| Γνωριμία με το Mathematica | ||
| Quick Tips for Mathematica (nb) | ||
| Plotting with Mathematica (nb) |
Week 1: |
Student's goals for this week: 1. To know how to do 2D and 3D parametric plots and how to take derivatives of curves given parametrically. 2. To know how to do area and volume measurements with double integrals using the Gauss-Green formula (whenever possible) for easier calculations. |
| Parametric Plot (pdf) | 2D Integrals (pdf) | |
| Basics (nb) | Basics (nb) | |
| Tutorials (nb) | Tutorials (nb) | |
| Give It a Try (nb) | Give It a Try (nb) | |
| Literacy (nb) | Literacy (nb) |
Week 2: |
Student's goals for this week: To review vector properties in 2D and 3D. Dot and Cross products, perpandicular (normal), tangent and unit vectors. |
| Vectors (pdf) | Perpendicularity (pdf) | |
| Basics (nb) | Basics (nb) | |
| Tutorials (nb) | Tutorials (nb) | |
| Give It a Try (nb) | Give It a Try (nb) | |
| Literacy (nb) | Literacy (nb) |
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Week 3: |
Student's goals for this week: 1. To know the definition of Gradient, the direction in which it points, and its applications. 2. To know about level curves, level surfaces and that the gradient is perpandicular to them. 3. To know the Total Differential and how it relates to the Chain Rule. 4. To know Lagrange's method for constrained optimization. |
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| Gradients (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1, G2, G3, G4 | |
| Literacy (nb) | L1, L2, L5, L7, L11, L12, L13, L14, L15, L21 |
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Week 4: |
Student's goals for this week: 1. To know about vector fields and their trajectories; in particular about: a) Gradient fields (the most important of the vector fields), b) Differential Equations and their associated vector fields, and c) 2D Electric fields. 2. To be able to visually determine the flow of a vector field ACROSS and ALONG a curve. 3. To be able to determine the flow: a) ACROSS a curve from the sign of the dot product Field[x[t], y[t]].{y'[t], -x'[t]} b) ALONG a curve from the sign of the dot product Field[x[t], y[t]].{x'[t], y'[t]} | |
| Trajectories (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1-G5 | |
| Literacy (nb) | L2, L3, L4, L5, L6, L9, L10, L11, L15 |
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Week 5: |
Student's goals for this week: 1. To know how to measure the flow across a curve with the integral of the dot product Field[x[t], y[t]].{y'[t], -x'[t]} 2. To know how to measure the flow along a curve with the integral of the dot product Field[x[t], y[t]].{x'[t], y'[t]} 3. To recognize gradient fields and to know how to do flow across and flow along a curve measurements using path integrals. | |
| 2DMeasurements (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1-G6 | |
| Literacy (nb) | L1, L4, L9, L10, L11, L18 |
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Week 6: |
Student's goals for this week: 1. To know how to measure flow across closed curves with the divergence of the vector field. 2. To know how to measure flow along a closed curve with the rotation (2D-curl) of the vector field. 3. To know that singularities might be sinks or sources and how to deal with them. | |
| Sources (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1-G6 | |
| Literacy (nb) | L1, L2, L3, L14, L18, L22 |
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Week 7: |
Student's goals for this week: 1. To know how to transform 2D integrals for easier computations. 2. To know that the Jacobian is just the "area conversion" factor. | |
| Transform 2D Integrals (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1, G2, G3, G6, G9, (G10, G11) | |
| Literacy (nb) | L1, L2, L4, L8, L9, L11 |
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Week 8: |
Student's goals for this week: 1. To know how to transform 3D integrals for easier computations. 2. To know that the Jacobian is just the "volume conversion" factor. | |
| Transform 3D Integrals (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1, G2 | |
| Literacy (nb) | L1, L2, L3, L4, L5, L7, L8 |
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Week 9: |
Student's goals for this week: 1. To know about spherical coordinates and how to plot and integrate with them. | |
| Spherical Coordinates (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1, G2 | |
| Literacy (nb) | L2, L3, L4, L6, L11, L13 |
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Week 10: |
Student's goals for this week: 1. To know Gauss' formula in 3D and how to compute surface integrals. 2. To measure the flow of a vector field ACROSS a surface | |
| 3D Measurements (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G1, G2, G3, G4 | |
| Literacy (nb) | L2, L4, L7, L8, L9, L12, L13, L18 |
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Week 11: |
Student's goals for this week: 1. To know the curl of a 3D vector field and Stokes' formula in theory and practice. 2. To know about the gradient test in 3D and path independence. | |
| 3D Flowalong (pdf) | ||
| Basics (nb) | ||
| Tutorials (nb) | ||
| Give It a Try (nb) | G4, G5, G8 | |
| Literacy (nb) | L2, L6, L8, L9, L10, L11, L12, L13, L18 |