introduction class(3d) - Day 25
106.68 MB
Some Examples of Exercise 3A of Straight Line - Day 26
401.33 MB
Transformation of Equation of Line From General Form to Symmetrical Form & its Examples - Day 27
425.03 MB
Condition for the Line to be a Coplanar in all its 3 forms - Day 28
413.49 MB
Examples of Line to be a Coplanar & Skew Lines- Day 29
480.07 MB
Shortest Distance of Skew Lines + Sphere Introduction - Day 30
411.66 MB
Sphere (3D)
5 Parts
Examples of Sphere Passing through 3 Points & Plane Section of Sphere - Day 31
400.04 MB
Equation of Tangent Plane & Its Example - Day 32
476.02 MB
Some IMP Examples of Sphere Part I - Day 33
370.45 MB
Some IMP Examples of Sphere Part II - Day 34
461.82 MB
Some IMP Examples of Sphere Part III - Day 35
358.23 MB
Cone & Cylinder (3D)
4 Parts
Cone & Cylinder Introduction and its Example - Day 36
403.33 MB
Example of Lines in which the plane cuts the Cone & Reciprocal Cone - Day 37
481.39 MB
Enveloping Cone & Right Circular Cone - Day 38
362.46 MB
Enveloping Cylinder & Right Circular Cylinder - Day 39
394.28 MB
Central Conicoid (3D)
4 Parts
Day-40 central conicoid- Introduction and equation of tangent
450.32 MB
Day-41 Central conicoid- condition of tangency+ equation of normal+ six normals from given point
412.69 MB
Day 42 central conicoid- Examples of central conicoid
393.79 MB
Day 43 Central conicoid- Examples of central conicoid
391.38 MB
Product of 3 or More Vectors (Vector Analysis)
4 Parts
Scalar Triple Product & its Properties - Day 44
407.91 MB
Vector Triple Product and Its Examples - Day 45
489.44 MB
Scalar and Vector Product of 4 Vectors - Day 46
483.36 MB
Reciprocal System of Vector & Vector Diff Introduction - Day 47
424.41 MB
Differentiation & Integration of Vector (Vector Analysis)
1 Parts
Derivatives of Vector Function & Necessary and Sufficient Condition for Vector - Class 48
497.58 MB
Gradient, Divergence & Curl (Vector Analysis)
3 Parts
Introduction to Gradient, Divergence & Curl - Day 49
405.57 MB
Use of Vector Differential Operator for Product Functions - Day 50
409.1 MB
Second Order Differential Operator - Class 51
431.98 MB
2D New Classes
28 Parts
Day-1- Transformation of coordinates- introduction +examples of translation
413.45 MB
Day-2- Transformation of coordinates- proof and examples of rotation+ invariants
428.63 MB
Day-3- Transformation of coordinates- Transformation where linear term missing
291.38 MB
Day-4- The ellipse-Introduction+ formula+Auxiliary circle+Eccentricity
448.97 MB
Day-5- The ellipse- Important question of solved example
381.78 MB
Day-6- The ellipse- Condition to be tangent+ equation of tangent+point of contact
382.71 MB
Day -7- The ellipse- Equation of normal+ Director circle and their example
380.77 MB
Day -8- The ellipse- Some important examples of ellipse
294.04 MB
Day -9- The ellipse-joint equation of tangent+ chord of contact+ pole and polar+ diameter+ conjugate diameter
462.79 MB
Day-10- The hyperbola- introduction to it and formula
410.95 MB
Day -11-The hyperbola- Important examples
416.64 MB
Day-12-The hyperbola- Asymptotes of hyperbola + example
365.09 MB
Day -13- Polar equation of a conic- equation of polar conic, directrix,tangents
422.4 MB
Day -14- polar equation of a conic- Examples of it of one kind
421.58 MB
Day -15- polar equation of a conic- important examples of it
413.05 MB
Day -16- General equation of second degree- conditions for general equation of second degree to represent conic section
348.36 MB
Day -17- General equation of second degree- Find nature and position ( parabola)
509.48 MB
Day-18-General equation of second degree- To find centre of a conic
397.53 MB
Day -19- General equation of second degree- Tracing curve of ellipse and hyperbola
458.22 MB
Day 20
437.36 MB
Day 21
408.55 MB
Day-22- central conicoid- Introduction and equation of tangent
450.32 MB
Day-23- Central conicoid- condition of tangency+ equation of normal+ six normals from given point
412.69 MB
Day 24
393.79 MB
Day 25
391.38 MB
Day-26- The sphere- Recall of important formula and examples
461.82 MB
Day -27- The sphere- some recall of examples of sphere
370.45 MB
Day-28- The sphere- Recall of examples of sphere
358.23 MB
Hyperbola
2 Parts
Hyperbola IMP Questions
314.51 MB
Hyperbola Formula and example
612.55 MB
Ellipse
2 Parts
Ellipse Theory + Example Solutions
846.32 MB
Ellipse Exercise
805.88 MB
PDF Notes
9 Parts
Coordinate in 3 Space and Plane PDF
11.25 MB
Ellipse & Hyperbola PDF
6.16 MB
General Equation of Second Degree PDF
16.15 MB
Gradient Divergence & Curl PDF
9.09 MB
Product of 3 or More Vector PDF
22.06 MB
Sphere Notes PDF
11.44 MB
Straight Line PDF
55.46 MB
Transformation of Coordinate
5.36 MB
Vector Differentiation
8.96 MB
New Class Recordings
2 Parts
Day 1
-
Day 2
-
Plane (4-7 Marks)
3 Parts
Introduction of 3D and Plane (Class 1)
441.32 MB
Angle Between Two Planes and Plane through 3 Points (Class 2)
430.74 MB
Plane Through Intersetion of Two Planes and Tier of Planes (Class 4)
387.73 MB
Straight Line (4-7 Marks)
6 Parts
Examples on Straight Line for Exercise 3A (Class 5)
401.33 MB
Transformation of the Equation of a Line and Condition for a line to lay in a Plane (Class 6)
425.03 MB
Condition for a line to be Coplanner (Class 7)
413.49 MB
Example of Coplanner (Class 7.1)
81.58 MB
Examples for a line to be coplanner and introduction to SD (Class 8)
480.07 MB
Examples on Shortage Distance and Introduction to Sphere (Class 9)
411.66 MB
Sphere
3 Parts
Examples of Exercise 4A and Plane Section of Sphere (Class 10)
400.04 MB
Example of Exercise 4(B) (Class 11)
476.02 MB
Equation of Tangent Plane and Condition of Tangency Example (Class 12)
491.48 MB
Cone & Cylinder
4 Parts
Introduction to Cone and Example of Excercise 5A (Class 13)
403.33 MB
Angle Between Line in which a Plane Cuts a Cone and Reciprocal Cone (Class 14)
481.39 MB
Enveloping Cone and Right Circular Cone (Class 15)
362.46 MB
Cylinder, Enveloping Cylinder and Right Circular Cylinder (Class 16)
394.28 MB
Product of 3 or 4 Vectors
4 Parts
Scalar triple Product and its properties (Class 17)
407.91 MB
Vector Triple Product and Its Examples (Class 18)
489.44 MB
Product of 4 Vectors (Class 19)
483.36 MB
Reciprocal Systek of Vectors and Introduction to Differentiation (Class 20)
424.41 MB
Differentiation and Integration of Vectors
1 Parts
Contiuity, Deriviability and necessary and Sufficient Condition (Class 21)
497.58 MB
Gradient, Divergence and Curl
3 Parts
Vector Integration, Gradient, Divergence and Curl (Class 22)
405.57 MB
Use of Vector, Differential Operator for Product Function (Class 23)
409.1 MB
Second Order Differential Operator (Class 24)
431.98 MB
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