Syllabus for Math 63
This syllabus is tentative and will be updated irregularly. The homework page will be updated on the regular basis.
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Lectures |
Sections in Text |
Brief Description |
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Day 1, Monday 1/6/20 |
Chapter 1 |
Ordered sets, fields, Real field |
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Day 2, Wednesday 1/8/20 |
Chapter 1 |
Extended real number system, complex field |
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Day 3, Thursday 1/9/20 x-hour |
Chapter 1 and start Chapter 2 |
Euclidian spaces; Finite, Countable and Uncountable sets |
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Day 4, Friday 1/10/20 |
Chapter 2 |
Metric spaces and compact sets |
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Day 5, Monday 1/13/20 |
Chapter 2 |
Perfect and connected sets |
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Day 6, Wednesday 1/15/20 |
Chapter 3 |
Numerical sequences, convergent sequences, subsequences |
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Day 7, Friday 1/17/20 |
Chapter 3 |
Cauchy Sequences |
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Monday 1/20/20 MLK day Courses switched to x-hour on 1/9/20 . |
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Day 8, Wednesday 1/22/20 |
Chapter 4 |
Upper and lower limits, some special sequences |
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Day 9, Thursday 1/23/20 x-hour |
Chapter 4 |
Series, nonnegative term series |
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Day 10, Friday 1/24/20 |
Chapter 4 |
Number e, root and the ratio tests |
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Day 11, Monday 1/27/20 |
Chapter 4 |
Power series, alternating series, absolute convergence |
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Day 12, Wednesday 1/29/20 Takehome Midterm will be distributed on this day and it will be due on Monday 2/3/20 |
Chapter 4 |
Addition and multiplication of series, rearrangements |
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Day 13, Thursday 1/30/20 x-hour |
Chapter 5 |
Limits of functions and continuous functions |
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Day 14 Friday 1/31/20 |
Chapter 5 |
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Day 15, Monday 2/3/20 Midterm Exam is due |
Chapter 5 |
Intermediate value theorems and various types of discontinuities |
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Day 16, Wednesday 2/5/20 |
Chapter 5 |
Monotonic functions and limits involving infinity |
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Day 17, Thursday 2/6/20 x-hour |
Chapter 5 |
Derivative of a function of one variable, behavior of the derivative under elementary operations on functions |
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Day 18, Friday 2/7/20 |
Chapter 5 |
Mean value Theorem, L’Hopital’s rule |
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Day 19, Monday 2/10/20 |
Chapter 5 |
Higher order derivatives, Taylor Theorem |
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Day 20, Wednesday 2/12/20 |
Chapter 5 |
Taylor Theorem |
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Day 21, Thursday 2/13/20 x-hour |
Chapter 6 |
Riemann integral, partitions, refinements |
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Day 22, Friday 2/14/20
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Chapter 6 |
Important classes of integrable functions |
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Day 23, Monday 2/17/20 |
Chapter 6 |
More of the important classes of integrable functions, properties of the integral |
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Day 25, Wednesday 2/19/20 |
Chapter 6 |
Change of Variables under the integral sign |
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Day 26 Thursday 2/20/20 x-hour |
Chapter 6 |
Integration by parts and the Fundamental Theorem of Calculus |
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Day 25, Friday 2/21/20 Final Day to Withdraw from a class |
Chapter 6 |
Wrap up integration |
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Monday 2/24/20 No Class |
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Day 26, Wednesday 2/26/20 |
Chapter 7 |
Sequence and Series of functions, Examples |
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Day 27, Friday 2/28/20 |
Chapter 7 |
Uniform Convergence and continuity |
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Day 28, Monday 3/2/20 |
Chapter 7 |
Uniform Convergence and differentiation |
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Day 29 Wednesday 3/4/20 |
Chapter 7 |
Uniform Convergence and Integration |
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Day 30, Friday 3/6/20 Takehome Final Exams will be distributed on this day |
Chapter 7 |
Finish Uniform Convergence and Integration, equicontinuous families of functions. |
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Wednesday 3/11/20 Final Exam is Due |
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