Mat 215

Assignments

Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Practice Midterm [Solutions]
Midterm Solutions
Problem Set 6
Problem Set 7
Problem Set 8
Problem Set 9
Problem Set 10
Practice Final [Solutions]
Final Solutions

Recordings

2/22-Cauchy Sequences and Series
2/22-Series Tests and Functional Limits

Schedule

Introduction, Set Theory, Functions, Sections 1.1-1.2
Natural Numbers, Rationals, Real Number Axioms, Sections 1.3-1.4
Cardinality, Sections 1.5-1.6
Topology of the Reals, Open Sets, Closed sets, Section 3.2
Compact Sets, Section 3.3
Connected Sets, Section 3.4
Sequences, Monotone Convergence Sections 2.2-2.4
Bolzano-Weierstrass, Cauchy Sequences, Sections 2.5-2.6
Series, Double Summation, Sections 2.7-2.8
Construction of the Reals
Continuous Functions, Section 4.3
Extreme Value Theorem, Intermediate Value Theorem, Sections 4.4-4.5
Differentiation, Section 5.2
Properties of Derivatives, Section 5.3
Riemann integral, Sections 7.2-7.4
Fundamental Theorem of Calculus, Section 7.5
Sequences of Functions, Sections 6.2-6.3
Series of Functions and Power Series, Sections 6.4-6.5
Taylor's Theorem, Sections 6.6-6.7