Math 135 Syllabus, Winter 2015

Month	Date	Topic	Book	Notes
		Linear Equations
January	5	Introduction: Initial-Value Problems	14, 15	1.1-1.3, 2.1, 2.2
	7	Homogeneous: Key Identity, Characteristic Polynomials	17, 22	2.3-2.4, 3.1-3.4
	9	Nonhomogeneous: Green Functions and Key Identity Evaluations	18	4.1, 4.2, 5.4, 5.1
	12	Nonhomogeneous: Undetermined Coefficients and Composite Forcing	18	5.2, 5.3
		Laplace Transform Method
	14	The Laplace Transform	48, 49	6.1, 6.2
	16	Theory of the Laplace Transform	49, 51	6.2 6.3
	21	Tranform of Derivatives and Initial-Value Problems	50, 51	6.4, 6.5,
	23	Piecewice Forcing and Inverse Transforms	50, 53	6.6 6.7
	26	Green Functions, Convolutions, and Impulse Forcing	52, 53	6.8, 6.9, 6.10
		Existence and Uniqueness for Initial-Value Problems
	28	Theory for Linear First-Order Equations		7.1, 7.2
	30	Theory for Separable First-Order Eqautions		7.3
February	2	Theory for General First-Order Equations	68, 69	7.4
	4	Finish Picard Theorem Proof, Remarks on Systems	69, 70	7.4, 8.1-8.3
	6	Midterm Exam
		Fourier Series
	9	Approximating Periodic Functions	33
	11	Fourier Series	35, 36
	13	Mean-Square Convergence of Fourier Series	38
	18	Scalar Products and Orthogonality	37
	20	Pointwise Convergence of Fourier Series	34, 38
		Application to Partial Differential Equations
	23	Eigenpairs and the Vibrating String	39, 40
	25	One-Dimensional Heat Equation	41
	27	Laplace Equation over a Disk	42
March	2	Poisson Integral and Sturm-Liouville Problems	42, 43
	4	Sturm-Liouville Problems and Orthogonality	43
		Calculus of Variations
	6	Introduction, Euler Equations	65, 66
	9	Euler Equations, Examples	66
	11	Isoparametric Problems	67
	13	Isoparametric Problems, Examples	67
	19	Final Exam, 11:30am - 2:30pm