Homepage for Math 54
Linear Algebra & Differential Equations -- [4 units]
Course Format: Three hours of lecture and two hours of discussion/workshop per week; at the discretion of the instructor, an additional hour of discussion/workshop or computer laboratory per week.
Prerequisites: 1A-1B or equivalent. Note: calculus courses at most institutions either have no differential equations, or less than Berkeley's Math 1B. Transfer students who have taken such a course need to learn that differential equations material (Stewart, Calculus: Early Transcendentals, 5th Ed., Ch.s 9 and 17) on their own, by approximately the 10th week of Math 54. The instructor and TA's should emphasize this fact.
Description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. (F,SP)
Textbooks: Lay, Linear Algebra and It's Applications, 3rd edition, UC Berkeley paperback edition.
Nagle, Saff and Snider, Fundamentals of Differential Equations and Boundary Value Problems, UC Berkeley paperback edition.
Lay, Ch. 1: Linear Equations
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4 hours
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(Sections 1.1-1.5, 1.7-1.9)
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Lay, Ch. 2: Matrix Algebra
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4 hours
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(Sections 2.1-2.3, 2.8-2.9)
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Lay, Ch. 3: Determinants
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2 hours
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(Sections 3.1-3.3)
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Lay, Ch. 4: Vector Spaces
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6 hours
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(Sections 4.1-4.7)
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(Spend more than 1 hour on Section 4.7)
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Lay, Ch. 5: Eigenvalues and Eigenvectors
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4 hours
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(Sections 5.1-5.4)
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Lay, Ch. 6: Orthogonality
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5 hours
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(Sections 6.1-6.5, 6.7)
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Lay, Ch. 7: Symmetric Matrices
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1 hour
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(Sections 7.1)
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Total No. of Hours on Linear Algebra
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26 hours
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NS&S, Ch. 4: Second Order Linear ODE
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3 hours
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(Sections 4.2-4.5)
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Note: Sections 4.3 and 4.4 review Math 1B.
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NS&S, Ch. 6: Higher Order Linear ODE
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2 hours
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(Sections 6.1-6.2)
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NS&S, Ch. 9: Systems of Linear ODE
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3 hours
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(Sections 9.1, 9.4, 9.5, 9.6)
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NS&S, Ch. 10: Fourier Series, PDE
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7 hours
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(Sections 10.1-10.6)
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Total No. of Hours on ODE, Fourier Analysis
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15 hours
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Total
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41 hours
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Midterms
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2 hours
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Holidays & Reviews
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2 hours
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45 hours
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