121126-094123: Faking the graph of $x^{1/2}\cos(\frac12\log x)$.
 12_267-{ 121204-100949: The amplitudes when $q\to L$ (3). 121204-100307: The amplitudes when $q\to L$ (2). 121204-095516: The amplitudes when $q\to L$. 121204-095148: Bounding amplitudes on the other side. 121204-094026: The basic amplitudes theorem (2). 121204-093507: The basic amplitudes theorem. 121204-093124: Chaninging the independent variable (2). 121204-092337: Chaninging the independent variable. 121204-092329: Notes. 121203-100051: Changing the independent variable (2). 121203-095636: Changing the independent variable. 121203-094744: The Sturm comparison theorem - comparing with Euler (3). 121203-094157: The Sturm comparison theorem - comparing with Euler (2). 121203-093704: The Sturm comparison theorem - comparing with Euler. 121203-093037: The Sturm comparison theorem - studying Bessel. 121203-092424: The Sturm comparison theorem - self comparisons (2). 121203-091617: The Sturm comparison theorem - self comparisons. 121203-091524: Notes and riddle. 121130-100324: More on $y''+x^\alpha y=0$. 121130-095719: The Sturm Comparison Theorem (3). 121130-095336: The Sturm Comparison Theorem (2). 121130-095035: The Sturm Comparison Theorem. 121130-094519: $y''+x^\alpha y=0$. 121130-094107: The non-oscillation theorem (5). 121130-093715: The non-oscillation theorem (4). 121130-093107: The non-oscillation theorem (3). 121130-092351: The non-oscillation theorem (2). 121130-091916: The non-oscillation theorem. 121130-091418: Reminders 121130-091002: Today's Catalan. 121127-100434: Changing the dependent variable (3). 121127-095841: Changing the dependent variable (2). 121127-095243: Changing the dependent variable. 121127-094605: The basic oscillation theorem (3). 121127-094055: The basic oscillation theorem (2). 121127-093543: The basic oscillation theorem. 121127-093006: Restoring forces, the case of $q<0$. 121127-091026: Airy's equation - why? 121127-091017: Announcements. 121126-100200: The hardest case - $\alpha_1-\alpha_2\in{\mathbb N}_{>0}$. 121126-095126: The case of a double root (2). 121126-094748: The case of a double root. 121126-094123: Faking the graph of $x^{1/2}\cos(\frac12\log x)$. 121126-093828: The easy case with complex numbers. 121126-093307: The easy case. 121126-092606: The fundamental series of $J_{1/3}$. 121126-091701: Reminders, the fundamental series. 121123-100409: RSP at order 2 (5). 121123-100024: RSP at order 2 (4). 121123-095637: RSP at order 2 (3). 121123-095031: RSP at order 2 (2). 121123-094756: RSP at order 2. 121123-094145: RSP at order 1 (4). 121123-093629: RSP at order 1 (3). 121123-093057: RSP at order 1 (2). 121123-092500: RSP at order 1. 121123-091716: Today's topics. 121123-091132: Riddle along. 121120-100237: Proof of Fuchs' theorem (3). 121120-095532: Proof of Fuchs' theorem (2). 121120-094617: Proof of Fuchs' theorem. 121120-093509: Fuchs' theorem. 121120-092913: The Airy equation by power series (4). 121120-091425: The Airy equation by power series (3). 121119-100238: The Airy equation by power series (2). 121119-095656: The Airy equation by power series. 121119-095030: Examples for functions given by a formula (2). 121119-094324: Examples for functions given by a formula. 121119-093656: On functions given by a formula. 121119-093305: The radius of convergence of a series (2). 121119-092529: The radius of convergence of a series. 121119-092128: $\pi$ is irrational. 121119-091004: A proposition by Samer Seraj. 121116-100323: A bit about convergence of series (2). 121116-095425: A bit about convergence of series. 121116-094936: Solving using power series (2). 121116-094011: Solving using power series. 121116-092615: Power series - motivation. 121116-091938: Wronskians and $\cos^2 x + \sin^2 x$. 121116-091126: Riddle Along. 121109-100032: The case of 2nd order linear ODEs. 121109-095425: Differetiating the Wronskian. 121109-094907: Differetiating derivatives (3). 121109-094707: Differetiating derivatives (2). 121109-094123: Differetiating derivatives. 121109-093513: The Wronskian. 121109-093219: Global existence for linear systems (2). 121109-092640: Global existence for linear systems. 121109-091529: Claims and Debts of systems of ODEs. 121106-215845: Challenges. 121106-215829: A differential equation for the generating function of the $A_n$ (2). 121106-215243: A differential equation for the generating function of the $A_n$. 121106-215031: A recursion for $A_n$. 121106-214712: The generating function of $C_n$ (2). 121106-214107: The generating function of $C_n$. 121106-213547: A recursive formula for the Catalan numbers $C_n$. 121106-212459: $A_n$ and $C_n$. 121106-212016: Debts on systems. 121106-210901: Riddles Along. 121105-110135: Proof of the invertibility claim (2). 121105-105750: Proof of the invertibility claim. 121105-105456: The non-homogeneous case using a Fundamental Matrix (4). 121105-105104: The non-homogeneous case using a Fundamental Matrix (3). 121105-104645: The non-homogeneous case using a Fundamental Matrix (2). 121105-104144: The non-homogeneous case using a Fundamental Matrix. 121105-103615: The non-homogeneous case by diagonalization (5). 121105-103301: The non-homogeneous case by diagonalization (4). 121105-102738: The non-homogeneous case by diagonalization (3). 121105-102024: The non-homogeneous case by diagonalization (2). 121105-101538: The non-homogeneous case by diagonalization. 121105-101031: Read ahead, riddle along. 121030-095809: Example with a repeated eigenvalue (2). 121030-095415: Example with a repeated eigenvalue. 121030-095102: Exponentiating a Jordan block. 121030-094321: The Jordan form theorem (2). 121030-093500: The Jordan form theorem. 121030-093236: Example with distinct eigenvalues (3). 121030-092306: Example with distinct eigenvalues (2). 121030-091915: Example with distinct eigenvalues. 121030-091559: Reminders. 121030-091036: Announcements. 121029-100048: Properties of matrix exponentiation (6). 121029-095744: Properties of matrix exponentiation (5). 121029-095326: Properties of matrix exponentiation (4). 121029-094547: Properties of matrix exponentiation (3). 121029-094025: Properties of matrix exponentiation (2). 121029-093558: Properties of matrix exponentiation. 121029-092858: Convergence. 121029-091928: Exponentiation via the Taylor series. 121029-091107: Announcements. 121023-100040: Matrix exponentiation (2). 121023-095938: Matrix exponentiation. 121023-095149: A baby version. 121023-094809: Systems of linear equations. 121023-093831: Undetermined coefficients (4). 121023-092351: Undetermined coefficients (3). 121023-091741: Undetermined coefficients (2). 121023-091718: Pre-exam office hours. 121022-100052: Undetermined coefficients. 121022-095206: Reduction of order. 121022-094433: Multiple roots (5). 121022-093955: Multiple roots (4). 121022-093804: Multiple roots (3). 121022-093504: An aside on the Leibniz rule for higher derivatives. 121022-092921: Multiple roots (2). 121022-092104: Multiple roots. 121022-091332: The case of distinct roots. 121022-090631: TT, Read Along, Riddle Along. 121019-095816: From complex back to real. 121019-095806: Distinct real roots, complex root. 121019-094930: Differential operator language. 121019-094408: The guessing method. 121019-094033: Constant coefficients homogeneous high order ODEs (2). 121019-094024: Constant coefficients homogeneous high order ODEs. 121019-093128: Numerical Integration (3). 121019-093058: Numerical Integration (2). 121019-091840: Numerical Integration. 121016-093936: Runge-Kutta. 121016-093634: A general scheme. 121016-093057: Local analysis of improved Euler (2). 121016-092401: Local analysis of improved Euler. 121016-091448: Euler and improved Euler. 121016-090737: Term test info and riddle. 121012-095603: Numerical methods, starting from the silly (3). 121012-095555: Numerical methods, starting from the silly (2). 121012-094800: Numerical methods, starting from the silly. 121012-094127: E-L is a gradient! 121012-093338: Lagrange multipliers in CoV. 121012-092651: The Lagrange Multipliers Theorem (3). 121012-092050: The Lagrange Multipliers Theorem (2). 121012-091426: The Lagrange Multipliers Theorem. 121012-090625: Read along and riddle along. 121009-095640: Directional derivatives. 121009-095113: The isoperimetric inequality (4). 121009-094819: The isoperimetric inequality (3). 121009-094131: The isoperimetric inequality (2). 121009-093631: Lagrange multipliers in ${\mathbb R}^2$ (4). 121009-093049: Lagrange multipliers in ${\mathbb R}^2$ (3). 121009-092523: Lagrange multipliers in ${\mathbb R}^2$ (2). 121009-092511: Lagrange multipliers in ${\mathbb R}^2$. 121009-091240: The isoperimetric inequality. 121005-095531: Bread with least crust. 121005-094811: The brachistochrone, again. 121005-094413: Conservation of energy (2). 121005-094106: Conservation of energy. 121005-092726: Conservation of momentum. 121005-092109: Reminder of Euler-Lagrange. 121005-090823: Notes and riddles. 121002-103950: Properly writing Euler-Lagrange and the brachistochrone. 121002-103247: $F=ma$ (2). 121002-102822: Deriving Euler-Lagrange (5), $F=ma$. 121002-102506: Deriving Euler-Lagrange (4). 121002-101904: Deriving Euler-Lagrange (3). 121002-101423: Deriving Euler-Lagrange (2). 121002-095520: Deriving Euler-Lagrange. 121002-095243: Example: The brachistochrone. 121002-094521: Example: Classical mechanics. 121002-094030: Example: Power lines. 121002-092726: The basic calculus of variations problem. 121002-092032: Back to the chain rule (2). 121002-091704: Back to the chain rule. 121002-090739: Today's riddle. 121001-095749: Calculus of variations (2). 121001-095740: Higher order equations, calculus of variations. 121001-094905: The fundamental theorem: higher order equations. 121001-094116: The fundamental theorem: systems (2). 121001-093509: The fundamental theorem: systems. 121001-093010: The fundamental theorem: uniqueness (2). 121001-092946: The fundamental theorem: uniqueness. 121001-091541: Review of the fundamental theorem. 121001-090909: Computing $(x^x)'$. 120928-095846: The Fundamental Theorem: Uniform Convergence. 120928-094804: The Fundamental Theorem: $\phi_n-\phi_{n-1}$ is well-bounded (2). 120928-094102: The Fundamental Theorem: $\phi_n-\phi_{n-1}$ is well-bounded. 120928-093027: The Fundamental Theorem: $\phi_n$ is well-defined. 120928-092238: The Fundamental Theorem: the $y'=y$ example. 120928-091714: The Fundamental Theorem: Statement. 120925-095319: The Fundamental Theorem (3). 120925-094906: The Fundamental Theorem (2). 120925-094303: The Fundamental Theorem. 120925-093754: The Lipschitz Condition. 120925-092443: Wishful thinking (3). 120925-092029: Wishful thinking (2). 120925-091230: Wishful thinking. 120925-090721: Riddle Along. 120924-095914: Integrating factors (3). 120924-095800: Integrating factors (2). 120924-095319: Integrating factors. 120924-095019: Exact equations (5). 120924-094422: Exact equations (4). 120924-093936: Exact equations (3). 120924-093412: Exact equations (2). 120924-092906: Exact equations. 120924-092111: Partial derivatives commute (2). 120924-091545: Partial derivatives commute. 120924-090840: Show and tell (2). 120924-090831: Show and tell. 120921-095745: Notes for September 21 (6). 120921-095252: Notes for September 21 (5). 120921-095245: Notes for September 21 (4). 120921-093121: Notes for September 21 (3). 120921-092710: Notes for September 21 (2). 120921-092353: Notes for September 21. 120918-095852: Homogeneous Equations (2). 120918-095416: Homogeneous Equations. 120918-094717: Autonomous Equations (2). 120918-094527: Autonomous Equations. 120918-093915: Changing source and target coordinates (2). 120918-093421: Changing source and target coordinates. 120918-091850: Escape Velocities (2). 120918-091728: Escape Velocities. 120918-090713: Riddle Along. 120917-095813: Escape velocities (2). 120917-095323: Escape velocities. 120917-094437: Separable equations: the easy to justify way (2). 120917-093948: Separable equations: the easy to justify way. 120917-093027: Separable equations: the easy to remember way. 120917-091853: The general problem, separable equations. 120917-090926: Comments and riddles. 120914-095607: First order linear, non-homgeneous (5). 120914-095435: First order linear, non-homgeneous (4). 120914-095224: First order linear, non-homgeneous (3). 120914-094700: First order linear, non-homgeneous (2). 120914-093953: First order linear, non-homgeneous. 120914-093309: First order linear homogeneous (2). 120914-092628: First order linear homogeneous. 120914-091936: $y'=f$ and first order linear homogeneous. 120914-090342: Read along and riddle along. 120911-094639: This is a cycloid (2). 120911-093941: This is a cycloid. 120911-093629: Solving the equation (2). 120911-093043: Solving the equation. 120911-092453: Brachistochrone review. 120910-100221: Deriving the brachistochrone equation (2). 120910-095542: Deriving the brachistochrone equation. 120910-094435: Fermat's principle and Snell's law. 120910-093559: The Brachistochrone problem. 120910-092814: A messy example. 120910-092025: What's a differential equation? }