MATH 241 F1H: Calculus III Honors
Professor A.J. Hildebrand
Final Exam Results and Course Grades
Final exam scores and course grades are now available. For grading purposes, I
set the "perfect" score at 170, so that a score of 170 points is 100 percent,
and any points above 170 count as bonus points. The average score average
130/170, the highest scores were 181/170 and 170/170 (with bonus points).
If you want to see the final exam, send me an email (email@example.com) to set up
You can access your score as usual
this link. The grade shown at the end of the online score display (including
plusses and minuses) is the grade that has been reported as your official course
grade; it is based strictly on the total number of accumulated points and
is nonnegotiable. Cutoffs between letter grades were chosen to minimize
hardships and close calls. As a result, nobody was within a few points of
he next higher grade, and most gaps were substantially larger.
Have a good and relaxing break and enjoy your summer!
Course Policies, Exams, Grades
Math 241 F1H Honors FAQ.
This page answers questions about the "honors" nature of this course, and
how it differs from regular Math 241 sections.
BE SURE TO READ THIS FIRST.
- Course Information Sheet.
General course information: Everything you need to know about this course:
Instructor contact, text and syllabus, exam and homework information, grading
Sample exams. Links to sample exams from past Math 241 Honors
classes. These should give you a good idea of what to expect.
- Midterm Exam 1: Feb. 15 (in class)
- Midterm Exam 2: March 14 (in class)
- Midterm Exam 3: April 18 (in class)
- Final Exam: Wednesday, May 9, 7:00 pm - 10:00 pm, 143 Henry.
Link to Online Scores.
Click on this link and log in with your NetID and password to access
your scores. The display shows all the scores on all assignments and exams
given out so far, and your total accumulated score. If a score is missing
or incorrect, let me know right away.
- Add/drop deadlines: January 30 and March 9. The first date
(January 30) is the last date you can add a course; if you want to switch to a
non-honors section, you have to do so by that date since a section
switch involves dropping one course and adding another.
The second date (March 9) is the campus deadline for dropping a course.
Engineering students need to get their Dean's approval if they drop a course
after the 10th day of class.
- U of I Undergraduate Math Contest, Saturday, 3/3/2012, 10 am - 1 pm,
145 Altgeld Hall. A math problems contest open to all U of I
undergraduates. Registration not required; just show up!
For more informationon visit the U of I Math Contests
- Open House Hours:
Tuesdays/Thursdays, beginning at around 5:15 pm and Sundays, beginning at around
3:15 pm, in 159 Altgeld, beginning the second week of class. The Open
House is an informal office hour and get-together for students in my
classes, and the primary point of contact for my students. I will stay
as long as necessary - typically at least an hour, and sometimes much
longer. The Open House room, 159 Altgeld, is a small classroom located
in the basement of Altgeld Hall on the south side of the building. We
have exclusive use of this room during the above Open House hours.
The first graded homework assignment will be due the second week of class (week
of Monday, Jan. 23).
- Textbook and WebAssign access:
Our text is Stewart, Calculus: Early Transcendentals, 6th Edition.
Be sure to get the 6th Edition, not the newer 7th Edition (which has a white
cover). Click on the above link for more information on the text and on
setting up WebAssign, an online homework system with access to a variety of
online materials. The use of WebAssign is optional, and I will not be using
the homework feature of WebAssign, but you may want to check it out for the
other features it provides.
- Illinois Geometry Lab
(IGL). The IGL is a recently established center that provides an
opportunity for undergraduates to participate in research projects. For
more information, click on the above link, email firstname.lastname@example.org, or visit
the IGL open house on January 17, 5 pm, in 102 Altgeld Hall.
- Wednesday, 5/2.
Derivation of the limit formula for divergence. More generally, derivation of
a formula expressing an integrand function at a given point as a limit of
integrals over balls centered at this point.
The limit formula for divergence derived in class can be found at the end of
- Tuesday, 5/1:
Recap of the Fundamental Theorems. Emphasis on connections and analogies
between these theorems and on the general form of the theorems:
Integral of f over delta D equals the integral of delta f over D.
- Monday, 4/30:
A real-world illustration of flux: Calculating the amount of rain collected in a box
moving at a given speed. Do you get more wet or less wet if you move faster?
Interpretation of divergence as flux density.
Homework: HW 15 (not graded)..
- Thursday, 4/26:
Stokes' Theorem. Statement, examples, and analogies to FTC, FTLI, and Green's
Theorem. "Independence of surface" property.
- Wednesday, 4/25:
More on vector surface integrals. Flux interpretation.
Applications of the Divergence Theorem to inverse square fields.
- Tuesday, 4/24:
Examples of surface integral computations of various types.
Sections 16.7 and 16.9.
- Monday, 4/23:
- Thursday, 4/19:
Overview of surfaces, surface integrals, and Gauss' Theorem. Analogies to curves,
line integrals, and Green's Theorem. Parameter representation of surfaces.
Standard parametrizations for sphere and plane.
- Wednesday, 4/18: Midterm Exam 3.
- Tuesday, 4/17:
Curl test and mixed partials test.
Green's Theorem. Vector/curl version and explicit coordinate form.
- Read: Section 16.4.
Handout: Green's Theorem..
- Monday, 4/16:
Grad, div, and curl. Definitions and same examples. Combinations: Curl/grad and
div/curl. Curl test for conservative fields. Potential of an inverse square
- Read: Section 16.5.
Homework: HW 13, due Monday, 4/23.
- Thursday, 4/12:
Recap of Fundamental Theorem for Line Integrals and related properties:
Conservative fields, existence of potential/anti-gradient; independence of path;
loop integral zero; mixed partial test. Proof of the FTLI via chain rule for
derivatives in Rn.
- Wednesday, 4/11:
Conservative vector fields and potentials ("anti-gradients"). "Mixed partials"
test for "conservativeness". Finding potentials by "reverse partial
In particular, read up on the "mixed partials" test for conservative fields
(Theorems 5 and 6 and Examples 2 and 3) and the technique for finding
potentials via "inverse partial differentiation" (Examples 4 and 5).
- Tuesday, 4/10:
Line integrals continued. Connections between the different versions of line
integrals. Examples of line integral computations using different methods.
Fundmamental Theorem for Line Integrals.
- Read: Sections 16.2 and 16.3.
Handout: Line integrals.
- Monday, 4/9:
Section 16.2, line integrals. Definition and interpretation of line integrals of
scalar functions and line integrals of vector fields.
- Read: Section 16.2.
Homework: HW 12, due Monday, 4/16.
- Thursday, 4/5:
Started Chapter 16. Overview and goals of this chapter.
Vector fields, examples, and formal definition.
- Read: Section 16.1.
- Wednesday, 4/4:
Linear algebra excursion, continued. Determinants. Recursive computation
of n by n determinants. Algebraic properties of determinants. Volume
interpretation. Determinants of diagonal and triangular matrices.
- Read/do: Tomorrow's quiz will be on the linear algebra material covered
this week. In preparation, review this material, using your classnotes and the Linear Algebra handout as guide.
- Tuesday, 4/3:
Excursion into linear algebra. Geometric properties of linear functions from Rn
to Rn. Conversion factor for areas and volumes. Determinants. (To be continued
Linear Algebra, II.
- Monday, 4/2:
- Thursday, 3/29:
Change of variables formula for multiple integrals. The Jacobian determinant
as the "correct" conversion factor. Connection with matrix derivative of the
- Wednesday, 3/28:
More triple integral practice. Volume of icecream cones of various shapes.
Finish reading Sections 15.7 and 15.8. There will a short quiz tomorrow on these
sections (in particular, on the various conversion formulas for cylindrical and
- Tuesday, 3/27:
Triple integral practice. Integrals over spherical regions.
- Monday, 3/26:
Triple integrals. Cylindrical and spherical coordinates.
Section 15.6 on triple integrals in rectangular coordinates (focus on Examples 2
and 4 in this section). Also, get familiar with cylindrical and spherical
coordinates that are introduced at the beginning of Sections 15.7 and 15.8. You
should know the conversion formulas between rectangular, cylindrical, and
spherical coordinates, and the equations of simple surfaces (such as cones,
spheres, half-planes) in cylindrical and spherical coordinates.
Do: HW 10.
- Thursday, 3/15:
Fun with n-dimensional integrals: the volume of n-dimensional cubes,
n-dimensional tetrahedra, and n-dimensional spheres.
Do/read: If you have not done so, be sure to read/review sections
15.4 and 15.5, which were the subject of this week's regular HW assignment
(HW 9). The applications you need to know are those covered in HW 9. You
can skip over the part dealing with moments of inertia (p. 983/984), but
you should be familar with applications to mass and center of mass, and
with probability applications of the type covered in Tuesday's class and
in HW 9.
After the break, I will go straight to triple integrals (Sections
Homework: Honors HW Assignment 3,
due Monday, 4/2.
- Wednesday, 3/14: Midterm Exam 2.
- Tuesday, 3/13:
Application of double integrals to probability.
- Monday, 3/12:
Application of double integrals in polar coordinates:
Volume of a sphere, sphere cap, and "sphere with hole".
Evaluation of Gaussian integral by converting to a double integral and changing
to polar coordinates. (The remarkable trick involved here is described in
Exercise 36 of 15.4.)
Homework: HW 9.
- Thursday, 3/8:
Double integrals in polar coordinates. Applications of double integrals.
Do/read:Finish HW 8 and Honors HW 2, which are both due on Monday.
Get ready for Wednesday's midterm exam, using the
Exam 2 Study Guide and the
Exam 2 Syllabus and Checklist as study guide.
- Wednesday, 3/7:
Computation of double integrals. Fubini's theorem. Double integrals over
rectangles and over general regions. Reversing order of integration.
Read: Read sections 15.2 and 15.3 in preparation of tomorrow's quiz.
- Tuesday, 3/6:
Wrapped up excursion into derivatives in Rn. Illustration of Taylor's formula
in a concrete situation. Connection with differentials,
linear approximation, and tangent planes.
Started Chapter 15 on multiple integrals. Review of the one-variable case. The
integral as an area and as an antiderivative. Generalization of the area
interpretation to double integrals.
Homework: HW 8.
- Monday, 3/5:
Excursion: Derivatives in Rn, part II.
Formal definition of differentiability and derivatives of functions from
Rm to Rn via Taylor's formula.
Limit formulas for derivatives of vector functions and directional
Handout: Differentiability and Derivatives in
Rn, Part II.
Read/do: No new assignment, but use the time to review Chapter 14
in preparation for the upcoming midterm.
- Thursday, 3/1:
Maxima, minima, and saddle points.
First and second derivative tests for functions of one and two variables.
Motivation for first/second derivative tests via Taylor's formula.
- Wednesday, 2/29:
More application of the Lagrange multiplier method.
Maximizing the Cobb-Doublas production function. The meaning of
the Lagrange multiplier. Proof of Cauchy-Schwarz
inequality via Lagrange multipliers.
Read: Section 14.7.
Focus on the first part of this section
dealing with critical points and the second derivative test
(p. 923 - 926, and Examples 1-4).
(For other examples such as Examples 5 and 6, the Lagrange multiplier method
is the more natural approach, and you should be able to do these examples with
Lagrange multipliers. The same goes for many of the exercises in this section.
In fact, most of the problems on p. 932 come up again in 14.8, this time as
Lagrange multiplier exercises.)
- Tuesday, 2/28:
- Monday, 2/27:
- Thursday, 2/23:
Wrapped up the discussion of gradients, directional derivatives, and tangent
- Wednesday, 2/22:
Directional derivatives, gradients, level curves/surfaces.
Read Section 14.6.
- Tuesday, 2/21:
- Monday, 2/20:
Linear algebra excursion, continued. Some examples. Checking whether a function is
linear. Finding the matrix A associated with a linear function.
Formula for A in terms of partial derivatives.
- Do: Finish HW 5 (due Wednesday).
- Thursday, 2/16:
Excursion into linear algebra. Linear combinations. Linear functions,
definition and key properties. Key Fact: The linear functions from Rm to Rn
are exactly the functions of the form f(x) = A x, where A is an n x m
Handout: Linear Algebra
Homework: HW Assignment 5.
Read Section 14.5 and get started with the new HW assignment.
- Wednesday, 2/15: Midterm Exam 1.
- Monday, 2/13:
Section 14.4. Differentials, motivation, and applications (e.g., error
No additional assignment (the next HW won't be
due until at least Tuesday or Wedensday next week), but use the time to
prepare for Wednesday's midterm! See the Exam Study Guide linked above.
- Thursday, 2/9:
Partial derivatives, continued. Geometric interpretations. Partial
derivative calculations in ideal gas law.
HW 4 is due Monday.
Read Section 14.3 if you have not done so; the midterm will cover the
material through this section (14.3) and HW 4.
- Wednesday, 2/8:
Level curves and level surfaces. Started 14.3. Partial derivatives,
definition and notation. Clairaut's Theorem on mixed partials.
- Tuesday, 2/7:
Started Chapter 14. Multivariable functions, overview. Interpretation as
"black box" with vector input and scalar output. Domain and graph.
Homework: HW Assignment 4.
Read Section 14.1. This section lots of computer-generated sketches of
domains, graphs, and level curves to help develop a good intution for
these concepts. The section also has a number of examples similar to this
week's homework problems.
- Monday, 2/6:
Kepler's Laws. Proof of the First and Second Laws.
Since we are at the end of Chapter 13 and the first midterm is approaching
soon, this is a good time to begin reviewing the material covered so far.
An excellent starting point for such an exam review are the end-of-chapter
sections titled "Concept checks": p. 849-850 and p. 812-813.
- Thursday, 2/2:
Representation of acceleration in TNB frame,
normal and tangential components of acceleration,
derivation of formulas.
Read Section 13.4. Focus on the first part (Examples 1 - 4), and the
discussion of tangential and normal components of acceleration (p.
842-844). You can skip over the projectile problems in Examples 5 and 6.
Also, get started on the homework on 13.2-13.4; don't wait till the last
- Wednesday, 2/1:
Normal and osculating planes. Curvature.
Finish reading 13.3. You can skip formula (11) and Example 5 (curvature
formula for plane curve), but the rest of this section is important
and relevant for this week's homework, for tomorrow's quiz, and for the next
midterm (in two weeks). In particular, study the examples illustrating
the computation of the various quantities (arclength, curvature, T, N, B,
normal and osculating planes) in concrete situations such as the helix.
HW 3 has a number of problems of this type.
- Tuesday, 1/31:
More on derivatives of vector functions. Geometric interpretation. Limit
definition. Vector function of constant magnitude.
The TNB frame.
Homework: HW Assignment 3.
Read: Section 13.3.
In particular, read the first part, on arclength, and the last part of
this section, dealing with the TNB frame. In tomorrow's class, we will
cover the remaining topic of this section, curvature.
- Monday, 1/30:
Started Chapter 13. (Section 12.6 will be covered
later.) Vector functions, overview. Derivatives of vector functions,
componentwise definition, algebraic properties, examples.
Read: 13.1 and 13.2. In 13.1 you can skip over theoretical
aspects such as limits and continuity (we will cover this later).
However, 13.2 is an important section, with lots of good applications
and problems. I will spend another class hour on this section, and
there will be around ten problems from 13.2 on the next HW assignment
Homework: Honors HW Assignment 1,
due Thursday next week.
- Thursday, 1/26:
Lines and planes:
big picture, underlying ideas, and connections between the various types
Read/do: HW 2 is due Tuesday. Get started if you have not done so.
Also, finish reading 12.5. We will start with Chapter 13 next week.
- Wednesday, 1/25:
Quiz 1. Problems/proofs from the handout on n-dimensional spaces and the
Cauchy-Schwarz and Triangle Inequalities.
Application: The GPA Problem.
Read/do: If you have not done so, finish HW 1 (due tomorrow).
Also, read Section 12.5 lines and planes) in preparation for tomorrow's class
(and HW 2).
- Tuesday, 1/24:
Finished discussion of cross product, algebraic definition via
determinants, why cross product makes only sense in 3 dimensions.
Started excursion into n-dimensional space (one of the occasional ventures
beyond the standard material). Definition of basic operations (addition,
scalar multiplications, dot product, norm) for n-dimensional vectors.
Statement of Cauchy-Schwarz and Triangle Inequalities.
- Handout: n-dimensional space,
Cauchy-Schwarz and Triangle Inequalities
Homework: HW Assignment 2 (due Tuesday next
Read/do: If you have not done so, be sure to finish studying 12.4.
There will be a short quiz tomorrow on the properties and formulas involving dot
and cross products (Sections 12.3 and 12.4).
Also, work on HW 1 (due Thursday)
- Monday, 1/23:
The cross product. Geometric definition, properties, and applications.
Do: Read 12.4 in preparation for tomorrow's class. In particular,
familiarize yourself with 3 x 3 determinants, which are needed for the
computation of cross products.
- Thursday, 1/19:
More on the dot product. Algebraic properties of the dot product, and using
these properties in formal proofs. Orthogonal (perpendicular) and
parallel vectors, formal definition. Scalar and vector projections.
HW Assignment 1.
Do: Finish reading 12.3 if you have not done so.
Get started on the HW Assignment.
- Wednesday, 1/18:
Recap of 12.2. Basic arithmetic operations with vectors and their algebraic and
geometric descriptions. Representation of arbitrary vectors as linear
combinations of basis vectors. Examples of using vector methods to prove
Started 12.3. Products of two vectors, overview. The dot product and the cross
product. Definition of dot product and geometric interpretation in terms of
magnitude and angles.
Do: Read 12.3 in preparation for tomorrow's class.
- Tuesday, 1/17:
General course information; handed out the
Course Information Sheet
and the Honors FAQ.
Overview of the calculus sequence. One variable calculus versus
multivariable calculus. The n-dimensional space Rn. Vectors.
In preparation for tomorrow's class, read Sections 12.1 and 12.2.
Last modified: Fri 11 May 2012 05:25:49 PM CDT