Math 3100 - Sequences and Series - Spring 2018

Lecture Notes


  • Preliminaries

Homework 1    (Due Wednesday the 17th of January)
Homework 1 with Solutions

  • Sequences

Homework 2    (Due Friday the 26th of January)
Homework 2 with Solutions


Homework 3    (Due Friday the 2nd of February)
Homework 3 with Solutions


Homework 4    (Due Friday the 9th of February)

Homework 4 with Solutions





  • Exam 1 Materials
    •  Exam 1   (Exam 1 with Solutions)





  • Infinite Series
    • Summary (Overview of the results we will establish) [* We did not discuss Lemma 11 - so non-examinable]
    • Definition, Notation, and Examples
      • A "Test for Divergence" and further examples
    • Series on non-negative terms
      • Direct and Limit Comparison Tests
      • Cauchy Condensation and variations on p-series [* Proof of "Cauchy Condensation" is non-examinable]
      • Ratio Test

Homework 5    (Due Monday the 26th of February)
Homework 5 with Solutions

    • Series with both positive and negative terms
      • Alternating Series Test
      • The notion of Absolute and Conditional Convergence
      • The Ratio and Root Tests
      • Cauchy Criterion and proof that absolute convergence implies convergence (two proofs)

Homework 6    (Due Friday the 2nd of March)
Homework 6 with Solutions

    • The Integral Test, Euler's constant, and the sum of the alternating harmonic series  [* We didn't discuss this - so non-examinable]
    • Rearrangements  [* We didn't discuss this - so non-examinable]




  • Power Series and Continuity
    • Power Series
      • Radius and Interval of Convergence
      • Examples
    • Definition of Continuity
    • Sequential Characterization
      • Operations with continuous functions
      • Examples of discontinuous functions


Homework 7    (Due Friday the 9th of March)

Homework 7 with Solutions





  • Exam 2 Materials
    • Exam 2   (Exam 1 with Solutions)





  • Continuity and Differentiation
    • Continuity and the Intermediate and Extreme Value Theorems
    • Functional Limits (including the Sequential Characterization)
    • Differentiation
      • Interior Extrema Theorem
      • Rolle's Theorem and the (Generalized) Mean Value Theorem
      • L'Hopital's Rule (only proved the "0/0" case)


Homework 8    (Due Friday the 6th of April)

Homework 8 with Solutions

  • Power Series and Taylor Series
    • Power Series can be differentiated (and integrated) term-by-term inside their radius of convergence 
           [* Only the proof that the original and differentiated series have the same radius of convergence is examinable]
    • Lagrangian Remainder Estimate for Maclaurin Series and Applications
    • Alternating Series Remainder Estimate
    • Examples (including approximating the derivative of a function)

Homework 9    (Due Friday the 13th of April)

Homework 9 with Solutions





  • Exam 3 Materials
    • Exam 3   (Exam 3 with Solutions)





  • Final Exam Materials