Syllabus: M408K
DIFFERENTIAL CALCULUS
Text: Stewart,
Calculus, Fifth Edition
Responsible
Parties: Kathy Davis, John Gilbert, Gary Hamrick June 19 2003
Prerequisite and degree relevance:
Either four years of high school mathematics and a Mathematics Level I or IC Test score of at least 520, or M 305G with a grade of at least C. Note: Students who score less than 600/580 on the Mathematics Level I or IC Test are advised to take the M408KLM sequence rather than M408CD.
Only one of the follwing may be counted: M 403K, 408C, 408K.
Calculus is offered in two
equivalent sequences: a two-semester sequence, M 408C/408D, which is
recommended only for students who score at least 600 on the mathematics Level I
or IC Test, and a three-semester sequence, M 408K/408L/408M.
For some degrees, the two-semester
sequence M 408K/408L satisfies the calculus requirement . This sequence is also
a valid prerequisite for some upper-division mathematics courses, including
M325K, 427K, 340L, and 362K.
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:
M408K is one of two first-year calculus courses. It is directed at students in
the natural and social sciences and at engineering students. In comparison with
M408C, it covers fewer chapters of the text. However, some material is covered
in greater depth, and extra time is devoted the development of skills in
algebra and problem solving. This is not a course in the theory of
calculus.
The syllabus for M408K covers differential calculus: limits, continuity, derivatives, maxima and minima, trigonometric, logarithmic and exponential functions.
A 'typical' semester has 43 MWF days; a day or so will be
lost to course-instructor evaluations, etc. The syllabus contains material for
40 days; you cannot afford to lose class periods. Those teaching on TTh should
adjust the syllabus; a MWF lecture lasts 50 min; a TTh therefore 75 min.
Forty Class Days As:
Appendixes (assigned as reading and reference)
A Numbers,
Inequalities, and Absolute Values
B Coordinate Geometry
and Lines
C Graphs of Second-Degree Equations
D Trigonometry
1 Functions and
Models (assigned as reading and reference)
1.1
Four Ways to Represent
a Function
1.2
Mathematical Models: A
Catalog of Essential Functions
1.3 New
Functions from Old Functions
2 Limits and Rates of
Change (seven 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
2.5 Continuity
2.6 Tangents,
Velocities, and Other Rates of Change
3 Derivatives (eleven 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
3.10 Linear Approximations
and Differentials
4 Applications of
Differentiation (eleven 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
4.8 Applications
to Business and Economics
4.9 Newton's
Method (optional)
4.10 Antiderivatives (light)
7 Exponential
Logarithmic and Inverse Trigonometric Functions (eight days)
7.1 Inverse
Functions
7.2 Exponential Functions
Their Derivatives
7.3
Logarithmic Functions
7.4
Derivatives of
Logarithmic Functions
7.5
Inverse
Trigonometric Functions (skip material with integration)
7.7 Indeterminate
Forms and L'Hospital's Rule