Two textbooks have been adopted for this course. Ask in the bookstore or ask your instructor which text has been ordered for your class.
Handout for Allison text
Handout for Marsden and Tromba text
Text: Vector Calculus, a photocopied manuscript by Dennis
Allison, RGC
MTH 2254-Calculus IV covers Chapters 2,3,5,6,7 of the manuscript. This course serves as an extension of the traditional calculus sequence and contains additional topics relevant to students majoring in engineering, physics, and applied mathematics, including:
(i) differentiability generalized to multivariable functions
(ii) an introduction to vector fields and flow lines
(iii) a description of four differential operators: gradient, divergence, curl, and Laplacian
(iv) the change-or-variables theorem for double and triple integrals
(v) path integrals and line integrals
(vi) parametrization of surfaces
(vii) surface integrals
(viii) Green's theorem, Stokes' theorem, the divergence theorem
(ix) conservative vector fields
(x) Maxwell's equations
The prerequisite for this course is satisfactory completion (grade
C or higher) of either MTH 2154-Calculus III at ACC or a comparable
course at another institution.
On the first day of class your instructor will distribute written
information regarding exams, homework, and grading policy. You
should be aware that the Parallel Studies Department offers an
optional one-hour lab that accompanies this course. The lab provides
an opportunity for you to receive assistance from a tutor in a
small-group setting at least twice each week. See listings under
"Parallel Studies" in the semester schedule for more
information. In addition you may drop by the Parallel Studies
lab at most ACC campuses on a walk-in basis and receive assistance
for free. Of course, your instructor will also have office hours
each week to assist you so take advantage of them.
Should you wish to withdraw from this course at some time during
the semester, be aware that you must initiate this procedure by
going to the Registrar's Office at any ACC campus. Do not expect
the instructor to withdraw you. However, the instructor may withdraw
you for excessive absences (4) or for failure to meet course objectives.
The deadline for withdrawals is listed in the calendar in the
semester schedule.
Incomplete grades (I) are given only in the rarest of circumstances.
Generally, to receive an incomplete the student must have taken
all examinations given prior to the final three weeks of class,
be passing, and have a personal tragedy that has occurred within
the last three weeks of the semester that prevents course completion.
Incompletes cannot be given merely to allow the student an opportunity
to avoid receiving a grade of F.
The semester schedule for this course will likely proceed as follows:
| 16-week Semester | 11-Week Semester | |
| Week | ||
| 1 | Sections 2.2-2.3 | Sections 2.2-2.4 |
| 2 | Sections 2.3(cont)-2.4 | Sections 2.4(cont)-2.6 |
| 3 | Sections 2.4(cont)-2.5 | Sections 3.2-3.3 |
| 4 | Sections 2.6,3.2 | Sections 3.4, 5.1-5.2 |
| 5 | Section 3.3 | Sections 5.3-5.4 |
| 6 | Sections 3.4 | Sections 5.5, 6.1 |
| 7 | Sections 5.1-5.2 | Sections 6.2-6.3 |
| 8 | Sections 5.3-5.4 | Sections 6.4-6.5 |
| 9 | Sections 5.4(cont)-5.5 | Sections 7.1-7.2 |
| 10 | Sections 5.5(cont)-6.1 | Sections 7.2(cont)-7.3 |
| 11 | Sections 6.2-6.3 | Sections 7.4, Review, Exam |
| 12 | Sections 6.3(cont)-6.4 | |
| 13 | Sections 6.5,7.1 | |
| 14 | Sections 7.1(cont)-7.2 | |
| 15 | Sections 7.3-7.4 | |
| 16 | Review, Exam |
Text: Vector Calculus, 4th edition, Marsden & Tromba,
W.H. Freeman and Co., 1996.
MTH 2254-Calculus IV covers Chapters 2,4,5,6,7,8. This course serves as an extension of the traditional calculus sequence and contains additional topics relevant to students majoring in engineering, physics, and applied mathematics, including:
(i) differentiability generalized to multivariable functions
(ii) an introduction to vector fields and flow lines
(iii) a description of four differential operators: gradient, divergence, curl, and Laplacian
(iv) the change-or-variables theorem for double and triple integrals
(v) path integrals and line integrals
(vi) parametrization of surfaces
(vii) surface integrals
(viii) Green's theorem, Stokes' theorem, the divergence theorem
(ix) conservative vector fields
(x) Maxwell's equations
The prerequisite for this course is satisfactory completion (grade
C or higher) of either MTH 2154-Calculus III at ACC or a comparable
course at another institution.
On the first day of class your instructor will distribute written
information regarding exams, homework, and grading policy. You
should be aware that the Parallel Studies Department offers an
optional one-hour lab that accompanies this course. The lab provides
an opportunity for you to receive assistance from a tutor in a
small-group setting at least twice each week. See listings under
"Parallel Studies" in the semester schedule for more
information. In addition you may drop by the Parallel Studies
lab at most ACC campuses on a walk-in basis and receive assistance
for free. Of course, your instructor will also have office hours
each week to assist you so take advantage of them.
Should you wish to withdraw from this course at some time during
the semester, be aware that you must initiate this procedure by
going to the Registrar's Office at any ACC campus. Do not expect
the instructor to withdraw you. However, the instructor may withdraw
you for excessive absences (4) or for failure to meet course objectives.
The deadline for withdrawals is listed in the calendar in the
semester schedule.
Incomplete grades (I) are given only in the rarest of circumstances.
Generally, to receive an incomplete the student must have taken
all examinations given prior to the final three weeks of class,
be passing, and have a personal tragedy that has occurred within
the last three weeks of the semester that prevents course completion.
Incompletes cannot be given merely to allow the student an opportunity
to avoid receiving a grade of F.
The semester schedule for this course will likely proceed as follows:
| 16-Week Semester | 11-Week Semester | |
| Week | ||
| 1 | Sections 2.2-2.3 | Sections 2.2-2.4 |
| 2 | Sections 2.4-2.5 | Sections 2.4(cont)-2.6 |
| 3 | Section 2.6 | Sections 4.1,4.3-4.4 |
| 4 | Sections 4.1,4.3 | Sections 5.1-5.3 |
| 5 | Sections 4.4,5.1 | Sections 5.4,5.6,6.1 |
| 6 | Sections 5.2-5.4 | Sections 6.1(cont)-6.3 |
| 7 | Sections 5.6,6.1 | Sections 6.3(cont).7.1-7.2 |
| 8 | Sections 6.2-6.3 | Sections 7.2(cont)-7.4 |
| 9 | Sections 6.3(cont),7.1 | Sections 7.5-7.6,8.1 |
| 10 | Section 7.2 | Sections 8.2-8.3 |
| 11 | Sections 7.3-7.4 | Sections 8.4, Review, Exam |
| 12 | Sections 7.5-7.6 | |
| 13 | Sections 7.6(cont),8.1 | |
| 14 | Sections 8.2-8.3 | |
| 15 | Sections 8.3(cont)-8.4 | |
| 16 | Review, Exam |