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 » MIT OpenCourseWare » Mathematics » Mathematical Methods for Engineers I, Fall 2002

Calendar

SES # TOPICS LECTURES PROBLEM SETS PROBLEM SET KEY
1 Applied Linear Algebra Gaussian Elimination and Pivots (1.2) Sec 1.2: 1, 3, 4, 6, 9, 10, 11, 12, 13, 15
2 Applied Linear Algebra Factorization A = LU and Positive Definite Matrices (1.2, 1.3) Sec 1.3: 1, 2, 3, 5, 6, 8, 9, 11, 13, 16
3 Applied Linear Algebra Positive Definite Matrices: 2 X 2 (Omit: Detailed proof for n X n) (1.3) Sec 1.3: 1, 2, 3, 5, 6, 8, 9, 11, 13, 16
4 Applied Linear Algebra Least squares: AT A (1.4) Sec 1.4: 1, 2, 3, 4, 5, 6, 7, 8, 10, 11
5 Applied Linear Algebra Systems of Springs and Masses (1.4) Sec 1.4: 1, 2, 3, 4, 5, 6, 7, 8, 10, 11
6 Equilibrium Equations: Discrete Case Fundamental Equations of Equilibrium (2.1) Sec 2.1: 1, 2, 3, 4, 6, 7, 9a, 10, 11
7 Equilibrium Equations: Discrete Case Electrical Networks: AT CA (Omit: RLC circuit and Loop currents) (2.3) Sec 2.3: 1, 2, 5, 9, 12
8 Equilibrium Equations: Discrete Case Structures in Equilibrium: Determinate or Indeterminate (2.4) Sec 2.4: 1, 2, 3, 4, 7, 8, 11, 13, 14, 15
9 Equilibrium Equations: Discrete Case Instability: Rigid Motion and Mechanism (2.4) Sec 2.4: 1, 2, 3, 4, 7, 8, 11, 13, 14, 15
10 Equilibrium Equations: Discrete Case Review of Lectures 1-9
11 Equilibrium Equations: Discrete Case Minimizing with Constraints: Lagrange Multipliers (Omit: Projections) (2.4) Sec 2.2: 1, 2, 3, 4, 5, 7, 8
12 Equilibrium Equations: Discrete Case Duality. Energy and Co-energy (2.2, 2.4) Sec 2.2: 1, 2, 3, 4, 5, 7, 8
Sec 2.4: 1, 2, 3, 4, 7, 8, 11, 13, 14, 15
13 Equilibrium Equations: Discrete Case Weighted Least Squares (2.5) Sec 2.5: 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15
14 Equilibrium Equations: Discrete Case Review for Exam 1
15 Equilibrium Equations: Discrete Case EXAM 1: Chapters 1 and 2
16 Equilibrium Equations: Continuous Case Equilibrium of an Elastic Bar (3.1) Sec 3.1: 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14
17 Equilibrium Equations: Continuous Case Sturm-Liouville Problem, Boundary Layers and delta Function (3.1) Sec 3.1: 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14
18 Equilibrium Equations: Continuous Case Equilibrium of an Elastic Beam (Omit: Spline Approximations) (3.2) Sec 3.2: 1, 2, 3, 6, 10, 11, 13
19 Equilibrium Equations: Continuous Case Potential flow, Stokes and Divergence Theorems (3.3) Sec 3.3: 1, 2, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18
20 Equilibrium Equations: Continuous Case Green's Theorem, Boundary Conditions and Poisson's Equation (3.3) Sec 3.3: 1, 2, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18
21 Equilibrium Equations: Continuous Case Calculus of Variations: Introduction (Omit: Complementary Minimum Principle) (3.2) Sec 3.2: 1, 2, 3, 6, 10, 11, 13
22 Equilibrium Equations: Continuous Case Calculus of Variations: Examples (Omit: Lagrangians and Hamilton's equation) (3.6) up to page 248
23 Equilibrium Equations: Continuous Case Line Integrals, Potentials, Curl and Gradient in 3D (Omit: Electricity and magnetism) (3.4) Sec 3.4: 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 21, 22, 23, 25, 27, 28, 29, 31, 32, 33
24 Equilibrium Equations: Continuous Case Vector Calculus and Curvilinear Coordinate Systems (3.4) Sec 3.4: 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 21, 22, 23, 25, 27, 28, 29, 31, 32, 33
25 Equilibrium Equations: Continuous Case Fluid Mechanics (3.5) Sec 3.5: 15, 17, 18, 19, 27
26 Equilibrium Equations: Continuous Case Review for Exam 2
27 Equilibrium Equations: Continuous Case EXAM 2: Chapter 3
28 Fourier Series and Transforms Fourier Coefficients (4.1) Sec 4.1: 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 16, 19, 20, 22, 23, 24a & c , 25, 26, 27, 29, 30, 31, 35
29 Fourier Series and Transforms Sine and Cosine Series, Parseval's Formula (4.1) Sec 4.1: 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 16, 19, 20, 22, 23, 24a & c , 25, 26, 27, 29, 30, 31, 35
30 Fourier Series and Transforms Fourier Solution to Laplace Equation and Convergence (4.1) Sec 4.1: 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 16, 19, 20, 22, 23, 24a & c , 25, 26, 27, 29, 30, 31, 35
31 Fourier Series and Transforms Orthogonal Functions; Bessel Functions (4.1) Sec 4.1: 2, 3, 4, 5, 6, 7, 8, 10, 13, 14, 16, 19, 20, 22, 23, 24a & c , 25, 26, 27, 29, 30, 31, 35
32 Fourier Series and Transforms Discrete Fourier Series and the n roots of Unity (4.2) Sec 4.2: 1, 2, 4, 5, 7, 10a, 16, 17, 18a & b, 22, 24, 26
33 Fourier Series and Transforms Convolution Rule and Signal Processing (4.2) Sec 4.2: 1, 2, 4, 5, 7, 10a, 16, 17, 18a & b, 22, 24, 26
34 Fourier Series and Transforms Constant-diagonal Matrices (4.2) Sec 4.2: 1, 2, 4, 5, 7, 10a, 16, 17, 18a & b, 22, 24, 26
35 Fourier Series and Transforms Fourier transforms: Plancherel's Formula and Uncertainty Principle (4.3) Sec 4.3: 1, 3, 6, 7, 8, 9, 10, 14, 15, 29, 16, 30, 31, 32, 33, 34
36 Fourier Series and Transforms Transform Rules (Omit: Integral Equations and Sampling Theorem) (4.3) Sec 4.3: 1, 3, 6, 7, 8, 9, 10, 14, 15, 29, 16, 30, 31, 32, 33, 34
37 Fourier Series and Transforms Solutions of ODE's and Green's Function (4.3) Sec 4.3: 1, 3, 6, 7, 8, 9, 10, 14, 15, 29, 16, 30, 31, 32, 33, 34
38 Fourier Series and Transforms Review for Exam 3
39 Fourier Series and Transforms EXAM 3: Chapter 4
 
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