| 12_267-{ | hide text |
| 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? |
| } |
Notes for BBS/12_267-120914-090342.jpg: [edit]