What's Next?
Congratulations
You have completed all 15 lessons. You can now implement the core algorithms of Calculus 1 in C — from numerical limits and derivatives through Riemann sums, Simpson's rule, and volumes of revolution.
What to Explore Next
- Calculus 2 -- Integration techniques (by parts, trig substitution, partial fractions), sequences and series, Taylor series, polar coordinates
- Multivariable Calculus -- Partial derivatives, gradient, divergence, curl, multiple integrals, Stokes' theorem
- Numerical Analysis -- Adaptive step-size methods, Gaussian quadrature, spline interpolation — the professional tools built on these foundations
- Differential Equations -- Everything here feeds directly into ODEs and PDEs
Key Formulas to Remember
| Concept | Formula |
|---|---|
| Central difference | f'(x) ≈ (f(x+h) - f(x-h)) / (2h) |
| Second derivative | f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h² |
| Newton's method | xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) |
| Trapezoidal rule | h/2·[f(x₀) + 2f(x₁) + ... + 2f(xₙ₋₁) + f(xₙ)] |
| Simpson's rule | h/3·[f(x₀) + 4f(x₁) + 2f(x₂) + ... + 4f(xₙ₋₁) + f(xₙ)] |
| Volume of revolution | π ∫_a^b f(x)² dx |
References
- Calculus by James Stewart -- the standard university textbook
- Calculus Made Easy by Silvanus P. Thompson -- free, clear, and written in 1910
- Numerical Recipes in C -- the practitioner's guide to numerical algorithms