Math. 241 (EL1): Fall 2009
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You must submit home work solutions according to the list of collected problems Click here to see the lists of collected problems and due dates. |
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If you have questions connected with grading of homework assignments or exams, please contact your recitation section instructor. You can visit office hours of any of the sections ED1, ED3, ED5 and ED6
If you decided to drop Math. 241:
There is a substitute: Math. 299
For students who are dropping from Math 241 into the second-eight-week course Math 299, the class is starting this week. For students who were registered by last Thursday, the meeting is today at 4pm in 239 Altgeld (registered students were sent an e-mail). A large number of students have added the course today, and I will meet with them at 5:15 on Wednesday in 239 Altgeld Hall. I will be sending an e-mail to the students at the end of the day.
Melissa Dennison [masimmon@illinois.edu] (October 19, 2009)
| Section # | Time -- Room | Instructor (click for web page when available) | Office hours | |
| MATH 241 ED1 | 8am-8:50am TR 343AH | Kim, Eunmi | ekim67@illinois.edu | Mon, Wed
2pm-2:50pm AH 108 |
| MATH 241 ED3 | 9am-9:50am TR 343AH | Kim, Eunmi | ekim67@illinois.edu | Mon, Wed
2pm-2:50pm AH 108 |
| MATH 241 ED4 | 9am-9:50am TR 347AH | Yuttanan, Boonrod | byuttan2@illinois.edu | Tu, Th, 11am-11:50am, B1A Cable Hall |
| MATH 241 ED5 | 10am-10:50am TR 441AH | Yuttanan, Boonrod | byuttan2@illinois.edu | Tu, Th, 11am-11:50am, B1A Cable Hall |
| MATH 241 ED6 | 10am-10:50am TR 443AH | Zheng, Zhi | zzheng4@illinois.edu | Th. 4pm-4:50pm, AH110
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Date |
Lecture snap-shot*.mhtml fileUse only Internet Explorer to veiw |
Lecture snap-shot*.pdf file |
Current lecture notes | Chapter: Section | Topics |
| 08.24 | 1 | 1 | 1 | 12.1, 12.2 | Scalars and vectors. Free and bound vectors. Equality of free vectors. Addition, subtruction and multiplication by a number of vectors (geometric definition); the triangle law of addition, the parallelogram law of addition and subtraction. Algebraic properties of vectors (properties 1-8). Introduction of a system of coordinates; real line R, Cartesian line R^2. Position vector of a point. Coordinates of vectors and points. Algebraic operations and coordinates of a vector. |
| 08.26 | 2 | 2 | 2 | 12.1, 12.2 | Algebraic operations and coordinates of a vector. Length of a vector; formula for length. Unit vector in the direction of a nonzero vector. Direction angle and coordinates of a nonzero vector. Coordinate vectors i and j. Representation: a=<x,y> the same as a=xi+yj; representation for non-zero vectors: a=|a|[costi+costi], where t is the direction angle. Space, Cartesian coordinates in space, coordinate planes, projection of points into coordinate planes and coordinate line. Examples. Examples of sketching solution sets in space. |
| 08.28 | 3 | 3 | 3 | 12.2, 12.3 | Distance formula. Examples: sphere and equidistant plane. Dot product. Properties of dot product. Cauchy's inequality. Calculation of dot product in coordinates. Triangle inequality. Formula for angle. Direction angles and coordinates of a unit vector. |
| 08.31 | 4 | 4 | 4 | 12.3, 12.4 | Scalar and vector projections. Dot product and work done by a constant force. Cross product; magnitude of cross product, right hand rule. Cross product and parallelism of vectors. Review of determinants. Symbolic formula for cross product. |
| 09.02 | 5 | 5 | 5 | 12.4, 12.5 | Symbolic formula for cross product: examples. Triple scalar products. Volume of parallelipiped an triple scalar product. Formula in coordinates, properties examples.Vector equation of line. Parametric and symmetric equations of line. |
| 09.04 | 6 | 6 | 6 | 12.4, 12.5 |
Parametric and symmetric equations of line. Examples. Line trough two points. Parallel, intersected and skew lines. Example. Distance between skew lines. Condition ensuring that lines are skew. Example. Scalar triple product and equation of plane; equation of plane through a point and two nonparallel vectors. |
| 09.09 | 7 | 7 | 7 | 12.5, 12.6 | Equation of plane through 3 points. Line as intersection of planes. Parallel planes, angle between planes. Distance from a point to plane. Examples. Vector functions. Short review of limits, L'Hopital rule. (Quadric surfaces will be covered in your recitation sections). |
| 09.11 | 8 | 8 | 8 | 13.1, 13.2 | Vector functions, limit of vector functions, continuity of vector functions. Examples. Parametrized curve. Construction of sketchs of curves as intersection of surfaces. Examples. Construction of parametrization of a curve. Example. Derivative of a vector function. |
| 09.14 | 9 | 9 | 9 | 14.3 | Definition of partial derivatives w.r.t. x and y. Examples of calculation of partial derivatives. x-curve and y-curve. Geometric interpretation of partial derivatives. Equation of the tangent plane to the surface S: z=f(x,y). |
| 09.16 | 10 | 10 | 10 | 13.1, 13.2 | Derivative of a vector function and the tangent line. Unit tangent vector. Examples. Parametric and symmetric equations of the tangent line. Examples. Smooth curves. Examples. Angle between intersecting curves. Rules of differentiation of vector fieds. |
| 09.18 | 11 | 11 | 11 | 13.2, 13.3 | Integral of a vector function. Example. Length of a smooth curve, formula for length. Examples. Reparametrization of curve. Arc length parametrization. |
| 09.21 | 12 | 12 | 12 | 13.3 | Arc length parametrization. Examples: helix, straight line. Definition of curvature of curves. Examples. |
| 09.23 | 13 | 13 | 13 | 13.3, 13.4 | Unit tangent vector, principal normal vector, binormal vector. Osculating plane. Normal and tangential components of acceleration. Formula for curvature of curves. |
| 09.25 | 14 | 14 | 14 | 13.3, 13.4 | Examples connected with calculation of normal and tangential component of acceleration, curvature of space and plane curves. Equation of osculating circle. Start example. |
| 09.28 | 15 | 15 | 15 | 13.4, 14.1, 14.2 | Continue example connected with the osculating circle. Review of limit of function of one variable. Definition of limit of function of several variables. |
| 09.30 | 16 | 16 | 16 | 14.2 | Limit laws. Examples. Non-existence of limit. |
| 10.02 | 17 | 17 | 17 | 14.2 | Continuity: definition, laws of continuity. Examples. |
| 10.05 | 18 | 18 | 18 | 14.3, 14.4 | Examples of calculation of partial derivatives. Definition of differentiability; existence of tangent plane. Examples. |
| 10.07 | 19 | 19 | 19 | 14.4 | The fundamental theorem of calculus. Examples. Differential. Increments and linear approximations. Examples. |
| 10.09 | 20 | 20 | 20 | 14.5 | Chain Rule. Examples. General Chain Rule. Examples. Start Euler's theorem. |
| 10.12 | 21 | 21 | 21 | 14.5 | Complete the proof of Euler's theorem. Implicit function theorem. Differentiation of implicit functions. Examples. |
| 10.14 | 22 | 22 | 22 | 14.5 | Chain rule for higher derivatives; symbolic chain rule; examples. |
| 10.16 | 23 | 23 | 23 | 14.5, 14.6 | Examples on the chain rule for higher derivatives. Gradient, directional derivative. |
| 10.19 | 24 | 24 | 24 | 14.6 | Directional derivative and rate of change of a function, maximum of the directional derivative. Examples. |
| 10.21 | 25 | 25 | 25 | 14.6 | Gradient and normal vector to the surface. Local maximum and local minimum. Absolute maximum and absolute minimum, local and absolute extrema. |
| 10.23 | 26 | 26 | 26 | 14.7 | Local maximum and local minimum. Absolute maximum and absolute minimum, local and absolute extrema. Necessary condition for local extrema. Critical points. Second derivative test. |
| 10.26 | 27 | 27 | 27 | 14.7, 14.8 | Finding absolute extrema of a function on a closed bounded domain; example. Lagrange multipliers, constraints or side conditions. Lagrange function and critical points of the Lagrange multipliers problem. |
| 10.28 | 28 | 28 | 28 | 14.8 | Examples on the Lagrange multipliers with one constraint. Start: Lagrange multipliers with two constraints. |
| 10.30 | 29 | 29 | 29 | 14.8, 15.1 | Lagrange multipliers with two constraints; extrema in regions defined by inequalities. Start review of the Riemann integral. |
| 11.02 | 30 | 30 | 30 | 15.1 | Continue review of the Riemann integral: calculation of mass of a long thing rod. Double integral over a rectangle: definition, mass of a rectangular plate, properties of double integral. The midpoint rule. Exampes. |
| 11.04 | 31 | 31 | 31 | 15.1, 15.2 | Iterated integrals; examples. Fubini's theorem for rectangular domains. Examples (Example 3 of Lecture 31 will be discussed in your recitation section). Double integrals over more general regions: vertically simple (type I) regions. |
| 11.06 | 32 | 32 | 32 | 15.2, 15.3 | Double integrals over more general regions: vertically simple (type I) regions, horizontally simpe (type II) regions. Calculation of double integrals. Examples connected with calculation of double integrals. |
| 11.09 | 33 | 33 | 33 | 15.4, 15.5 | Converting double integrals to polar coordinates. Examples, calculation of area and volume. (Examples 6 and 9 of Lecture 33, in the file 32 will be discussed in your recitation sessions). Aplications of double integral: calculation of mass and charge of a lamina; moments of inertia w..r.t. x-axis and y-axis; calculation of the center of mass of a lamina. |
| 11.11 | 34 | 34 | 34 | Sec. 16.6 | Surface area, area element, formula for area. Coefficients E,F,G and calculation of area. Special case: area of the surface given in a non-parametric form. Example (Examples 2, 3, 5, 6 will be discussed in the recitation sections). |
| 11.13 | 35 | 35 | 35 | Sec. 16.6, 15.6 | Calculation of the surface area of a torus. Triple integral over a box. Fubini's theorem for triple integral over a box. Triple integral over a general bounded region: type I,II and III regions. Examples. (Examples 3, 4, 5, 7, 8, see 35, will be discussed in the recitation sections). |
| 11.16 | 36 | 36 | 36 | 15.7, 15.8 | Integration in cylindrical coordinates. Examples. Integration in spherical coordinates. Start example. |
| 11.18 | 37 | 37 | 37 | 15.8, 15.9 | Complete example on change of variables to spherical coordinates. Change of variables, transforamtion. Examples of transforamtions of domains. Jacobian and examples of calculation of Jacobians. Change of variables formula for double integrals. Start example. |
| 11.20 | 38 | 38 | 38 | 15.9, 16.1, 16.5 | Complete example on change of variables. Scalar fields and vecor fields. How to plot vector fields. Gradient vector fields. Example: potential of the gravitational force. Divergence. Solenoidal vector fields. Examples. Curl. Irrotational vector fields. Examples. Properties of basic operations. |
| 11.30 | 39 | 39 | 39 | ||
| 12.02 | 40 | 40 | 40 | ||
| 12.04 | 41 | 41 | 41 | ||
| 12.07 | 42 | 42 | 42 | ||
| 12.09 | 43 | 43 | 43 | ||
| 12.15 | Final Exam |