Syllabus: M408C
DIFFERENTIAL AND INTEGRAL CALCULUS
Text: Stewart,
Calculus, Fifth Edition
Responsible Parties:
Kathy Davis, John Gilbert, Gary Hamrick June 19 2003
Prerequisite and degree relevance:
Either a 560 on the Mathematics IC Test or 560 on Mathematics Level IIC or a grade of at least C in M304E or M305G. Note: Students who score less than 600 on the Mathematics Level IC Test should be aware that studies show taking M305G first is likely to improve their grade in M408C.
Only one of the following may be counted: M 403K, 408C, 408K, 308K.
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.
Course description:
M408C is our standard first-semester calculus course. 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, its primary objective is not the production
of theorem-provers.
The syllabus for M408C includes most of the elementary topics in the theory of real-valued functions of a real variable: limits, continuity, derivatives, maxima and minima, integration, area under a curve, volumes of revolution, trigonometric, logarithmic and exponential functions and techniques of integration.
Overview and Course Goals
The following pages comprise the syllabus for M408C, 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. Remember that 408C/D 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:
Appendixes (for reference and reading by student)
A Numbers,
Inequalities, and Absolute Values
B Coordinate Geometry
and Lines
C Graphs of Second-Degree
Equations
D Trigonometry
E Sigma
Notation
1 Functions and
Models (for reference and reading
by student)
1.1
Four Ways to Represent
a Function
1.2
Mathematical Models: A
Catalog of Essential Functions
1.3 New
Functions from Old Functions
Principles of Problem
Solving
2 Limits and Rates of
Change (Five Days)
2.1 The Tangent
and Velocity Problems
2.2 The Limit
of a Function
2.3 Calculating
Limits Using the Limit Laws
2.4 The Precise
Definition of a Limit (briefly)
2.5 Continuity
2.6 Tangents,
Velocities, and Other Rates of Change
3 Derivatives (Seven Days)
3.1 Derivatives
3.2 The
Derivative as a Function
3.2 Differentiation
Formulas
3.4 Rates of
Change in the Natural and Social Sciences
3.5 Derivatives
of Trigonometric Functions
3.6 The Chain
Rule
3.7 Implicit
Differentiation
3.8 Higher
Derivatives
3.9 Related
Rates
4 Applications of
Differentiation (Seven Days)
4.1 Maximum and
Minimum Values
4.2 The Mean
Value Theorem
4.3 How
Derivatives Affect the Shape of a Graph
4.4 Limits at
Infinity; Horizontal Asymptotes
4.5 Summary of
Curve Sketching
4.7
Optimization Problems
4.10 Antiderivatives
5 Integrals (Six Days)
5.1 Areas and
Distances
5.2 The
Definite Integral
5.3 The
Fundamental Theorem of Calculus
5.4 Indefinite
Integrals and the Net Change Theorem
5.5 The
Substitution Rule
6 Applications of
Integration (Two Days)
6.1 Areas
between Curves
6.2 Volumes
7 Inverse Functions:
Exp Log and Inverse Trig (Six
Days)
7.1 Inverse Functions
Sections 7.2-7.4 or
Sections 7.2*-7.4* at discretion of instructor
7.2
Exponential Functions
Their Derivatives
7.3
Logarithmic Functions
7.4
Derivatives of
Logarithmic Functions
7.5 Inverse
Trigonometric Functions
8 Techniques of
Integration (Seven Days)
8.1 Integration
by Parts
8.2 Trigonometric
Integrals
8.3 Trigonometric
Substitution
8.4 Integration
of Rational Functions by Partial Fractions
8.5 Strategy
for Integration