Module 1: Basic Calculus
| Sub Topic | G.L | H.L | H.L | P.M |
| Evaluation of Improper Integrals (Type-I and Type-II). | 1.3 | 1 | ||
Beta Function (Definition and Properties). | 1 | |||
Gamma Function (Definition and Properties). | 1.1 | 1 | ||
Relationship between Beta and Gamma Functions. | 1.1 | 1.2 | 1.3 | 1 |
Applications of Definite Integrals. | 1.1 | 1.3 | 1 | |
Volumes of Solids of Revolution. | 1.1 | 1.3 | 1 | |
Areas of Surfaces of Revolution. | 1.1 | 1.3 | 1 |
Module 2: Single-variable Calculus (Differentiation)
| Sub Topic | G.L | H.L | H.L | P.M |
Taylor’s and Maclaurin’s theorem for a function of one variable | 2.1 | 2.3 | 2 | |
Taylor’s and Maclaurin’s series of a function using statement of the theorems | 2.1 | 2.3 | 2 | |
Extreme values of functions | 2.1 | 2.2 | 2.3 | 2 |
Indeterminate forms and L' Hospital's rule | 2.3 | 2 |
Module 3: Sequences and series
| Sub Topic | G.L | H.L | H.L | P.M |
Convergence and Divergence of Sequences. | 3.1 | 3.2 | 3.3 | 3 |
Convergence and Divergence of Infinite Series. | 3.1 | 3.3 | 3 | |
Tests for Convergence/Divergence: | 3.1 | 3.2 | 3 | |
Telescoping Series | 3.1 | 3.2 | 3.3 | 3 |
Geometric Series Test | 3.1 | 3.3 | 3 | |
p-Series Test | 3.2 | 3.3 | 3 | |
integral Test | 3.1 | 3.2 | 3.3 | 3 |
Comparison Test | 3.3 | 3 | ||
Limit Comparison Test | 3.1 | 3.2 | 3.3 | 3 |
D’Alembert’s Ratio Test | 3.3 | 3 | ||
Cauchy’s Root Test | 3.3 | 3 | ||
Alternating Series Test | 3.2 | 3.3 | 3 | |
Absolute vs. Conditional Convergence. | 3.2 | 3.3 | 3 | |
Power Series. | 3.1 | 3.2 | 3.3 | 3 |
Radius and Interval of Convergence. | 3.2 | 3.3 | 3 |
Module 4: Multivariable Calculus (Differentiation)
| Sub Topic | G.L | H.L | H.L | P.M |
Functions of Several Variables. | 4.1 | 4.2 | 4.3 | 4 |
Limits and Continuity. | 4.2 | 4 | ||
Partial Derivatives. (1-2 Order) | 4.3 | 4 | ||
Mixed Derivative Theorem (Clairaut’s Theorem). | 4.1 | 4.2 | 4.3 | 4 |
Total Derivative and Differentiability. | 4.1 | 4.2 | 4.3 | 4 |
Chain Rule. | 4.1 | 4.3 | 4 | |
Gradient Vector. | 4.3 | 4 | ||
Directional Derivatives. | 4.3 | 4 | ||
Tangent Planes and Normal Lines to a Surface. | 4.3 | 4 | ||
Local Extreme Values (Maxima, Minima). | 4.3 | 4 | ||
Saddle Points. | 4.1 | 4.2 | 4.3 | 4 |
Method of Lagrange Multipliers (for Constrained Optimization). | 4 |
Module 5: Multivariable Calculus (Integration)
| Sub Topic | G.L | H.L | H.L | P.M |
Double Integrals (over Rectangular and General Regions). | 5.1 | 5.2 | 5.3 | 5 |
Change of Order of Integration. | 5.1 | 5.2 | 5.3 | 5 |
Double Integrals in Polar Coordinates. | 5.1 | 5.2 | 5.3 | 5 |
Applications of Double Integrals (Area, Volume). | 5.1 | 5.2 | 5.3 | 5 |
Triple Integrals (in Rectangular) | 5.1 | 5.2 | 5.3 | 5 |
Triple Integrals (in Cylindrical) | 5.1 | 5.2 | 5.3 | 5 |
Triple Integrals (in Spherical Coordinates). | 5.1 | 5.2 | 5.3 | 5 |
Applications of Triple Integrals (Volume, Mass, Center of Mass/Gravity). | 5.1 | 5.2 | 5.3 | 5 |
Module-5 All ST in One | Part-1 | Part-2 | Part-3 | 5 |