Homework

The homeworks sheets are longer sets of harder questions which accompany the chapters of the course. Each sheet has a solution set available too.

• Exercise 1: Bounded sets
• Exercise 2: Rational and irrational numbers, open sets
• Exercise 3: Convergent for sequences
• Exercise 4: Convergence for sequences
• Exercise 5: Continuous functions, open and closed sets
• Exercise 6: Logarithms
• Exercise 7: Metric spaces
• Exercise 8: Subsequences and sequential compactness
• Exercise 9: Uniform continuity and compactness
• Exercise 10: Unifrom continuity and series
• Exercise 11: Series
• Exercise 12: Power series and transcendental functions
• Exercise 13: Conditional and absolute convergence
• Exercise 14: Integration

Labs

The labs are short sets of quick easier questions intended to build confidence in the techniques of analysis. They are suitable for group study sessions. Each sheet has a linked set of solutions.

• Lab 1: Ordered sets
• Lab 2: Open sets, ordered fields, and the triangle inequality
• Lab 3: Convergence of sequences
• Lab 4: Convergenece of sequences
• Lab 5: Closed subsets of reals
• Lab 6: Limit points and continuous functions
• Lab 7: Limit points, interiors, differentiable functions
• Lab 8: Limits of functions
• Lab 9: Limits of functions; open and closed sets
• Lab 10: Connected sets
• Lab 11: Compact sets
• Lab 12: Sequential compactness