Extrema and Lagrange Multipliers

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Introduces Cartesian product and induction for proofs using integers and sets.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Covers continuous differentiability, the Bernoulli-l'Hôpital rule, and finding extrema using derivatives.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers absolute value, subtraction in integers, and comparisons between integers.

Covers the construction of integers through equivalence relations and their properties in mathematics.

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.