Mathematical Analysis
Real Analysis lecture photos:
Sofia Kovalevskaya 1850 – 1891
Cathleen Morawetz 1923 -2017
I find that I may have emphasized the need to escape from the devils of mathematics to embark on the pleasures of the real world. But it works both ways, and sometimes the devils of the real world drive one into the pleasures of studying mathematics.
Mathematicians on Creativity by Peter Borwein
Mathematical Analysis
Below is a set of notes on Mathematical Analysis
Introductory CHAPTER: Mathematical Logic, Proof, and Sets
Complete Solutions to Exercise 1j
Supplementary Problems on Mathematical Induction
Complete Solutions to Supplementary Problems on Mathematical Induction
Chapter 1 : Logic and Proof
Notes on inequalities
SECTION D Inequalities Exercise 4d
Video on Inequalities Part I
Test on Inequalities
Video on Modulus Function
Video on Inequality Properties of the modulus function
Notes on Inequality Properties of the modulus function
Chapter 2 : Infinite Series
| Section A:
Introduction to Infinite Series Video on Introduction to Infinite Series |
userfiles/Introduction to Infinite Series(1).pdf | Exercise 2a | Solutions 2a |
| Section B:
Telescoping and Harmonic Series |
userfiles/Telescoping and Harmonic Series.pdf | userfiles/Exercise 2b(1).pdf | Solutions 2b |
| Section C:
Properties of Convergent and Divergent Series |
Section 2C | userfiles/Exercise 2c(1).pdf | Solutions 2c |
| Section D:
Comparison Test and p-series |
userfiles/Section 2D Comparison Test and p-series.pdf | userfiles/Exercise 2d.pdf | Solutions 2d |
| Section E:
Ratio Test |
userfiles/Section 2E Ratio Test.pdf |
Exercise 2e |
Solutions 2e |
| Section F:
Integral Test |
userfiles/Section 2F Integral Test.pdf | userfiles/Exercise 2f.pdf | Solutions 2f |
| Section G:
Alternating Series |
userfiles/Section 2G Alternating Series.pdf | userfiles/Exercise 2g.pdf | Solutions 2g |
| Section H to be added later.
Section I: Power Series |
userfiles/Section 2I Power Series.pdf | userfiles/Exercise 2i.pdf |
Notes on Pointwise and Uniform Convergence
| Sequences of Functions
Pointwise Convergence |
| Section B Uniform Convergence |
| Section C
Taylor Series and Largest Error |
Chapter 3 : Functions
| Section A
Introduction to Functions Videos on |
Chapter 3A Functions | userfiles/Exercise 3a(1).pdf |
| Section B:
Injective and Surjective Videos on |
SECTION 3B Injective and Surjective functions | userfiles/Exercise 3b(1).pdf |
| Section C:
Inverse Functions Videos |
Section 3c Inverse functions | userfiles/Exercise 3c(1).pdf |
| Section D:
Composite Functions |
userfiles/SECTION D Composite Functions.pdf | userfiles/Exercise 3d(1).pdf |
| Section E:
Properties of Composite Functions |
userfiles/SECTION E Properties of Composite Functions.pdf | userfiles/Exercise 3e(1).pdf |
| Section F:
Graphs of Functions |
userfiles/SECTION F Graphs of Functions.doc | userfiles/Exercise 3f.pdf |
Chapter 5 : Sequences and Real Numbers
| Section A:
Upper and Lower Bounds |
userfiles/Section A Upper and Lower Bounds.pdf | userfiles/Exercise 5a(1).pdf | |
| Section B:
Properties of Upper and Lower Bounds |
userfiles/5B Properties of Upper and Lower Bounds.pdf | userfiles/Exercise 5b(1).pdf | |
| Section C:
Limit of a Sequence Video on |
userfiles/Section C The Limit of a Sequence.pdf | Exercise 5c | userfiles/Complete Solutions to Exercise 5c(1).pdf |
| Section D:
Properties of the Limit of a Sequence |
Section D Properties of The Limit of a Sequence | userfiles/Exercise 5d.pdf | userfiles/Complete Solutions to Exercise 5d.pdf |
| Section E:
Evaluating Limits |
userfiles/Section E Evaluating Limits.pdf | userfiles/Exercise 5e.pdf | userfiles/Complete Solutions to Exercise 5e.pdf |
| Section F:
Monotone Sequences |
userfiles/Section F Monotone Sequences.pdf | userfiles/Exercise 5f.pdf | userfiles/Complete solutions to Exercise 5f.pdf |
| Section G:
Subsequences |
userfiles/Section G Subsequences.pdf |