MAT 412 Introduction to Real Analysis I

Spring 2017

Exams

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

Homework

• 1.1: Review of sets
• 1.2: Proving inequalities
• 1.3a: Supremum and infimum
• 1.3b: Supremum and infimum 2
• 2.1a: Limits of sequences
• 2.1b: Properties of limits
• 2.2a: Limit theorems
• 2.2b: Infinite limits
• 2.3a: Monotone sequences
• 2.3b: Bolzano-Weierstrass theorem
• 2.4: Cauchy sequences
• 3.1a: Two-sided limits
• 3.1b: Two-sided limits with limit theorems
• 3.2: Other notions of limit: one-sided, infinite, at infinity
• 3.3a: Continuity
• 3.3b: Applications of Continuity
• 3.4a: Uniform Continuity 1
• 3.4b: Uniform Continuity 2
• 4.1: Definition of Derivative
• 4.2: Derivative Theorems
• 4.3a: Mean Value Theorem 1
• 4.3b: Mean Value Theorem 2
• 4.3c: Mean Value Theorem 3
• 4.4a: Taylor's formula
• 4.4b: L'Hopital's formula
• 4.5: Inverse Function Theorem
• 4.x: Practice using derivatives
• 5.1a: Definition of integral 1
• 5.1b: Definition of integral 2
• 5.2a: Properties of integral 1
• 5.2b: Properties of integral 2
• 5.3a: Fundamental Theorem of Calculus
• 5.3b: Change of variable; integration by parts

Spring 2016

Exams

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

Fall 2014

Exams

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