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Differential Equation 1
Textbook: Advanced Engineering Mathematics (6th Edition) by Dennis G. Zill Week 1: 2.2 Separable Equations: 1,6,9,12,13,17,20,23,26,30,33,382.3 Linear Equations: 3,11,17,22,25,28,30,37,39,522.4 Exact Equations: 21,27,31,37,45Week 2:2.5 Solutions by Substitutions: 1,5,9,11,16,19,21,23,25,29,36,372.6 A Numerical Method: 3,42.7 Linear Models: 3,5,6,9,11,12,13,16,19,23,25,29,36,392.8 Nonlinear Models: 3,5,11Week 3:3.1 Theory of Linear Equations: 3,4,6,9,12,15,21,24,27,30,33,363.2 Reduction of Order: 3,6,9,12,18,(optional 21,24)3.3 Homogeneous Linear Equations with Constant Coefficients: 3,6,9,12,21,30,33,39,42,57Week4:3.4 Undetermined Coefficients: 3,9,15,21,33,45,483.5 Variation of Parameters: 3,9,15,21,243.6 Cauchy-Euler Equations:3,6,12,15,21,27,39,45,51Week 53.7 Nonlinear Equations: 3,9,15,183.8 Linear Models (IVP): 3,6,9,12,27,30,33,39,51,573.9 Linear Models (BVP): 3,12,24,27,30,Week 64.1 Definition of Laplace Transform: 9,12,21,30,36,42,45,54,574.2 The Inverse Transform and Transforms of Derivatives:6,9,12,18,27,33,36,484.3 Translation Theorems:3,6,12,18,21,27,39,45,48,51,54,60,63,69Week 7 4.4 Additional Operational Properties: 6,9,12,18,21,27,33,36,42,45,54,57,604.5 The Dirac Delta Function:3,6,94.6 Systems of Linear Differential Equations:3,9,15Week 85.1 Solutions about ordinary points: 3, 6, 9, 12, 15, 18, 335.2 Solutions about singular points: 3,6,9,12,15, 24, 275.3 Special functions: 3, 6, 9, 12,15,18, 21, 30Differential Equation 1
Differential Equation 2
Textbook: Advanced Engineering Mathematics (6th Edition) by Dennis G. Zill Week 18.2 Systems of Linear Algebraic Equation 3,6,9,12,258.4 Determinant 12,15,18,248.8 Eigenvalue problem 9,12,15,18,21,2710.1 Theory of Linear Systems 3,6,9,12,15,18,21,2410.2 Homogeneous Linear Systems 3,6,9,12,15,21,24,27,30,33,36,39,42,48,51Week 28.12 Diagonalization 3,6,9,12,15,18,21,24,27,33,36,39,10.3 Solution by Diagonalization 3.6.910.4 Nonhomogeneous Linear Systems 3,6,9,15,18,24,3310.5 Matrix Exponential 3,6,9,12,21,Week 311.1 Autonomous System 3,6,9,12,15,18,2111.2 Stability of Linear system 3,6,9,12,15,18,21,24,11.3 Linearization and local stability 3,6,9,12,15,18,21,24,30.33Week 412.1: 3,6,9,15,18,21,2412.2:3,6,1512.3:3,6,9,12,18,21,36Week 512.4: 3,6,1212.5: 3,6,912.6: 3,6,18,21Week 613.1: 3,6,9,12,18,21,2413.2: 3,6,9,1213.3: 3,6,9Week 713.4: 3,6,9,2113.5: 3,613.6: 3,6Week 813.7: 3,613.8: 314.1: 3,6,914.2: 3,6,9Week 914.3: 3,615.1: 3,6,9,12,1515.2: 3,6,9,12,1518,21Week 1015.3: 3,6,9,12,15,1815.4: 3,6,9,12,15,2115.5: 3,9Differential Equation 2
Multivariable Calculus
Goals:1) Optimization problems for several variables2) Integration over curves and surfacesMultivariable Calculus
Textbook: Thomas' Calculus (in SI unit, 13th edition)Lecture Videos: available from ICU Moodle Website
Week 1:-Partial derivatives (14.3) and the chain rule (14.4)-Directional derivatives (14.5)-Tangent planes and the linearization (14.6)-Taylor's formula (14.9)14.3:51,5314.4:1,5,7,25,27,29,33,3914.5:3,5,9,11,13,25,27,29,31,3314.6:1,5,9,13,25,33,3914.9:1,3,5Week 2:-Extreme values and the optimization problem (14.7)14.7: 1,2,3,12,14,16,23,24,33,35,39.41,42,49, 50, 66,67Week 3:-The optimization problem with a constraint; Lagrangian multipliers (14.8)14.8: 1, 4, 15, 16, 17, 27, 30, 31, 32, 37, 40Week 4:-Areas and Volumes by double and triple integrals (15.1, 15.2, 15.3, 15.5)15.3: 4,6,10,15, 2115.5: 23,26,29,32,42Week 5:-Polar coordinates, Cylindrical coordinates, Spherical coordinates (15.4, 15.7)15.4: 2, 6, 12, 14, 18, 28, 29, 46, 4815.7: 8, 14, 16, 17, 27, 28, 34, 38, 46Week 6:-Moments and Centers of Mass (6.6 and 15.6)-Substitution methods in multiple integrals (15.8)6.6: 13, 2715.6: 6, 13, 24, 3015.8: 1, 6, 9, 10, 12, 15, 20Week 7:-Integration of a function against arc length along a curve (16.1)-Integrating vector fields along a curve (16.2)16.1: 15,22,33,34,35,3616.2: 2,5,6,18,19,26,29,31,33,39,40Week 8:-Path independence (16.3)16.3: 6,8,10,24,26,28,29,31,38Week 9-Greens' theorem (16.4)16.4: 1,2,7,16,20,22,26,29,32,35,37,39 Week 10-Integration of a function against area (and of a vector field) over a surface (16.6)-Stokes' theorem (16.7)-The divergence Theorem (16.8)16.5: 5,11,21,27,31,37,3916.6: 1,2,5,9,13,17,19,21,27,3916.7: 1,5,7,9,13,20,21,28,16.8: 3,9,11,18,22,25,28
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