# Math 246H Schedule of Lectures & Notes, Spring 2015

 Lecture Date What was covered Online Chapter(s) Notes 1 Jan.27 Classification and First-Order Equations. Method of the integrating factor 0, I.1,I.2 First lecture 2 Jan.29 Separable First-Order Equations and Existence, Uniqueness and Interval of Definition for Solutions I.3, I.4 3 Feb. 3 Direction Fields and Models I.4,I.5 Quiz 1 4 Feb. 5 Population Models. Stability of 1-D systems. I.6 5 Feb.10 Numerical Methods: The Euler, Improved Euler (Runge-Trapezoidal), Modified Euler (Runge-MidPoint) and Runge-Kutta Integration Methods I.7 Quiz 2; Matlab Project I due 6 Feb.12 Exact Equations and Integrating Factors (I) I.8 7 Feb.17 Exact Equations and Integrating Factors (II) I.8,I.9 Quiz 3; Review at 3pm University closed due to weather 8 Feb.19 Integrating Factors; 2nd & higher order homogeneous linear equations and the Wronskian I.9,II.1,II.2 Quiz 3; Online II.3 - linear algebra supplement Feb.23 Review Session: 12:15pm-1:45pm MATH 0401 Feb.24 1st In-Class Test Score is used for Early Warning Grade; Matlab Project II due 9 Feb.26 2nd order homogeneous const. coeffs. II.1.3, II.2.2, II.2.3, II.2.4,II.4 (n=2) 9' Feb.27, Mar.2 2nd order homogeneous const. coeffs. II.1.3, II.2.2, II.2.3, II.2.4,II.4 (n=2) make-ups: 11:00am-2:00pm in MATH 2300 (Fri.) and MATH 0305 (Mon.) 10 Mar. 3 Reduction of order; Higher order homogeneous equation with const. coeffs. (I) II.4 Quiz 4 11 Mar. 5 Higher order homogeneous w/ const. coeffs. (II) II.4 University closed due to weather. 12 Mar.10 reduction of order; higher-order homogeneous with constant coefficients;non-homogeneous: undetermined coeffs (I) II.4,II.5,II.6 Matlab Project III due 13 Mar.12 non-homogeneous: undetermined coeffs. (II); non-homogeneous: variation of parameters (I) II.6 Quiz 5 Mar.17 No Class Spring break Mar.19 No Class Spring break 14 Mar.24 non-homogeneous: variation of parameters (II) II.7 Quiz 6 15 Mar.26 Free Vibrations II.8 Review at 2pm in MATH B0423 16 Mar.31 Forced Vibrations II.8 Quiz 7 Apr. 2 2nd In-Class Test Matlab Project IV due 17 Apr. 7 Laplace Transform II.9 18 Apr. 9 Step functions & discontinuous forcing II.9 19 Apr.14 systems of 1st order diff. eqns. III.1,III.2 Quiz 8; III.3 - supplement 20 Apr.16 Modeling Tank Systems and Spring-Mass Systems; Numerical Methods; Matrix Exponential: Using a Natural Fundamental Set of Solutions III.1, III.4 Matlab Project V due 21 Apr.21 Solving 2D linear systems: Eigenmethods III.5 Quiz 9 22 Apr.23 Repeated Eigenvalues. Matrix Exponential III.5 23 Apr.28 Phase portaits for 2D systems III.6 Quiz 10 Stability Diagram 24 Apr.30 Nonlinear planar systems: Linearization III.6,III.7 Review at 3pm in MATH 0103 May 5 3rd In-Class Test 25 May 7 Nonlinear planar systems: Phase portraits (I) III.8 Matlab Project VI due 26 May 12 Nonlinear planar systems: Phase portraits (II), Stability III8,III.9 Quiz 11; Last Class

Last update: April 28, 2015.