Syllabus: M408L
INTEGRAL CALCULUS
Text: Stewart,
Calculus, Fifth Edition
Responsible
Parties: Kathy Davis, John Gilbert, Gary Hamrick June 19 2003
Prerequisite and degree relevance:
A grade of C or better in either M408C or in M408K.
Only one of the following may be counted: M 403L, 408D, 408L.
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:
M408L 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
M408D, 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.
Introduction to the theory and applications of integral calculus of functions of one variable; topics include integration, the fundamental theorem of calculus, transcendental functions, sequences, and infinite series.
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:
5 Integrals (Seven Days)
4.10 Antiderivatives (review)
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 (Two
Days)
7.2
Exponential Functions
Their Derivatives (material with integrals)
7.4
Derivatives of
Logarithmic Functions (material with integrals)
7.5 Inverse
Trigonometric Functions (material
with integrals)
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
8.7 Approximate
Integration (optional)
8.8 Improper
Integrals
15 Partial Derivatives
(One Day)
15.3 Partial Derivatives
16 Multiple Integrals (Three Days)
16.1 Double Integrals over
Rectangles
16.2 Iterated Integrals
16.3 Double Integrals over
General Regions
12 Infinite Sequences
and Series (Seventeen 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
12.12 Applications of Taylor
Polynomials