MATH 2443.170 - Calculus and Analytic Geometry IV - Summer 2013
MTWRF 1:00-2:15 p.m., Carson Engineering Center 121

Instructor: Nikola Petrov, 802 PHSC, (405)325-4316, npetrov AT math.ou.edu

Office Hours: Tue 12-1 p.m., Thu 2:15-3:15 p.m., or by appointment.

Math Center: You can get help in the Math Center located at PHSC 209; it is open daily from 9:30 a.m. to 1:30 p.m.

Course catalog description: Prerequisite: 2433. Vector calculus; functions of several variables; partial derivatives; gradients, extreme values and differentials of multivariate functions; multiple integrals; line and surface integrals (F, Sp, Su)

Text: J. Stewart, Calculus, 7th edition, Brooks/Cole, 2012.

Check out the OU Math Blog! It is REALLY interesting!

Homework:

• Homework 1 (problems given on May 13, 14, 15), due May 17 (Friday).
• Homework 2 (problems given on May 16, 17, 20), due May 22 (Wednesday).
• Homework 3 (problems given on May 21, 22, 23), due May 28 (Tuesday).
• Homework 4 (problems given on May 28, 29), due May 31 (Friday).
• Homework 5 (problems given on May 30, 31, June 3), due June 5 (Wednesday).
• Homework 6 (problems given on June 4, 5), due June 7 (Friday).
• Homework 7 (problems given on June 6, 7, 11, 12), due June 14 (Friday).
• Homework 8 (problems given on June 13, 14, 17), due June 19 (Wednesday).
• Homework 9 (problems given on June 18, 19), due June 21 (Friday).
• Homework 10 (problems given on June 20, 21, 25), due June 27 (Thursday).

Content of the lectures:

• Lecture 1 (Mon, May 13): Functions of several variables: functions of two variables, independent variables, dependent variable, domain, range, graph, level curves, examples; functions of three or more variables [Sec. 14.1]
  Homework: 14.1/14, 15 (hint), 18, 20, 36, 47 (hint).
  FFT: 14.1/19 (hint), 21, 25 (hint), 26, 32, 39−42, 59(hint)−64.
  Remark: The FFT ("Food For Thought") problems are to be solved like a regular homework problems, but do not have to be turned in.
• Lecture 2 (Tue, May 14): Limits and continuity: limits of functions of one and several variables, examples; continuity of functions of one and several variables, proving discontinuity of a function at a point by finding different values when approaching the point along different paths, examples [read Examples 1-3, 5-9 of Sec. 14.2]
  Homework: 14.2/5 (see Example 5), 9 (hint), 15 (see Example 3 and consider, e.g., the paths x=0 and y=2x²), 17 (use polar coordinates), 19, 32, 41.
  FFT: 14.2/13 (hint), 25 (hint), 33.
• Lecture 3 (Wed, May 15): Partial derivatives: definition of partial derivatives for functions of two variables, definition of partial derivatives for functions of n variables, practical rules for finding partial derivatives, higher derivatives, Clairaut's Theorem, examples, ordinary and partial differential equations; for any pair of smooth functions φ and ψ (each of them is a function of one variable), the function u(x,t)=φ(x−ct)+ψ(x+ct) is a solution of the wave equation, u_tt(x,t)=c²u_xx(x,t) (challenge: prove this!) [Sec. 14.3; skip Example 4 on page 929]
  Homework: 14.3/24, 26, 34, 40, 41, 52 (hint), 64, 71, 78(a,d).
  FFT: 14.3/10, 73 (hint), 74.
  The complete Homework 1 is due on May 17 (Friday).
• Lecture 4 (Thu, May 16): Partial derivatives (cont.): implicit differentiation [Example 4 on page 929 of Sectoin 14.3]
  Tangent planes and linear approximations: equation of the tangent plane to a surface defined as a graph of a function, linear approximation (tangent plane approximation) of a function at a point, examples; increments Δx=dx and Δy=dy of the independent variables and increment Δz=f(a+Δx,b+Δy)−f(a,b) of the function value for z=f(x,y), differential dz=f_x(a,b)dx+f_y(a,b)dy of the function z=f(x,y) at the point (a,b) for given increments dx and dy of the independent variables, using differentials to estimate increments of functions [Sec. 14.4; skip Equations 5, 6, Definition 7, and Theorem 8 on page 942, skip Example 6 on page 945]
  Remark: Reviewing pages 183-184 of Sec. 2.9 will be useful.
  Homework: 14.3/50, 92; 14.4/6, 11 (only find the linearization, hint), 19, 21 (hint), 30, 31 (hint).
  FFT: 14.3/39, 79.
• Lecture 5 (Fri, May 17): Tangent planes and linear approximations: a function that has partial derivatives but no tangent plane; a function f(x,y) is said to be differentiable at the point (a,b) if it has a tangent plane at (a,b,f(a,b)); the continuity of the partial derivatives of a function implies the differentiability of the function (Theorem 8); differentiability of a function at a point implies continuity of the function at that point; an example of using differentials to estimate the increment of the value of a function due to small changes of the values of the arguments - estimating the metal needed to make a cylindrical can (i.e., estimating the change of the volume of a cylinder when its radius and height increase by small amounts); linear approximation, differentiability, and differentials of functions of more than two variables [Exercise 14.4/46 on page 948, Example 6 on page 945 of Sec. 14.4]
  The chain rule: cases 1 and 2, and the general case of the chain rule for functions of several variables [pages 948-952 of Sec. 14.5]
  Remark: Reviewing pages 148-152 of Sec. 2.5 may be useful.
  Homework: 14.4/33, 42; 14.5/2, 10, 14, 16, 24, 41, 47 (hint).
• Lecture 6 (Mon, May 20): The chain rule: implicit differentiation of a function of one variable and a function of more than one variables, examples [pages 952-954 of Sec. 14.5]
  Directional derivatives and the gradient vector: directional derivative of a function of two variables, expressing D_uf(x₀,y₀) in terms of the partial derivatives of f and the components of the unit vector u, the gradient vector ∇f(x₀,y₀), expressing the directional derivative as a scalar product of a unit vector and the gradient vector: D_uf(x₀,y₀)=∇f(x₀,y₀)⋅u, maximizing the directional derivative; significance of the gradient vector - the tangent lines to level curves at (x₀,y₀) are perpendicular to ∇f(x₀,y₀), path of steepest descent/ascent [pages 957-964, 966 of Sec. 14.6]
  Homework: 14.5/30, 34; 14.6/5, 8, 13 (v is not a unit vector!), 20, 23 (hint), 37(a,b,d).
  FFT: 14.5/17 (hint); 14.6/7, 19 (hint), 56.
  The complete Homework 2 is due on May 22 (Wednesday).
• Lecture 7 (Tue, May 21): Directional derivatives and the gradient vector (cont.): tangent planes to level surfaces [pages 964-965 of Sec. 14.6]
  Maximum and minimum values: local minima and maxima, global (absolute) minima and maxima, if a differentiable function has an extremum (i.e., a minimum or a maximum) at (a,b), then f_x(a,b)=0 and f_y(a,b)=0 (Theorem 2), critical (stationary) points of a function, examples: (1) f(x,y)=x²+y²: (0,0) is a critical point and a local (and global) mimimum; (2) f(x,y)=x²−y²: (0,0) is a critical point but is not a local extremum; (3) f(x,y)=|x|: all points of the form (0,y) are critical points and they are all local (and global) minima; (4) f(x,y)=|x|+y: all points of the form (0,y) are critical points but none of them is a local extremum [pages 970-971 of Sec. 14.7]
  Homework: 14.6/43, 49, 56; 14.7/2, 19.
  FFT: 14.6/67 (hint); 14.7/1 (hint).
• Lecture 8 (Wed, May 22): Maximum and minimum values (cont.): second derivatives test, examples; global (absolute) maxima/minima, definition of a boundary point of a set, definition of a closed set, definition of a bounded set, extreme value theorem for continuous functions of two variables on a closed bounded set, algorithm for finding the absolute minima and maxima of a function on a domain D (don't forget the values on the boundary of the domain D!) [pages 971-976 of Sec. 14.7]
  Homework: 14.7/3 (hint), 31 (hint), 43 (hint), additional problem.
  FFT: 14.7/13 (hint), 41 (hint), 55.
• Lecture 9 (Thu, May 23): Double integral over rectangles: areas and single integrals in Calculus II, volumes and double integrals, double Riemann sums, double integral over a rectangle, volumes under graphs of functions of two variables over rectangles, midpoint rule for double integrals [pages 990-1002 of Sec. 15.1]
  Homework: No homework problems assigned.
  The complete Homework 3 is due on May 28 (Tuesday).
• Lecture 10 (Fri, May 24): Exam 1 [on Sec. 14.1-14.7]
• Lecture 11 (Tue, May 28): Double integral over rectangles (cont.): average value, linearity of double integrals, monotonicity of double integrals [pages 1003-1005 of Sec. 15.1]
  Iterated integrals: the concept of an iterated integral, Fubini's theorem, examples [Sec. 15.2]
  Homework: 15.1/12, 14, 18; 15.2/2, 9 (hint), 11, 17 (hint), 22, 37.
  FFT: Chapter 14 Concept Check (page 991); 15.2/23 (hint), 27 (hint), 35 (hint).
• Lecture 12 (Wed, May 29): Double integrals over general regions: definition of a double integral over a general region D (by continuing the function on a rectangle R containing D and integrating over the rectangle), type I regions, integrals over a type I region; type II regions, integrals over a type II regions; computing integrals over general regions, properties of double integrals, examples [Sec. 15.3]
  Homework: 15.3/8, 14, 17 (hint), 25 (hint), 58, 64.
  FFT: Chapter 14 True-False Quiz (pages 991-992); 15.3/11, 12, 37, 56.
  The complete Homework 4 is due on May 31 (Friday).
• Lecture 13 (Thu, May 30): Double integrals over general regions (cont.): more examples (Exercises 15.2/37, 15.3/46 and 15.3/56).
  Double integrals in polar coordinates: polar coordinates, areas of polar rectangles, change to polar coordinates in double integrals, discussion on change of variables in functions, examples [Sec. 15.4]
  Homework: 15.3/48, 51; 15.4/2, 4, 11 (hint), 13 (hint), 25 (hint), 31.
  FFT: 15.3/15, 47 (hint), 62; 15.4/6, 39 (hint), 40.
• Lecture 14 (Fri, May 31): Double integrals in polar coordinates (cont.): calculating the area of a circle using different methods: (1) by a single integral (as in Calculus II), (2) by a double integral in Cartesian coordinates, (3) by a double integral in polar coordinates, with a coordinate system centered at the center of the circle, (4) by a double integral in polar coordinates, with a coordinate system centered at the periphery of the circle and the x-axis passing through the center of the circle, with two different order of integration.
  Triple integrals: a triple integral over a box as a triple Riemann sum, Fubini's Theorem for triple integrals, computing a triple integral over a Type-1 domain [pages 1041-1043 of Sec. 15.7]
  Homework: 15.4/17, 32; 15.7/5, 10.
  Hints to 15.4/32: you may use that the relation y=(2x−x²)^1/2 is equivalent to (x−1)²+y²=1; when you convert it to polar coordinates, it is easier to have the integration over θ outside and the integration over r inside − if you do this, you will have to integrate cos³θ − this integral is very easy if you use that cos³θ=(1−sin²θ)cos(θ) which can be integrated by using substitution; the final answer is 16/9).
• Lecture 15 (Mon, June 3): Triple integrals (cont.): examples [Exercises 15.3/33 and 15.3/35 of Sec. 15.7]
  Homework: 15.7/13 (hint), 19 (hint), 34, 36, 55(a).
  FFT: 15.7/23 (hint), 27 (hint), 33 (a detailed solution), 35 (hint).
  The complete Homework 5 is due on June 5 (Wednesday).
• Lecture 16 (Tue, June 4): Triple integrals in cylindrical coordinates: cylindrical coordinates in R³; computing triple integrals in cylindrical coordinates [Sec. 15.8]
  Homework: 15.8/8, 10, 16, 21 (hint), 29.
  FFT: 15.7/53 (hint).
• Lecture 17 (Wed, June 5): Triple integrals in spherical coordinates: spherical coordinates, volume element in spherical coordinates [Sec. 15.9]
  Homework: 15.9/4, 8, 10, 14, 28, 40.
  FFT: 15.9/5 (hint), 6, 7, 9, 13, 15.
  The complete Homework 6 is due on June 7 (Friday).
• Lecture 18 (Thu, June 6): Triple integrals in spherical coordinates (cont.): examples of computations useing spherical coordinates: (1) computing the average value of the y coordinate in the half of the unit ball (centered at the origin) with y≥0 by using a triple integral; (2) computing the same quantity as in (1) by "slicing" the half-ball with many densely-spaced parallel planes (all of them perpendicular to the y-axis) and finding the limit of the Riemann sum by using a triple integral; (3) computing the volume V_n(R) of the ball of radius R in Rⁿ by integrating the function exp(−|x|²) over Rⁿ in two different ways - by representing this integral as a product of n identical integrals (each of which is computed in Exercise 15.4/40(c)), or by considering the space Rⁿ as a union of concentric thin shells ("onion"-like structure) and then using a single integral; the result for the volume V_n(R) is V_n(R)=π^n/2Rⁿ/Γ(n/2+1), where Γ(z) is the Gamma function.
  Homework: Click here for the assigned homework.
  FFT: Chapter 15 Concept Check (page 1073; skip questions 4(b,c,d), 8(b,c,d), and 10), Chapter 15 True-False Quiz (pages 1073-1074; skip question 8).
• Lecture 19 (Fri, June 7): Vector fields: vector fields on subsets of R² and R³, plots of vector fields, gradient vector fields, conservative vector fields, potential function of a conservative vector field, examples (Newton's law of gravity, Coulomb's law of interaction between stationary electric charges), an example of a vector field that is not conservative: F(x,y)=−yi+xj (to show that it is not conservative, we assumed that it is conservative, i.e., that F=Pi+Qj=∇f=f_xi+f_xj, and using Clairaut's Theorem (Sec. 14.3) to come to a contradiction (because (f_x)_y=P_y=(−y)_y=−1 is different from (f_y)_x=Q_x=(x)_x=1) [Sec. 16.1]
  Homework: 16.1/10, 11-14, 24.
  FFT: 16.1/15-18, 29-32.
• Lecture 20 (Mon, June 10): Exam 2 [on Sec. 15.1-15.4, 15.7-15.9]
• Lecture 21 (Tue, June 11): Line integrals: line integral (with respect to arc length) of a function along a curve C in 2 and more dimensions, piecewise-smooth curves, velocity v(t)=r'(t) and speed v(t)=|v(t)|, expressing the arc length as ds=v(t)dt; line integrals with respect to x and y [pages 1087-1093 of Sec. 16.2, including Example 5 on page 1093]
  Homework: 16.2/5, 11 (hint), 13, 15, 33 (hint), 37.
• Lecture 22 (Wed, June 12): Line integrals (cont.): line integrals of vector fields, unit tangent vector T(t)=r'(t)/|r'(t)|; expressing work as an integral of F⋅T with respect to the arc length, as an integral of F(r(t))⋅r'(t) with respect to the parameter t, and as an integral of F(r)⋅dr; behavior of integrals with respect to arc length and with respect to x and y when changing the direction of traversing the curve C [pages 1094-1096 of Sec. 16.2]
  Homework: 16.2/21 (hint), 39 (hint), 43 (use that F=ma), 49.
  FFT: 16.2/17 (hint), 18, 35(a), 50, 52.
  The complete Homework 7 is due on June 14 (Friday).
• Lecture 23 (Thu, June 13): The Fundamental Theorem for line integrals: the Fundamental Theorem for line integrals (with proof using the Chain Rule and the Fundamental Theorem of Calculus); independence of path - definition; vanishing of the line integral over any closed path is a necessary and sufficient condition for path independence (Theorem 3); definitions of open domain and connected domain, path independence of a vector field over an open connected domain implies that the vector field is conservative (Theorem 4) [pages 1099-1102 of Sec. 16.3]
  Homework: 16.3/2, 11 (hint), 12, 20, 28, 32, 34.
  FFT: 16.3/1, 21, 22, 25 (hint).
• Lecture 24 (Fri, June 14): The Fundamental Theorem for line integrals (cont.): for a conservative vector field F(x,y)=P(x,y)i+Q(x,y)j, the equality ∂P/∂y=∂Q/∂x holds (Theorem 5); simple curve, simply-connected domain, necessary and sufficient condition for a vector field in a simply-connected domain in R² to be conservative (Theorem 6); an example: the vector field F(x,y)=(e^y+2x)i+(xe^y+y)j (defined in R² which is an open and simply-connected domain) is conservative: F(x,y)=∇f(x,y) for f(x,y)=xe^y+x²+y²/2 (check that F(x,y) satisfies the condition P_y=Q_x); on the other hand, the vector field F(x,y)=(e^y+2x)i+(xe^y+y+x²sin(y))j does not satisfy P_y=Q_x, so there is no function f(x,y) such that F(x,y)=∇f(x,y); the vector field F(x,y)=(−yi+xj)/(x²+x²) satisfies P_y=Q_x but is non-conservative because integral of it over the unit circle in counterclockwise direction is 2π - therefore, there exists a closed curve the integral of F over which is non-zero, which by Theorem 3 implies that the integral of F is not path-independent, so by the Fundamental Theorem for line integrals F is not conservative - these facts do not contradict Theorem 6 because F is not defined at (0,0), so that the domain D of F is not a simply-connected domain; conservation of energy [pages 1102-1105 of Section 16.3, and Exercise 16.3/35 (hint)]
  Homework: 16.3/5, 9, 18, 30, additional problem.
• Lecture 25 (Mon, June 17): Green's Theorem: orientation of the boundary of a planar domain, Green's Theorem, proof for a domain that is both type-I and type-II, proofs that the theorem works for domains that are not type-I and type-II, and for domains with holes [pages 1108-1112 of Sec. 16.4]
  Homework: 16.4/3 (hint), 7 (hint), 12, 17 (hint).
  The complete Homework 8 is due on June 19 (Wednesday).
• Lecture 26 (Tue, June 18): Green's Theorem (cont.): examples of using Green's Theorem for practical calculations, derivation of formulas for areas of planar domains; an example when the contour can be deformed to some extent but the value of the integral of a vector field does not change (because P_y=Q_x) - Example 5 (recall Exercise 16.3/35 considered in detail in Lecture 24) [pages 1110-1113 of Section 16.4]
  Parametric surfaces and their areas: parametric curves and parametric surfaces in R³, grid curves in a parameterized surface, examples (plane, sphere, cylinder), tangent vectors r_u(u₀,v₀) and r_v(u₀,v₀) to the surface r(u,v) at the point r(u₀,v₀), normal vector r_u(u₀,v₀)×r_v(u₀,v₀) to the tangent plane of the surface r(u,v) at the point r(u₀,v₀), equation of the tangent plane, |a×b| as the area of the parallelogram spanned by the vectors a and b, area ΔS of a surface element ΔS=|r_u×r_v|ΔA, where ΔA=(Δu)(Δv) [pages 1123-1128 of Sec. 16.6, skip "Surfaces of revolution" on page 1127, read the text around Figure 14 on page 1128]
  Reading assignment 1: Read the sketch of the proof of Theorem 16.3.6 on page 1113.
  Reading assignment 2: Look at Equation 4 on page 926 and Figure 1 on page 927, and reread "Interpretations of partial derivatives" on pages 927-928 of Sec. 14.3; look at Fig. 12 on page 1127 and Equations 4 and 5 on pages 1127-1128, and think about the connection with the definition and interpretation of partial derivatives from Sec. 14.3 that you just read.
  Homework: 16.4/19; 16.6/2, 3 (hint), 6, 19 (hint), 26 (hint), 34.
  FFT: 16.6/13-18.
• Lecture 27 (Wed, June 19): Parametric surfaces and their areas (cont.) area of a parametric surface as a limit of Riemann sums, area of a graph of a function; example: area of the unit sphere; remarks on scaling of physical quantities, derivation of the period of a pendulum by dimensional analysis, a proof of non-existence of Godzilla [pages 1127-1131 of Sec. 16.6]
  Surface integrals: motivation and definition of surface integrals, definition, surface integrals over graphs of functions z=g(x,y), physical applications: total mass; orientable surfaces, an example of a non-orientable surface - Moebius strip [pages 1134-1138 of Sec. 16.7]
  Homework: 16.6/30 (skip the graphing), 39 (hint), 49 (hint), 51, 59(a,c) (hint).
  FFT: Questions 1-8, 11, 12 of Chapter 16 Concept Check (page 1160).
  The complete Homework 9 is due on June 21 (Friday).
• Lecture 28 (Thu, June 20): Surface integrals: orientable surfaces, unit normal vector field to a parameterized surface: n is equal to (plus or minus) r_u×r_v/|r_u×r_v|, the positive orientation of a closed orientable surface is given by the outward unit normal vector to the surface; surface integrals of vector fields, flux of a vector field; examples from physics: fluid flow through a surface, Gauss's Law for the flux of the electric field E, heat flow; "natural" orientation of a parametric surface S defined by a vector equation r(u,v) - given by the unit normal vector n=r_u×r_v/|r_u×r_v| (Equation 6 on page 1139); alternative expressions for surface integrals ∫_SF•dS [pages 1139-1144 of Sec. 16.7]
  Homework: 16.7/9 (hint), 23 (hint), 39 (hint).
  FFT: 16.7/38.
• Lecture 29 (Fri, June 21): Curl and divergence: dot and cross product of vectors in R³, different methods for memorizing the expression for a×b, cyclic permutations; the gradient operator as a vector: ∇=i∂_x+j∂_y+k∂_z; definition of curl curl(F)=∇×F of a vector field F(x,y,z) in R³, curl(grad(f))=0 for any function f:R³→R, physical interpretation of ∇×F; definition of divergence div(F)=∇⋅F of a vector field F, div(curl(F))=0 for any vector field F(x,y,z), physical interpretation of div(F); condition for conservativeness in terms of curl; Laplacian of a scalar function; Laplace and the early history) of the concept of black holes (see also in the FAQ of the Hubble telescope and the Wikipedia article on black holes), history of Maxwell's equations [pages 1115-1119 of Sec. 16.5]
  Homework: 16.5/3, 16, 19 (hint), 21 (hint, "irrotational" means "with zero curl"), 25, 30, 31 (hint).
  FFT: 16.5/9, 11, 12; Chapter 16 True-False Quiz (page 1060; skip question 11).
• Lecture 30 (Mon, June 24): Exam 3 [on Sec. 16.1-16.7]
• Lecture 31 (Tue, June 25): Stokes' Theorem: orientation of the boundary of an oriented surface consistent with the orientation of the surface, Stokes' Theorem, circulation of a vector field over a simple closed curve, physical meaning of the curl of a vector field [pages 1146-1149 of Sec. 16.8]
  Homework: 16.8/1 (hint), 16, 20(a) (hint: use Exercise 16.5/26).
  FFT: 16.7/26, 27; 16.8/7 (hint), 20(b,c).
  The complete Homework 10 is due on June 27 (Thursday).
• Lecture 32 (Wed, June 26): Stokes' Theorem (cont.): Green's Theorem as a particular case of Stokes' Theorem; circulation of a vector field over a simple closed curve, physical meaning of the curl of a vector field [page 1150 of Sec. 16.8]
  The Divergence Theorem: the Divergence Theorem, examples; derivation of Coulomb's law from the equation div(E)=ρ/ε₀ [Sec. 16.9]
  Homework: 16.9/7 (hint), 24, 25 (hint), 27, 29. [Not to be turned in!]
  FFT: Questions 9, 10, 13-16 of Chapter 16 Concept Check (page 1160); Question 11 of Chapter 16 True-False Quiz (page 1060).
• Lecture 33 (Thu, June 27): Derivation of the heat/diffusion equation from the law of conservation of energy, Fourier's law, and the Divergence Theorem (the diffusion equation is the same, but instead of Fourier's law relies on Fick's law); Lord Kelvin's briliant miscalculation of the age of the Earth.
  On the curious history of Fermat's Last Theorem and its proof by Andrew Wiles.
• Lecture 34 (Fri, June 28): Final Exam [cumulative].

Attendance: You are required to attend class on those days when an examination is being given; attendance during other class periods is also expected. You are fully responsible for the material covered in each class, whether or not you attend. Make-ups for missed exams will be given only if there is a compelling reason for the absence, which I know about beforehand and can document independently of your testimony (for example, via a note or a phone call from a doctor or a parent).

Homework: It is absolutely essential to solve a large number of problems on a regular basis!
Homework will be assigned regularly and will be posted on the this web-site. The homework will be due at the start of class on the due date. Each homework will consist of several problems, of which some pseudo-randomly chosen problems will be graded. Your lowest homework grade will be dropped. Giving just an answer to a problem is not worthy any credit - you have to write a complete solution which gives your step-by-step reasoning and is written in grammatically correct English. Although good exposition takes time and effort, writing your thoughts carefully will greatly increase your understanding and retention of the material.
You are allowed (and encouraged) to work in small groups. However, each of you will need to prepare individual solutions written in your own words - this is the only way to achieve real understanding!
Your homework should have your name clearly written on it, and should be stapled; the problems should be in the same order in which they are given in the assignment. No late homework will be accepted!

Exams: There will be three in-class midterms and a (comprehensive) final.
Tentative dates for the midterms are May 24 (Friday), June 10 (Monday), June 24 (Monday).
The final will be given during the regular class time on June 28 (Friday).
All tests must be taken at the scheduled times, except in extraordinary circumstances.
Please do not arrange travel plans that prevent you from taking the exams at the scheduled times.

Grading: Your grade will be determined by your performance on the following coursework:

Useful links: the academic calendar, the class schedules.

Policy on W/I Grades : From May 17 (Friday) to June 6 (Thursday), you can withdraw from the course with an automatic "W". Dropping after June 7 (Friday) requires a petition to the Dean. (Such petitions are not often granted. Furthermore, even if the petition is granted, I will give you a grade of "Withdrawn Failing" if you are indeed failing at the time of your petition.) Please check the dates in the academic calendar!

The grade of "I" (Incomplete) is not intended to serve as a benign substitute for the grade of "F". I only give the "I" grade if a student has completed the majority of the work in the course (for example everything except the final exam), the coursework cannot be completed because of compelling and verifiable problems beyond the student's control, and the student expresses a clear intention of making up the missed work as soon as possible.

Academic Misconduct: All cases of suspected academic misconduct will be referred to the Dean of the College of Arts and Sciences for prosecution under the University's Academic Misconduct Code. The penalties can be quite severe. Don't do it!
For details on the University's policies concerning academic integrity see the Student's Guide to Academic Integrity at the Academic Integrity web-site. For information on your rights to appeal charges of academic misconduct consult the Academic Misconduct Code. Students are also bound by the provisions of the OU Student Code.

Students With Disabilities: The University of Oklahoma is committed to providing reasonable accommodation for all students with disabilities. Students with disabilities who require accommodations in this course are requested to speak with the instructor as early in the semester as possible. Students with disabilities must be registered with the Office of Disability Services prior to receiving accommodations in this course. The Office of Disability Services is located in Goddard Health Center, Suite 166: phone 405-325-3852 or TDD only 405-325-4173.

Good to know:

• The greek_alphabet.
• Some useful notations.