MAT 601 Fundamentals of Analysis I

Fall 2023

• Exams and solutions

Fall 2022

• Exams and solutions

Fall 2021

• Exams and solutions

Fall 2019

• All exams
• All homework

Fall 2016

Exams

• Exam 1
• Exam 2
• Exam 3
• Final Exam

Homework

• HW 1.1-2: Sets, order
• HW 1.3-4: Field of real numbers
• HW 1.6: Complex numbers
• HW 1.7: Euclidean spaces
• HW 2.1: Sets, countability
• HW 2.2a: Metric spaces, part 1
• HW 2.2b: Metric spaces, part 2
• HW 2.3a: Compact sets in general metric spaces
• HW 2.3b: Compact sets in R and R^n
• HW 2.4-5: Perfect sets and connected sets
• HW 3.1: Convergence of sequences
• HW 3.2-3: Subsequences, Cauchy sequences
• HW 3.3b: Completeness
• HW 3.4: Upper/lower and infinite limits
• HW 3.5: Evaluating limits
• HW 3.6: Series
• HW 3.7: Series with positive terms
• HW 3.8: Remainder estimation, irrationality
• HW 3.9-10: Root and ratio tests; power series
• HW 3.11: Summation by parts
• HW 3.12,14: Absolute convergence; Rearrangement
• HW 3.13: Addition and multiplication of series
• HW 4.1: Limits of functions
• HW 4.2: Continuity
• HW 4.3: Continuity and Compactness
• HW 4.4: Continuity and Connectedness
• HW 4.5-6: Discontinuities, Monotone functions
• HW 5.1: The notion of derivative
• HW 5.2: Mean Value Theorems
• HW 5.3-4: Derivatives and Limits
• HW 5.5-6: Higher Derivatives and the Taylor Theorem
• HW 5.7: Derivatives of complex and vector-valued functions

Fall 2010

Exams

• Exam 1
• Exam 2
• Exam 3
• Final Exam
• Final Exam: solutions

Fall 2009

Exams

• Exam 1
• Exam 2
• Exam 3
• Final Exam