Lectures in course MATH-101(c): Analysis I

Covers the basics of real analysis, including limits, sequences, and continuous functions.

Covers absolute value, density of rationals, and real line topology.

Explores convergence theorems, properties of limits, and infinite behaviors in sequences.

Explores the convergence of geometric series and their applications in real-world problems.

Covers convergence, divergence, and the Bolzano-Weierstrass theorem in sequences.

Explores complex numbers, their operations, and representations in Cartesian and polar forms.

Covers De Moivre's formula for finding roots of complex numbers and the concept of complex exponential.

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Explores the limit of the quotient for sequences and the periodicity of functions.

Covers the basics of real analysis, including functions, limits, and max/min functions.

Covers limits, continuity, and function extension by continuity, including lateral limits and infinite limits.

Explores continuity on a compact interval and its implications in limit calculations.

Explores finding the equation of the tangent line to a function's graph at a point.

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Explores derivatives, local extrema, and function variation in mathematical analysis.

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

Explores convexity, concavity, and limiting developments for functions, emphasizing extrema and derivative properties.

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Covers the calculation of limits using Taylor series and the composition of compound functions.

Explores Taylor series expansions and Riemann integrals, including limits, convergence, subdivisions, and sums.