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12th Mathematics

by admin ★ 5.0 expert
10 topics
60 lessons
0 quizzes

Course Curriculum

Unit 1: Applications of Matrices and Determinants 5 items ▼
▶ Introduction 🔒 Enroll to access
▶ Inverse of a Non-Singular Square Matrix 🔒 Enroll to access
▶ Adjoint of a square Matrix 🔒 Enroll to access
▶ Properties of Inverses of matrices 🔒 Enroll to access
▶ Row-Echelon form and others 🔒 Enroll to access
Unit 2: Complex Numbers 7 items ▼
▶ Introduction to Complex Numbers 🔒 Enroll to access
▶ Powers of Imaginary unit 🔒 Enroll to access
▶ Rectangular form 🔒 Enroll to access
▶ Properties of complex numbers 🔒 Enroll to access
▶ Geometrical representation of conjugate of a complex number 🔒 Enroll to access
▶ Properties of Complex Conjugates 🔒 Enroll to access
▶ others 🔒 Enroll to access
Unit 3: Theory of Equations 5 items ▼
▶ Introduction 🔒 Enroll to access
▶ Basics of Polynomial Equations 🔒 Enroll to access
▶ Different types of Polynomial Equations 🔒 Enroll to access
▶ Quadratic Equations 🔒 Enroll to access
▶ Vieta’s Formulae and Formation of Polynomial Equations and more 🔒 Enroll to access
Unit 4: Inverse Trigonometric Functions 6 items ▼
▶ Introduction 🔒 Enroll to access
▶ Some Fundamental Concepts 🔒 Enroll to access
▶ Domain and Range of trigonometric functions 🔒 Enroll to access
▶ Graphs of functions 🔒 Enroll to access
▶ Amplitude and Period of a graph 🔒 Enroll to access
▶ Inverse functions and more 🔒 Enroll to access
Unit 5: Two Dimensional Analytical Geometry-II 7 items ▼
▶ Introduction 🔒 Enroll to access
▶ Circle, Equation of a circle in standard form 🔒 Enroll to access
▶ Conics 🔒 Enroll to access
▶ The general equation of a Conic 🔒 Enroll to access
▶ Parabola 🔒 Enroll to access
▶ Hyperbola 🔒 Enroll to access
▶ Geometric description of conic section 🔒 Enroll to access
Unit 6: Applications of Vector Algebra 6 items ▼
▶ Introduction 🔒 Enroll to access
▶ Geometric Introduction to Vectors 🔒 Enroll to access
▶ Scalar Product and Vector Product 🔒 Enroll to access
▶ Geometrical interpretation 🔒 Enroll to access
▶ Application of dot and cross products in Geometry 🔒 Enroll to access
▶ Vector triple product and more 🔒 Enroll to access
Unit 7: Applications of Differential Calculus 5 items ▼
▶ Early Developments 🔒 Enroll to access
▶ Meaning of Derivatives 🔒 Enroll to access
▶ Derivative as rate of change 🔒 Enroll to access
▶ Equations of Tangent and Normal 🔒 Enroll to access
▶ A Limit Process and more 🔒 Enroll to access
Unit 8: Differentials and Partial Derivatives 6 items ▼
▶ Introduction 🔒 Enroll to access
▶ Linear Approximation and Differentials 🔒 Enroll to access
▶ Errors: Absolute Error 🔒 Enroll to access
▶ Relative Error 🔒 Enroll to access
▶ Percentage Error 🔒 Enroll to access
▶ Differentials 🔒 Enroll to access
Unit 9: Applications of Integration 6 items ▼
▶ Introduction 🔒 Enroll to access
▶ Fundamental Theorems of Integral Calculus and their Applications 🔒 Enroll to access
▶ Improper Integrals 🔒 Enroll to access
▶ Reduction Formulae 🔒 Enroll to access
▶ Gamma Integral 🔒 Enroll to access
▶ Evaluation of Bounded Plane Area by Integration 🔒 Enroll to access
Unit 10: Ordinary Differential Equations 7 items ▼
▶ Introduction 🔒 Enroll to access
▶ Differential Equation 🔒 Enroll to access
▶ Order 🔒 Enroll to access
▶ Degree 🔒 Enroll to access
▶ Formation of Differential Equations 🔒 Enroll to access
▶ Solution of First Order and First Degree Differential Equations 🔒 Enroll to access
▶ Applications of First Order Ordinary Differential Equations 🔒 Enroll to access

About this course

Mathematics Curriculum Overview

Unit 1: Applications of Matrices and Determinants

  • Core Concepts: Introduction to matrices, Inverse of a Non-Singular Square Matrix, and Adjoint of a Square Matrix.
  • Key Topics: Properties of Inverses, Row-Echelon form, and applications of matrix operations.

Unit 2: Complex Numbers

  • Core Concepts: Introduction to Complex Numbers, Powers of the Imaginary unit, and Rectangular form.
  • Key Topics: Properties of complex numbers, Geometrical representation of conjugates, and properties of Complex Conjugates.

Unit 3: Theory of Equations

  • Core Concepts: Basics of Polynomial Equations and different types of Polynomial Equations.
  • Key Topics: Quadratic Equations, Vieta’s Formulae, and the formation of Polynomial Equations.

Unit 4: Inverse Trigonometric Functions

  • Core Concepts: Fundamental concepts, Domain, and Range of trigonometric functions.
  • Key Topics: Graphs of functions (Amplitude and Period) and the study of Inverse functions.

Unit 5: Two Dimensional Analytical Geometry-II

  • Core Concepts: Introduction to the Circle (equation in standard form) and Conics.
  • Key Topics: The general equation of a Conic, Geometric description of conic sections, Parabola, and Hyperbola.

Unit 6: Applications of Vector Algebra

  • Core Concepts: Geometric introduction to Vectors.
  • Key Topics: Scalar Product and Vector Product (Geometrical interpretation), Applications of dot/cross products in Geometry, and Vector triple product.

Unit 7: Applications of Differential Calculus

  • Core Concepts: Early developments and the meaning of Derivatives.
  • Key Topics: Derivative as a rate of change, Equations of Tangent and Normal, and Limit Processes.

Unit 8: Differentials and Partial Derivatives

  • Core Concepts: Linear Approximation and Differentials.
  • Key Topics: Error Analysis (Absolute, Relative, and Percentage Error) and Partial Derivatives.

Unit 9: Applications of Integration

  • Core Concepts: Fundamental Theorems of Integral Calculus and their Applications.
  • Key Topics: Improper Integrals, Reduction Formulae, Gamma Integral, and evaluation of Bounded Plane Area by Integration.

Unit 10: Ordinary Differential Equations

  • Core Concepts: Differential Equation order and degree.
  • Key Topics: Formation of Differential Equations, Solution of First Order/First Degree Differential Equations, and their applications.

Unit 11: Probability Distributions

  • Core Concepts: Random Variables (Discrete and Continuous) and types of Random Variables.
  • Key Topics: Cumulative Distribution Function (CDF), Continuous Distributions, and deriving Distribution functions from Probability density functions.

Unit 12: Discrete Mathematics

  • Core Concepts: Binary Operations and Mathematical Logic.
  • Key Topics: Boolean Matrices, Modular Arithmetic, Compound Statements, Logical Connectives, Truth Tables, and Duality.
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