1. Relations and Functions
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Types of relations: universal and equivalence relations, transitive, empty, reflexive, etc.
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2. Inverse Trigonometric Functions
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Types of functions: the inverse of a function, composite functions, One to one and onto functions, Binary operations, etc.
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3. Matrices
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Concept, Types of matrices, Algebra of matrices, Symmetric and skew-symmetric matrices, Addition, multiplication, scalar multiplication, properties of square matrices of order n, inverse, etc.
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4. Determinants
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Determinants of matrices of order ≥ 3, Area of a triangle, minors, co-factors, inverse and adjoint of a matrix, solving linear equations, determining consistency.
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5. Continuity and Differentiability
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Continuity, composite functions, derivative of composite functions, logarithmic, exponential, parametric functions, derivatives of second order.
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6. Applications of Derivatives
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Applications such as rate of change, increasing and decreasing functions, maxima and minima, problems based on geometric interpretations.
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7. Integrals
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Basic properties of definite integrals, Evaluation of integrals by substitution, partial fractions, and parts, Fundamental Theorem of Calculus (without proof).
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8. Applications of the Integrals
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Solving differential equations using separation of variables, interpretation, area under curves, using integrals for various applications.
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9. Differential Equations
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Definition, degree, and order, solving first-order differential equations, vector functions, direction cosines and ratios, geometric interpretations.
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10. Vector Algebra
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Types of vectors, vector addition, properties, scalar and vector products.
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11. Three Dimensional Geometry
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Direction cosines, skew lines, Cartesian equations of a line, shortest distance between two lines.
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12. Linear Programming
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Concepts like constraints, optimization, graphical method of solution for two variables, feasible and infeasible regions, bounded and unbounded solutions.
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13. Probability
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Conditional probability, independent events, Bayes' theorem, Random variables, mean, variance, multiplication theorem, total probability.
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