Math 408: Topics in Analysis
This was an online class for the University of West Alabama in the Fall 2020 Semester. The subject matter is intermediate real analysis and brief survey of some fundamental methods in multivariate analysis. We used Introduction to Mathematical Analysis 1 by Beatriz Lafferriere, Gerardo Lafferriere and Mau Nam Nguyen. Their open-source text was quite nice for this course and it is freely available online. For example:

for textbook click here.

These were the lectures for the course, many of these are directly from the text with a little added commentary. Later in the course I used Advanced Calculus of Several Variables (Dover Books on Mathematics) Revised Edition by C. H. Edwards Jr.

Topics in Analysis (MH 4086220FA, online) Playlist on You Tube:

The Syllabus and Course Planner,

• Syllabus
• Course Planner

Lecture Notes for Topics in Analysis:

• Lecture 1: Set Theory
• Lecture 2: Relations
• Lecture 3: Functions
• Lecture 4: Cardinality
• Lecture 5: Induction
• Lecture 6: Ordered Fields
• Lecture 7: Completeness Axiom
• Lecture 8: Applications of Completness Axiom
• Lecture 9: Sequential Limits
• Lecture 10: Limit Laws
• Lecture 11: Monotone Sequences
• Lecture 12: Bolzano Weierstrauss
• Lecture 13: Limits Superior and Inferior
• Lecture 14: Topology
• Lecture 15: Limits of Functions
• Lecture 16: Limit Theorems
• Lecture 17: Continuity
• Lecture 18: Properties of Continuous Functions
• Lecture 19: Derivatives
• Lecture 20: Mean Value Theorem
• Lecture 21: Applications of Mean Value Theorem
• Lecture 22: Taylor's Theorem
• Lecture 23: Newton's Method and Contraction Mapping Theorem
• Lecture 24: Matrices
• Lecture 25: Frechet Derivative
• Lecture 26: Inverse Function Theorem, Intuitive Sketch
• Lecture 27: Eigenvectors and Quadratic Forms
• Lecture 28: Hessians and Eigenvalues

Missions from Topics in Analysis:

• Mission 1
• Solution of Mission 1 part A
• Solution of Mission 1 part B
• Mission 2
• Solution of Mission 2
• Mission 3
• Solution of Mission 3
• Mission 4
• Solution of Mission 4
• Mission 5
• Solution of Mission 5
• Mission 6
• Solution of Mission 6

Tests from Topics in Analysis:

• Test 1
• Solution of Test 1
• Test 2
• Solution of Test 2
• Test 3
• Solution of Test 3

Final Exam: (note, one of these problems is incorrect... which one ? )

• Final Exam

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Last Modified: 12-17-2020