Topics
Relations and Functions
Relations and Functions
Algebra
Inverse Trigonometric Functions
- Basics of Inverse Trigonometric Functions
- Domain, Range & Principal Value
- Graphs of Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions > Self-adjusting Property
- Properties of Inverse Trigonometric Functions > Reciprocal Property
- Properties of Inverse Trigonometric Functions > Negative Argument Property
- Properties of Inverse Trigonometric Functions > Complementary Property
- Properties of Inverse Trigonometric Functions > Conversion Property
- Properties of Inverse Trigonometric Functions > Addition & Subtraction Formula for Inverse Tangent
- Properties of Inverse Trigonometric Functions > Double-angle Property
- Properties of Inverse Trigonometric Functions > Triple-angle Property
- Properties of Inverse Trigonometric Functions > Addition–Subtraction Formula for Inverse Sine & Cosine
Calculus
Matrices
- Concept of Matrices
- Types of Matrices
- Equality of Matrices
- Operations on Matrices> Addition and Subtraction of Matrices
- Operations on Matrices>Scalar Multiplication
- Operations on Matrices> Matrix Multiplication
- Positive Integral Powers of Matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Invertible Matrices
Determinants
- Concept of Determinant
- Minors and Co-factors
- Theorems on Determinants
- Properties of Determinants
- Application of Determinants to Coordinate Geometry
- Simplification of Determinants using Properties
- Adjoint of a Matrix
- Inverse of a Square Matrix
- Singular and Non-singular Matrix
- Relations between a Matrix and its Adjoint
- Inverse of a Square Matrix
- Properties of Invertible Matrices
- Solution of System of Linear Equations
Vector Algebra
- Basic Concepts of Vector Algebra
- Direction Ratios, Direction Cosine & Direction Angles in Vector
- Types of Vectors in Algebra
- Algebra of Vectors > Addition & Subtraction of Two Vectors
- Algebra of Vectors > Scalar Multiplication
- Components of Vector in Algebra
- Section Formula in Vector Algebra
- Product of Two Vectors > Scalar (Dot) Product
- Product of Two Vectors > Vector (Cross) Product
Continuity and Differentiability
- Continuous and Discontinuous Functions
- Types of Discontinuity
- Properties of Continuous Function
- Algebra of Continuous Functions
- Concept of Differentiability
- Relationship Between Continuity and Differentiability
- Basic Rules of Differentiation
- Derivatives of Composite Functions
- Derivative of Trigonometric Function
- Derivative of Inverse Trigonometric Function
- Differentiation "ab initio" of Inverse Circular Functions
- Differentiation by Transformation/Substitution
- Differentiation of Implicit Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Differentiation with Respect to Another Function
- Higher Order Derivatives
Three - Dimensional Geometry
Linear Programming
Applications of Derivatives
- Tangents and Normals
- Approximations
- Rate Measure
- Sign of the Derivative
- Increasing and Decreasing Functions
- Maxima and Minima
- Application/Practical Problems on Maxima and Minima
Integrals
- Integration
- Standard Forms of Integrals
- Properties of Indefinite Integral
- Integration by Substitution(Change of Variable)
- Different Types of Integrals
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Some Special Integrals
- Integration Using Standard Algebraic Forms
- Integration of the form where K is Constant
- Integrals ∫√tanx dx and ∫√cot x dx
- Methods of Integration> Integration Using Partial Fraction
- Evaluation of Quadratic Equation
- Integration of Irrational Function> Type 1: Standard Radical Forms
- Integration of Irrational Function> Type 2: 1 / √(Quadratic)
- Integration of Irrational Function> Type 3: Linear / √(Quadratic)
- Integration of Irrational Function> Type 4: √(a² ± x²) and ∫√(x² − a²) dx Forms
- Integration of Irrational Function> Type 5: √(Quadratic)
- Integration of Irrational Function> Type 6: Linear × √(Quadratic)
- Integration of Irrational Function> Type 7: 1 / Linear Trigonometric Forms
- Integration of Irrational Function> Type 8: Linear Trig / Linear Trig
- Integration of Irrational Functions > Type 9: sin²x, cos²x Denominator Forms
- Fundamental Theorem of Calculus
- Evaluation of Definite Integrals
- Properties of Definite Integral
Probability
Application of Integrals
- Sketching of Curves
- Geometrical Interpretation of a Definite Integral.
- Area Under Simple Curves
- Area Bounded by Two Curves
Differential Equations
- Basic Concepts of Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Solution of a Differential Equation
- Forms of Solving Differential Equations> Variable Separable
- Forms of Solving Differential Equation>Reducible to variables separable
- Forms of Solving Differential Equations> Homogeneous Differential Equations
- Forms of Solving Differential Equations>Linear Differential Equations
- Forms of Solving Differential Equations>Linear Differential Equations
- Application of Differential Equation
left hand derivative and right hand derivative (need and concept)
Shaalaa.com | Relationship between continuity and differentiability-left hand derivative and right hand derivative
to track your progress
