# DOC BENTON'S VIDEO RANCH

## SINGLE VARIABLE CALCULUS

 Derivatives, Slope, Velocity, Rate of Change Limits, Continuity, Trigonometric Limits Derivatives of Products, Quotients, Sine, Cosine Chain Rule, Higher Derivatives Implicit Differentiation, Inverses Exponential and Log, Logarithmic Differentiation, Hyperbolic Functions Hyperbolic Functions Continued and Exam I Review Linear and Quadratic Approximations Curve Sketching Max-Min Problems Related Rates Newton's Method and other Applications Mean Value Theorem Inequalities Differentials, Antiderivatives Differential Equations, Separation of Variables Definite Integrals First Fundamental Theorem of Calculus Second Fundametal Theorem of Calculus Applications to Logarithms and Geometry Volumes by Disks and Shells Work, Average Value, Probability Numerical Integration Exam III Review

## MULTIVARIABLE CALCULUS

 The Dot Product Determinants and the Cross Product Matrices and Inverse Matrices Square Systems and Equations of Planes Parametric Equations for Lines and Planes Velocity, Acceleration, and Kepler's Second Law Review 1 Level Curves, Partial Derivatives, and Tangent Plane Approximations Maximum-Minimum Problems and Least Squares The Second Derivative Test, Boundaries, and Infinity Differentials and the Chain Rule The Gradient, Directional Derivative, and the Tangent Plane Lagrange Multipliers Non-Independent Variables Partial Differential Equations Review Double Integrals Double Integrals in Polar Coordinates Change of Variables Vector Fields and Line Integrals in the Plane Path Independence and Conservative Fields Gradient Fields and Potential Functions Green's Theorem Flux and the Normal Form of Green's Theorem Simply Connected Regions and Review Triple Integrals in Rectangular and Cylindrical Coordinates Spherical Coordinates and Surface Area Vector Fields in 3D, Surface Integrals, and Flux Divergence Theorem Divergence Theorem, Applications, and Proof Line Integrals in Space, Curl, Exactness, and Potentials Stoke's Theorem Stoke's Theorem and Review Topological Considerations and Maxwell's Equations Final Review Final Review Continued

## MULTIVARIABLE CALCULUS AT BERKELEY

 Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 12 Lecture 13 Lecture 14 Lecture 15 Lecture 18 Lecture 19 Lecture 20 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 28 Lecture 29 Lecture 30

## ABSTRACT ALGEBRA

 Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 Part 8 Part 9 Part 10 Part 11 Part 12 Part 13 Part 14 Proof The Pigeonhole Principle Construction of GF(8) Euler's Identity The Birthday Paradox Infinity Classification Theorem for Finite Simple Groups