CALCULUS ON METRIC SPACES
Syllabus - A. Bucki
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Mathematical Logic and Set Theory.
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Metric spaces.
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Metrics in $R$, $R^2$, and $R^3$; Equivalent metrics.
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Open Balls; Convergence.
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Continuity of Functions.
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Vector Space of Free Vectors with Applications (Review).
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Calculus.
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Differentiation of functions defined on $R^2$ and $R^3$ (Partial Differentiation;
Directional Differentiation).
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Integration of functions defined on $R^2$ and $R^3$ (Multiple Integrals).
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Some Elements of Differential Geometry (Curves, Surfaces).
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Vector Calculus.
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Integrability of functions defined on subsets of $R$; Cauchy criterion;
Fundamental Theorem of Calculus.