③ Real analysis

§1. Sequences in \(\mathbb{R}\)¶

Convergent sequences¶

TBD

Cauchy sequences¶

TBD

Subsequences¶

TBD

§2. Series in \(\mathbb{R}\)¶

Series¶

Convergence tests¶

Power series¶

§3. Continuity¶

Continuous functions¶

Uniform continuity¶

§4. Differentiation¶

Differentiation¶

Mean value theorem¶

L'Hôpital's rule¶

Taylor's theorem¶

§5. Integration¶

Riemann integral¶

TBD

Fundamental Theorem of Calculus¶

TBD

§7. Special functions¶

Exponential and logarithmic functions¶

Trigonometric functions¶

§8. Matrix calculus¶

Jacobian matrices¶

Hessian matrices¶

References¶

TBD