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Nov 21, 2024
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MAT 420 - Real Analysis I Foundational theory for the analysis of real-valued functions. Topics include the real number system, sequences, continuous functions and differentiation. Prerequisites: Grade of C- or better in MAT 224 and MAT 237. Fulfills: LASR. (3 cr. hr.)
Frequency code B = offered at least once per year
Student Learning Outcomes
Upon successful completion of this course, students will be able to:
- Describe the important differences between supremum and maximum, and between infimum and minimum and prove statements involving suprema and/or infima of sets.
- Give the formal definitions of concepts such as convergence, limit, and derivative and explain them.
- Apply formal definitions to prove statements about convergence, limits, and derivatives.
- Use limit laws to determine sequence convergence, limit values, and function limits.
- Articulate with examples and counterexamples, the relationships between the various properties of sequences and functions.
- Explain the Intermediate Value Theorem, Extreme Value Theorem, the Mean Value Theorem, the first derivative test, and l'Hôpital's Rule and their reliance on continuity or differentiability.
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