# Topics and Assignments

 Week Topics Assignments Sept 6 - 8 Complex Numbers. Complex Plane: 13.1 Polar Form of Complex Numbers. Powers and Roots: 13.2 13.1 # 1,2,5,7--17 13.2 # 1,3,5,7,9,11,15--17,21,23,25 Sept 11 - 15 Exponential Function: 13.5 Matrices, Vectors: Addition and Scalar Multiplication: 7.1 Matrix Multiplication: 7.2 13.5 # 3,5,7,9,11,13--15 7.1 # 1,5,7,9,12,14 7.2 # 1,2,4,13,20,21 Sept 18 - 22 Linear Systems of Equations. Gauss Elimination: 7.3 Linear Independence. Rank of a Matrix. Vector Space: 7.4 Solutions of Linear Systems: Existence, Uniqueness: 7.5 7.3 # 1,3,5,9,11,15,17,19 7.4 # 1,3,5,7,13,17,19,27,29,31 Sept 25 - 29 Determinants. Cramer's Rule: 7.7 Inverse of a Matrix. Gauss-Jordan Elimination: 7.8 Review 7.7 # 5,7,9,11,15,19,21,23 7.8 # 1,3,5,7,13,17,19 Oct 2 - 6 Basic Concepts. Modeling: 1.1 Geometric Meaning of y'=f(x,y). Direction Fields: 1.2 Exam I 1.1 # 1,3,5,7,9,11,13,15,17,21 1.2 # 1,3,5,7,11,13 October 5 Oct 9 - 13 Separable ODEs. Modeling: 1.3 Exact ODEs. Integrating Factors: 1.4 Linear ODEs. Bernoulli Equation. Population Dynamics: 1.5 1.3 # 3,5,7,9,11,13,15,23,25,27 1.4 # 1,5,7,9,11,13,15,17,21 1.5 # 3,5,7,11,15,19,21,23,25,27 Oct 16 - 20 Homogeneous Linear ODEs of Second Order: 2.1 Homogeneous Linear ODEs with Constant Coefficients: 2.2 Modeling: Free Oscillations (Mass-Spring System): 2.4 2.1 # 1,3,5,7,9,11,13,17,19,21,23 2.2 # 1,3,5,7,9,11,13,15,17,19,21,23,25,31 2.4 # 1,3,5,7,9,11,13,17 Oct 23 - 27 Euler-Cauchy Equations: 2.5 Existence and Uniqueness of Solutions. Wronskian: 2.6 Nonhomogeneous ODEs: 2.7 2.5 # 1,3,5,11 2.6 # 1,3,5,7,9,13,15,17 2.7 # 1,3,5,7,11,13,15,17,19 Oct 30 - Nov 3 Modeling: Forced Oscillations. Resonance: 2.8 Modeling: Electric Circuits: 2.9 Solution by Variation of Parameters: 2.10 2.8 # 1,3,9,11,15,17 2.9 # 1,3,5,7,9,11,13,15,17 2.10 # 1,3,5,7 Nov 6 - 10 Review Exam II November 9 Nov 13 - 17 Homogeneous Linear ODEs: 3.1 Homogeneous Linear ODEs with Constant Coefficients: 3.2 Nonhomogeneous Linear ODEs: 3.3 3.1 # 1,3,5,7,9,11,13,15,17,19 3.2 # 1,3,5,7,9,11,13,15,17 3.3 # 1,3,5,9 Nov 20 - 24 Basics of Matrices and Vectors: 4.0 Systems of ODEs as Models: 4.1 Happy Thanksgiving ! 4.1 # 5,7,11,13,15 Nov 27 - Dec 1 Basic Theory of Systems of ODEs: 4.2 Constant-Coefficient Systems. Phase Plane Method: 4.3 Criteria for Critical Points. Stability: 4.4 4.3 # 1,3,5,7,9,11,13,15 4.4 # 1,3,5,7,9,11,13,15,17 Dec 4 - 8 Qualitative Methods for Nonlinear Systems: 4.5 Nonhomogeneous Linear Systems of ODEs: 4.6 Review 4.5 # 1,3,5,7,9,11,13,15,17 4.6 # 3,5,7,9,11,13,15,17,19 Dec 19 Final!! 8:00-11:00 AM.