Advanced Calculus/Real Analysis with the Math Sorcerer

Udemy Advanced Calculus/Real Analysis with the Math Sorcerer

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Selected Topics in Advanced Calculus/Real Analysis with tons of Beautiful Proofs:)


What you'll learn
  • Understand Advanced Mathematical Notation
  • How to Write Proofs in Advanced Calculus
  • How to Prove the Triangle, Reverse Triangle, and Bernoulli's Inequality
  • How to Prove Various Important Results Regarding Sequences
  • How to Prove the Squeeze Theorem
  • How to Prove a Sequence Converges
  • How to Prove a Sequence Diverges
  • How to Prove Results Regarding Cauchy Sequences
  • How to Prove a Sequence is Cauchy
  • How to Write a Delta Epsilon Proof
  • How to Prove a Function is Continuous
  • How to Prove a Function is Uniformly Continuous
  • How to Prove Pointwise Convergence
  • How to Prove Uniform Convergence
  • How to Prove a Function is Differentiable
  • How to Prove a Function is Not Differentiable
  • Understand the Convergence of Infinite Series
  • How to Use Dirichlet's Test
  • How to Find a Pointwise Limit
  • How to Prove Various Key Results in Advanced Calculus
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Requirements
  • Calculus 1, 2, 3, Differential equations + some proof writing experience is the typical recommendation for this material
  • A strong desire to learn higher level mathematics

Description
This is a University Level course on Selected Topics in Advanced Calculus/Real Analysis with a major focus on WRITING PROOFS:)
Note: Advanced Calculus(aka Real Analysis) is typically considered the HARDEST course a mathematics major will take.
This course is a step above a general mathematics course. Students should have familiarity with writing proofs and mathematical notation.
Basically just,
1) Watch the videos, and try to follow along with a pencil and paper, take notes!
2) Try to learn to write the proofs as I do. If you understand the proofs then you have learned a great deal. If you can write the proofs on your own then you have really graduated to the next level.
3) Repeat!
If you finish even 50% of this course you will know A LOT of Advanced Calculus and more importantly your level of mathematical maturity will go up tremendously!
Advanced Calculus is a beautiful yet notoriously difficult subject to learn and teach. I hope you enjoy watching these videos and working through these problems as much as I have:)


Who this course is for:
  • Math Majors
  • Anyone with a strong desire to learn higher level mathematics
Author
TUTProfessor
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