- Calculus of Several Variables
The Geometry of Planes and Curves
Space Curves - an Introduction to Coordinates in 3D [ Saarth Deshpande ]
Equations of Planes and Lines [ Saarth Deshpande ]
General Parametric Curves [ Saarth Deshpande ]
Velocity and Differentiability [ Saarth Deshpande ]
Arc Length and Curvature [ Saarth Deshpande ]
The TNB Frame and Serret–Frenet Formulae [ Saarth Deshpande ]
Multivariable Functions and Partial Derivatives
Scalar Functions [ Nishan Poojary ]
Multivariable Functions [ Nishan Poojary ]
Multivariable Limits and Continuity [ Nishan Poojary ]
Partial Derivatives [ Nishan Poojary ]
Directional Derivatives [ Nishan Poojary ]
Approximations and Optimization
Critical Points [ Vaishnavi Bisht ]
The Second Derivative Test [ Vaishnavi Bisht ]
Tangent Plane Approximations [ Vaishnavi Bisht ]
Total Differential [ Vaishnavi Bisht ]
Lagrange Multipliers [ Vaishnavi Bisht ]
Integrals of Multivariable Functions
Double Integrals [ Somnath Pandit ]
Fubini's Theorem [ Somnath Pandit ]
Line Integrals [ Somnath Pandit ]
Gradient [ Padmapriya Mohan ]
Vector Fields [ Somnath Pandit ]
Div, Grad, Curl and all that
Curl and Divergence [ Padmapriya Mohan ]
Conservative Fields, Path Independance, Gradient Fields [ Padmapriya Mohan ]
$\vec F$ is conservative $\implies$ curl $\vec F = 0$ [ Padmapriya Mohan ]
The Fundamental Theorem of Line Integrals [ Somnath Pandit ]
Green's Theorem [ Padmapriya Mohan ]
Triple Integrals and Surface Integrals
- Linear Algebra
Vector Spaces
Vector Spaces [ Simran Chhattani ]
Polynomial and Functional Vector Spaces [ Simran Chhattani ]
Inner Product Spaces [ Simran Chhattani ]
Dual of a Vector Space [ Simran Chhattani ]
Basis of a Vector Space and its Subspace [ Simran Chhattani ]
Linear Transformations
Linear Transformations (Linear Maps) [ Archit Sangal ]
The Four Fundamental Subspaces [ Archit Sangal ]
Gram-Schmidt Orthogonalization Process [ Archit Sangal ]
Orthonormal Bases [ Archit Sangal ]
- Series and Transformations
Series
Power Series [ Sri Harsha G ]
Taylor Series [ Sri Harsha G ]
Transformations
Laplace Transform [ Sri Harsha G ]
Fourier Transform [ Sri Harsha G ]
Z-Transform [ Sri Harsha G ]
- Calculus
Introduction to Calculus
When Do Limits Exist? [ Aryan Singh ]
Infinite Sums In a Nutshell (Riemann Integrals) [ Aryan Singh ]
The Fundamental Theorem of Calculus [ DefaultDummy User ]
Infinite Sequences and Series [ Aryan Singh ]
The Volume and Surface Area of Gabriel's Horn [ Aryan Singh ]
How Fast am I Going? - An Introduction to Derivatives [ Aryan Singh ]
