Class 12 CBSE Mathematics (Hindi)

Description

Class 12 CBSE Mathematics (Hindi) – Animated Video Course

Mathematics is often seen as a subject that requires deep understanding, logical reasoning, and application of principles to solve real-world problems. The Class 12 Mathematics course under the CBSE (Central Board of Secondary Education) curriculum is designed to provide students with the necessary skills to tackle higher education studies and competitive exams. The topics covered in this course are extensive, and mastering them is crucial for students aiming to build a strong foundation in mathematics for future careers in engineering, science, economics, and various other fields.

To make this journey more engaging and effective, an animated video course for Class 12 CBSE Mathematics has been developed, aiming to simplify complex topics through visual aids, interactive graphics, and step-by-step explanations. Here is an in-depth overview of the various topics included in the course:

1. Three Dimensional Geometry

• Overview: Three-dimensional geometry extends the principles of coordinate geometry into three dimensions. It is crucial for students pursuing advanced studies in mathematics and physics, as it is used to describe physical phenomena and spatial relationships in three-dimensional space.

• Key Topics:

  • Coordinate axes and planes in 3D space.
  • Distance formula in three dimensions to calculate the distance between two points.
  • Direction ratios and direction cosines of a line.
  • Equations of a plane and lines in 3D, along with applications.
  • Angle between two lines and angle between a line and a plane.
  • Shortest distance between two skew lines.

• Animation Elements: Interactive 3D models showcasing the position of points, lines, and planes, with animated visualizations to demonstrate the angle between them and how to calculate various parameters.

2. Integrals

• Overview: Integration is the reverse process of differentiation and is a fundamental concept in calculus. It plays a crucial role in finding areas, volumes, and solving problems involving rates of change.

• Key Topics:

  • Indefinite integrals and basic integration formulas.
  • Definite integrals and their applications.
  • Techniques of integration, such as substitution, by parts, and partial fractions.
  • Application of integrals to find areas under curves and volumes of solids of revolution.

• Animation Elements: Dynamic visualizations of integration techniques, with animated graphs showing the area under a curve, along with step-by-step breakdowns of complex integration problems.

3. Probability

• Overview: Probability is the mathematical study of random events and is an essential part of statistical analysis and decision-making processes.

• Key Topics:

  • Random experiments and sample space.
  • Probability of events and conditional probability.
  • Bayes’ Theorem and its applications.
  • Addition and multiplication theorems of probability.
  • Probability distributions, including binomial and normal distribution.

• Animation Elements: Simulations of random experiments, such as tossing a coin or rolling a dice, with real-time probability calculation and graphical representations of probability distributions.

4. Algebra of Matrices

• Overview: Matrices form an essential part of linear algebra and are used to solve systems of equations, perform transformations, and in various applications across physics and engineering.

• Key Topics:

  • Types of matrices, including row, column, square, and diagonal matrices.
  • Matrix operations, such as addition, subtraction, and multiplication.
  • Transpose of a matrix and inverse of a matrix.
  • Determinants of matrices and properties.
  • Cramer’s rule and applications of matrices in solving linear equations.

• Animation Elements: Visual demonstrations of matrix manipulations, interactive matrices showing changes with each operation, and step-by-step breakdowns of solving systems of equations using matrices.

5. Determinants

• Overview: Determinants are used to solve linear equations, calculate areas and volumes, and in finding the inverse of a matrix.

• Key Topics:

  • Properties of determinants and rules for calculation.
  • Cofactor expansion and minor of a determinant.
  • Application of determinants in solving systems of linear equations using Cramer’s rule.

• Animation Elements: Animated steps showing the calculation of determinants, with interactive examples that allow students to modify matrices and observe how the determinant changes.

6. Relations and Functions

• Overview: Relations and functions are fundamental concepts in set theory that define how elements of one set are associated with elements of another set. Understanding them is crucial for mathematical analysis.

• Key Topics:

  • Definition of relations and their properties.
  • Types of relations, including reflexive, symmetric, transitive, and equivalence relations.
  • Functions: one-to-one, onto, and bijective functions.
  • Domain, range, and codomain of a function.

• Animation Elements: Interactive Venn diagrams to visualize different relations and functions, with examples that allow students to experiment and observe how changes affect the relation.

7. Inverse Trigonometric Functions

• Overview: Inverse trigonometric functions are used to find angles when the values of trigonometric functions are known. This is essential for solving various trigonometric equations and real-world applications.

• Key Topics:

  • Definition and graph of inverse trigonometric functions such as arcsin, arccos, arctan.
  • Properties of inverse trigonometric functions.
  • Trigonometric equations involving inverse trigonometric functions.

• Animation Elements: Animated graphs showing how inverse trigonometric functions are derived and their transformations, with step-by-step examples of solving trigonometric equations.

8. Vector Algebra

• Overview: Vector algebra deals with quantities that have both magnitude and direction, and it is widely used in physics, engineering, and computer graphics.

• Key Topics:

  • Vector addition and subtraction, and scalar multiplication.
  • Dot product and cross product of vectors, along with their applications.
  • Magnitude of a vector and unit vectors.
  • Scalar and vector triple product.

• Animation Elements: 3D vector illustrations showing the addition and subtraction of vectors, with animations to demonstrate the dot and cross product calculations.

9. Application of Derivatives

• Overview: Derivatives are used to determine rates of change and solve problems related to motion, optimization, and curve sketching.

• Key Topics:

  • Application of derivatives in finding tangents and normals to curves.
  • Maxima and minima: Finding critical points and determining whether they represent maxima, minima, or points of inflection.
  • Rate of change problems in real-world scenarios.

• Animation Elements: Visual simulations of tangents and normals to curves, with interactive graphs showing how derivatives are applied to find slopes and optimize functions.

10. Tangent and Normal

• Overview: The concept of tangents and normals is crucial in calculus, as it helps in understanding the geometry of curves and solving problems related to motion and optimization.

• Key Topics:

  • Equation of a tangent and normal to a curve at a given point.
  • Geometrical interpretation of tangents and normals.
  • Applications in motion, optimization, and curve sketching.

• Animation Elements: Animated visuals showing the tangent and normal lines to a curve, with step-by-step calculations and graphical representations.

11. Differential Equations

• Overview: Differential equations describe the relationship between a function and its derivatives and have applications in various fields, including physics, biology, and economics.

• Key Topics:

  • Formation of differential equations from physical problems.
  • Methods of solving first-order and first-degree differential equations.
  • Applications of differential equations in growth and decay, motion, and electrical circuits.

• Animation Elements: Real-world scenarios demonstrating how differential equations are formulated and solved, with dynamic graphs to visualize the solutions.

12. Linear Programming

• Overview: Linear programming is a mathematical method for determining the best outcome (such as maximum profit or minimum cost) in a model with linear relationships.

• Key Topics:

  • Formulation of linear programming problems.
  • Graphical method of solving linear programming problems.
  • Simplex method for solving larger linear programming problems.

• Animation Elements: Interactive graphical visualizations showing feasible regions, constraints, and optimal solutions, along with animated solutions to various linear programming problems.

13. Continuity and Differentiability

• Overview: Continuity and differentiability are fundamental concepts in calculus, determining whether a function is smooth and whether its derivative exists at each point.

• Key Topics:

  • Definition of continuity and conditions for continuity.
  • Differentiability and its relationship to continuity.
  • Theorems such as the Mean Value Theorem and Rolle’s Theorem.

• Animation Elements: Animated graphs showing continuous and discontinuous functions, with step-by-step visualizations of differentiability and applications of theorems.

14. Application of Integrals

• Overview: Integration is used extensively in real-world problems, including calculating areas, volumes, and solving physics problems.

• Key Topics:

  • Area under curves and volume of solids of revolution.
  • Application in finding lengths of curves, surface areas, and work done in physics problems.

• Animation Elements: Interactive graphics illustrating real-world applications of integrals, such as finding the area between curves or calculating the volume of a rotating object.

This animated video course offers a comprehensive, interactive learning experience designed to help students understand and master the concepts of Class 12 CBSE Mathematics. Each topic is presented with engaging animations, clear explanations, and interactive elements to ensure that students grasp even the most complex concepts with ease. Whether students are preparing for their exams or aiming to strengthen their foundational knowledge, this course will provide the necessary tools and techniques to excel in mathematics.