Daniel An's Youtube Lectures Organized as Playlists

Calculus 1 (Math 101)

  1. Review: Function Theory
  2. Review: Exponential and Logarithmic Functions
  3. Review: Trigonometry
  4. Evaluating Limits numerically or graphically
  5. Evaluating limits algebraically
  6. Continuity of a function
  7. The tangent line problem and limit definition of the derivative
  8. Basic differentiation rules
  9. Graph of the derivative
  10. Differentiation: The product rule and the quotient rule
  11. Differentiation: The chain rule
  12. Rectilinear motion and higher derivatives
  13. More chain rule practice
  14. Implicit differentiation
  15. Related rates
  16. Extrema and critical numbers
  17. Concavity and the 2nd derivative test
  18. Limits at infinity
  19. Curve Sketching
  20. Optimization
  21. Midterm Review
  22. Antiderivatives and particular solutions
  23. Calculus I Final Exam Review
  24. More Optimization Questions (Calculus I)
  25. More Related Rates (Calc 1)

Calculus 2 (Math102)

  1. Introduction to integral calculus
  2. u-substitution method for integration
  3. How to integrate trigonometric functions
  4. Integration by parts and tabular integration
  5. More integration techniques and examples
  6. Sigma notation and Riemann sum
  7. Area and second fundamental theorem of calculus
  8. Volume and arc length by integration
  9. Mass, center of mass and moment of inertia using integration
  10. Trig substitution and partial fraction decomposition for integration
  11. L'hopital's rule and improper integrals
  12. Introduction to sequences and infinite series
  13. Maclaurin series and Taylor series
  14. Tests for convergence and divergence of infinite series

Calculus 2 (Math102, older course. Some lectures on infinite series are missing. )

  1. Antiderivatives and Indefinite Integrals
  2. Riemann Sum and Approximation of Integrals
  3. Fundamental Theorem of Calculus and Definite Integrals
  4. Geometric Series and Telescoping Series
  5. Integration by Parts and Tabular Integration
  6. Integration by u substitution
  7. Partial Fraction Expansion and Integral of Rational Functions
  8. More Integrals
  9. Integration and Area
  10. Integration and Volume
  11. L'Hospitals Rule
  12. Infinite Series and Taylor Series 1
  13. Infinite Series and Taylor Series 2
  14. Math102Exam4 review
  15. Math102 Final Exam Review

Calculus 3 (Multivariable Calculus, Math 211)

  1. Vectors and Operations
  2. Basic Complex Number Calculations
  3. Matrix basics
  4. Lines and Planes in Space
  5. Curves and Vector Valued Functions
  6. Multivariable Functions
  7. Directional Derivative and the Gradient
  8. Extrema of Multivariable Functions
  9. Lagrange Multipliers
  10. Double Integrals
  11. Polar Coordinates and Integration
  12. Triple Integrals in Cartesian Cylindrical and Spherical Coordinates
  13. Vector Fields and Line Integrals
  14. Conservative Vector Fields
  15. Understanding and Using Greens Theorem
  16. Integration over Surfaces
  17. Calculus III Final Exam Review

Differential Equations

For these lectures, please also download my free ebook at http:/bit.ly/diffeqbook

  1. Introduction to Differential Equations
  2. Separable Differential Equations and Applications
  3. Linear first order differential equations
  4. Exact Differential Equations
  5. Linear independence of solutions
  6. Second order linear differential equations (constant coefficient and homogenous)
  7. Method of undetermined coefficients
  8. Variation of parameters
  9. Mechanical vibrations
  10. Power series solutions of ODE
  11. Frobenius method
  12. System of differential equations
  13. Differential Equations Midterm Review
  14. Fourier Series
  15. Fourier sine and cosine series + endpoint value problems
  16. Enpoint Value Problems
  17. Partial Differential Equations and Separation of Variables
  18. Laplace transforms and its use in solving differential equations
  19. Endpoint Value Problems and Trig integrals
  20. Fourier Sine and Cosine Series
  21. Laplace transforms
  22. Solving Differential Equations Using Laplace Transforms
  23. Final Exam Review
  24. DiffEq Misc

Machine Learning

  1. [Machine Learning] (https://www.youtube.com/playlist?list=PLP1OdTlavJNuA_qvG6xNWqAKxfN1HG2sG)

Partial Differential Equations (MAT 341 Applied Real Analysis, Stony Brook University)

  1. Introduction to PDEs
  2. Fourier Series for PDEs
  3. Fourier Sine and Cosine Series
  4. Basic Sturm Liouville Problems
  5. Heat Equation PDE and Separation of Variables
  6. PDE Laplace Equation and separation of variables
  7. Gaussian Integrals and Heat Kernel
  8. Bessel Functions
  9. Laplace PDE and Wave equation on a disk
  10. Uniqueness and Other Theorems of PDEs
  11. Legendre functions and Laplace PDE in spherical coordinates
  12. In-depth look at Sturm-Liouville problems

Applied Calculus 1 (Business Calculus, Math 111)

  1. Review: Lines and functions
  2. Review: Exponentials and Logarithms
  3. An introduction to limits
  4. Finding Limits Analytically
  5. Continuity and Limits Involving Infinity
  6. Instantaneous Rates of Change: Definition of Derivative
  7. Differentiation Rules
  8. Chain Rule
  9. Implicit Differentiation and Related Rates
  10. More Related Rates
  11. Math111 Midterm Review
  12. Introduction to Extrema
  13. f' and shape of f
  14. f'' and shape of f
  15. Curve Sketching
  16. Applied Extrema, Optimization
  17. Anti-derivatives and definite integrals
  18. Math111 Final Exam Review

Precalculus (Math 90)

  1. Precalculus
  2. Precalculus (older, missing trigs)
  3. Precalculus Final Exam Review

Elementary Algebra (Math 80)

  1. Elementary Algebra

Statistics (Math 251)

  1. Descriptive statistics and probability
  2. Statistical inference and hypothesis testing
  3. Linear regression
  4. Exam walkthrough: Actual exams I gave in class - solved and explained
  5. Some statistics homework problem solutions

Operations Research (Linear Programming, Math 446)

  1. Linear Programming
  2. Math446FinalExamReview
  3. Math446FinalExamReview2

ETC

  1. Sturm-Liouville Problem and Hermitian Operators
  2. Matrix Basics
  3. Cryptography and Blockchains
  4. Understanding Heat Equation and Laplace Equation PDE
  5. Krylov Subspace Methods and Linear Solvers
  6. Basics for Finite Element Method
  7. Machine Learning
  8. Learn Python Through Fun Projects
  9. Python simulation of the Monty Hall problem
  10. PCA explained with math

Some codes I wrote

http://100worksheets.com/mat5x5.htm