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SynopsisPartial derivatives. Differentiability and continuity. Linearization and differentials. The Chain Rule, Partial derivatives with constrained variables. Directional derivatives. Gradient, divergence and curl. Tangent planes. Taylor’s Theorem. Extremum problems of functions of two variables. Lagrange multipliers. Double integrals, iterated integrals and Fubini’s Theorem. Applications to areas and volumes.
Double integrals in polar form. Triple integrals, iterated integrals. Volumes and masses. Triple integrals in cylindrical and spherical coordinates forms. Substitution in multiple integrals, Jacobians.
Basic set theory. Functions, bijective functions, inverse functions. Finite and infinite sets, countable and uncountable sets. The Real Number system. Bounds, supremum and infimum. Archimedean property. Rational and irrational numbers. Properties of real numbers. Sequences of real numbers, convergence. Limit Theorems. Monotone sequences, Cauchy sequences and subsequences. Basic topology of the real line: Open and closed sets, accumulation points.
Double integrals in polar form. Triple integrals, iterated integrals. Volumes and masses. Triple integrals in cylindrical and spherical coordinates forms. Substitution in multiple integrals, Jacobians.
Basic set theory. Functions, bijective functions, inverse functions. Finite and infinite sets, countable and uncountable sets. The Real Number system. Bounds, supremum and infimum. Archimedean property. Rational and irrational numbers. Properties of real numbers. Sequences of real numbers, convergence. Limit Theorems. Monotone sequences, Cauchy sequences and subsequences. Basic topology of the real line: Open and closed sets, accumulation points.
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