Syllabus: M408D
DIFFERENTIAL AND
INTEGRAL CALCULUS
Text: Stewart,
Calculus, Fifth Edition
Responsible
Parties: Gary Hamrick December
2003
Prerequisite and degree relevance:
A grade of C or better in M408C or the equivalent. (Note: The pace of M408C and
M408D is brisk. For this reason, transfer students with one semester of
calculus at another institution are requested to consult with the Undergraduate
Adviser for Mathematics to determine whether M408D or an alternative, M408L, is
the appropriate second course.) 408D may not be counted by students with credit
for Mathematics 408L, 308M.
M408C and M408D (or the equivalent sequence M408K, M408L, M408M) are required
for mathematics majors, and mathematics majors are required to make grades of C
or better in these courses.
Certain sections of this course are reserved as advanced placement or honors sections; they are restricted to students who have scored well on the advanced placement AP/BC exam, or are honors students, or who have the approval of the Mathematics Advisor. Such sections and their restrictions are listed in the Course Schedule for each semester.
Course description:
M408C, M408D is our standard first-year calculus sequence. It is directed at students
in the natural and social sciences and at engineering students. The emphasis in
this course is on problem solving, not on the presentation of theoretical
considerations. While the course necessarily includes some discussion of
theoretical notions, it s primary objective is not the production of
theorem-provers. M408D contains a treatment of infinite series, and an
introduction to vectors and vector calculus in 2-space and 3-space, including
parametric equations, partial derivatives, gradients and multiple integrals.
Overview and Course Goals
The following pages comprise the syllabus for M408D, and advice on teaching it. Calculus is a service course, and the material in it was chosen after interdepartmental discussions. Please do not make drastic changes (for example, skipping techniques of integration). You will do your students a disservice and leave them ill equipped for subsequent courses.
This is not a course in the theory of calculus; the majority of the proofs in the text should not be covered in class. At the other extreme, some of our brightest math majors found their first passion in calculus; one ought not to bore them. In general it is fair to say that 408D students are somewhat better than 408C students; on the other hand 408D is a more difficult course. Please keep in mind that students who pass this course meet the prerequisite for M427K, where it assumed they have good calculus skills. DonÕt short-change the M427K faculty by providing a ÔweakÕ course. The 408C/D sequence is the ÔfastÕ sequence for students with good algebra skills; students who cannot maintain the pace are encouraged to take the M408KLM sequence.
Resources for Students
Some of our students have weak study skills. The Learning Skills Center in Jester has a wide variety of material ( drills, video-taped lectures, computer programs, counseling, math anxiety workshops, algebra and trig review, calculus review) as well as tutoring options, all designed to help students through calculus. On request, (471-3614) theyÕll come to your classroom and explain their services.
You can help your students by informing them of LSC services.
Timing and Optional Sections
A ÔtypicalÕ semester has 43 MWF days; a day or so will be lost to course-instructor evaluations, etc. The syllabus contains material for 39 days; you cannot afford to lose class periods. If you plan to give exams in lecture rather than in TA section, you will surely have to cut time somewhere. We have added some flexibility to the syllabus by designating all the application sections as optional. It is expected that you will choose three or four of these and cover them well; it is also expected that you will not have time to do all of them.
Those teaching on TTh
should adjust the syllabus; a MWF lecture lasts 50 min; a TTh therefore 75
Forty Class Days As:
7 Inverse Functions:
Exp Log and Inverse Trig (one day)
7.7 Indeterminate
Forms and L'Hospital's Rule
8 Techniques of
Integration (one day)
8.8
Improper Integrals
12 Infinite Sequences
and Series (twelve
days)
12.1 Sequences
12.2 Series
12.3 The Integral Test and
Estimates of Sums
12.4 The Comparison Tests
12.5 Alternating Series
12.6 Absolute Convergence and the
Ratio and Root Tests
12.7 Strategy for Testing
Series
12.8 Power Series
12.9 Representations of Functions
as Power Series
12.10 Taylor and Maclaurin Series
12.11 The Binomial Series
12.12 Applications of Taylor
Polynomials
11 Parametric
Equations and Polar Coordinates (four days)
11.1 Curves Defined by Parametric
Equations
11.2 Calculus with Parametric
Curves
11.3 Polar Coordinates
11.4 Areas and Lengths in Polar
Coordinates
11.5 Conic Sections
11.6 Conic Sections in Polar
Coordinates
13 Vectors and the
Geometry of Space (six days)
13.1 Three-Dimensional
Coordinate Systems
13.2 Vectors
13.3 The Dot Product
13.4 The Cross Product
13.5 Equations of Lines and
Planes
13.6 Cylinders and Quadric
Surfaces
13.7 Cylindrical and Spherical
Coordinates
14 Vector Functions (two days)
14.1 Vector Functions and Space
Curves
14.2 Derivatives and Integrals of
Vector Functions
14.3 Arc Length and Curvature
14.4 Motion in Space: Velocity and
Acceleration
15 Partial
Derivatives (seven days)
15.1 Functions of Several
Variables
15.2 Limits and Continuity
15.3 Partial Derivatives
15.4 Tangent Planes and Linear
Approximations
15.5
The Chain Rule
15.6
Directional Derivatives
and the Gradient Vector
15.7
Maximum and Minimum
Values
15.8 Lagrange
Multipliers
16 Multiple
Integrals (seven
days)
16.1 Double Integrals over
Rectangles
16.2 Iterated Integrals
16.3
Double Integrals over
General Regions
16.4
Double Integrals in
Polar Coordinates
16.5
Applications of double
Integrals
16.6
Surface Area
16.7
TripleIntegrals
16.8 Triple Integrals in
Cylindrical and Spherical Coordinates
16.9 Change of Variables in
Multiple Integrals 1077