A structured record of my self-study in mathematics, including study logs, problem walkthroughs, deeper explorations and reflections, and preparation for advanced coursework.
OCW 6.041SCLecture 1 Probability Models & AxiomsLecture 2: Conditioning and Bayes’ RuleTextbook – Introduction to Probability – Bertsekas & Tsitsiklis1.1 Sets1.2 Probabilistic Models1.3 Conditional Probability1.4 Total Probability Theory & Bayes’ Rule Looking forward at the plans I’m formulating for future…
Professor Leonard – Calculus 314.7: Triple Integrals Over Regions with Cylindrical or Spherical Coordinates14. 8: How to Change Variables in Multiple Integrals (Using the Jacobian)15.1: Introduction to Vector Fields (and what makes them Conservative)15.2: How to Find Divergence and Curl…
Professor Leonard – Calculus 314.4 – Center of Mass (and Moments of Mass and Inertia) for Lamina in 2-D14.6 – How to Solve Triple Integrals (Along with Center of Mass and Volume)Thomas – 15.5 Triple Integrals in Rectangular Coordinates; 15.6…
Constrained Optimization with LaGrange Multipliers Introduction to Double Integrals How to Solve Double/Repeated/Iterated Integrals Double Integrals Over Polar Regions I’ve just finished writing my latest update-on-life kind of blog. I’ve explained that I’ve been at odds with consistently writing my…
Professor Leonard – Calculus 313.8 – Finding Extrema of Functions of 2 Variables (Max and Min)Thomas – 14.7 Extrema and Saddle Points Quick Review of ExtremaIn Calculus 1, we learned the local (relative) extrema are points that are higher (local…
Professor Leonard – Calculus 3 13.4 – Finding Differentials of Multivariable Functions 13.7: Finding Tangent Planes and Normal Lines to SurfacesThomas – 14.6 Tangent Planes and Differentials Review: Derivatives, Tangent Lines, and LinearizationOne begins their Calculus journey learning about the derivative. We…
Professor Leonard – Calculus 3 – 13.6: Finding Directional Derivatives and GradientsThomas – 14.5 Directional Derivatives and Gradient VectorsThe Reason for Directional Derivatives At any point on a surface there are infinitely many directions in which we can travel. Each…
Professor Leonard – Calculus 3 – 13.5: The Chain Rule for Multivariable Functions Thomas – 14.4 The Chain Rule Our Old Friend, the Chain RuleThe Chain Rule is one of the first major tools one learns in Calculus. It is used…
Professor Leonard – Calculus 3 – Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions)Thomas – 14.3 Partial Derivatives The Partial DerivativeA function f(x, y) is represented by a surface in . In single-variable calculus, the derivative is the slope of the…
Professor Leonard – Calculus 3 – 13.2: The Limits of Continuity of Multivariable Functions (with Squeeze Theorem)Thomas – 14.2 Limits of Continuity in Higher Dimensions Why Can’t We Treat Limits of Multivariable Functions the Same as Single Variable FunctionsSingle-variable limit:…
