Review of elementary calculus, review of functions and elementary set theory, review of non-Cartesian co-ordinate systems, multivariable calculus, vector calculus, vector fields and their properties, Green's theorem, Gauss's theorem, Stokes' theorem, formal study of intuitively obvious theorems in calculus, differentiating under the integral sign, improper integrals, functional and differential equations, PDEs and their boundary conditions, stuff about transforming PDEs like hyperbolic PDEs, Jacobians, Green's functions and integral equations, Fourier analysis and integral transforms, Cauchy formula for repeated integration.

- Intuition to some basic ideas of calculus
- Limiting cases I: the integral of
*e*^{ax} and the finite-domain Fourier transform
- Limiting cases II: repeated roots of a differential equation
- Making sense of Euler's formula
- Intuition to convergence
- Discovering the Fourier transform
- Understanding variable substitutions and domain splitting in integrals

*Resources*
- Khan Academy Calculus[
*companion*]
- The Calculus of Friendship (Steven Strogatz)[
*companion*]
- Lang, Calculus [
*textbook*]
- (to be contd.)

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