Syllabus

Week 1. January 16 - 20

0.5: Real Numbers

1.1: Sequences and Convergence

Drop/Add Deadline: January 20

Week 2. January 23 - 27

1.2: Cauchy Sequences

1.3: Arithmetic Operations on Sequences

Week 3. January 30 - February 3

1.4: Subsequences and Monotone Sequences

2.1: Definition of Limit of a Function

Week 4. February 6 - 10

2.2: Limits of Functions and Sequences

2.3: Algebra of Limits

2.4: Limits of Monotone Functions

Week 5. February 13 - 17

3.1: Continuity of a Function at a Point

3.2: Algebra of Continuous Functions

Exam 1: Thursday, February 16

Week 6. February 20 - 24

3.3: Uniform Continuity

Week 7. February 27 - March 3

3.4: Properties of Continuous Functions

Week 8. March 6 - 10

4.1: The Derivative of a Function

4.2: The Algebra of Derivatives

Spring Break: March 13 - 17

Week 9. March 20 - 24

4.3: Rolle's Theorem, Mean Value Theorem

Exam 2: Thursday, March 23

Week 10. March 27 - 31

4.4: L'Hôpital's Rule, Inverse Function Theorem

Withdrawal Deadline: March 31

Week 11. April 3 - 7

5.1: The Riemann Integral

5.2: Integrable Functions

5.3: Riemann Sums

Week 12. April 10 - 14

5.4: The Fundamental Theorem of Calculus

5.5: Algebra of Integrable Functions

Week 13. April 17 - 21

5.6: Derivatives of Integrals

5.7: Mean Value Theorem, Change of Variable Theorem

Exam 3: Thursday, April 20

Week 14. April 24 - 28

6.1: Convergence of Series

6.2: Absolute Convergence, Comparison Test

6.3: Ratio Test, Root Test

6.5: Power Series

Week 15. May 1 - 2

6.6: Taylor Series, Taylor's Theorem

Final Exam: Thursday, May 4, 12:20-2:10