Navigation
Teaching
Applied Calculus II
Functions of a Single Variable
Volume: 15 weeks × 4 lecture periods/week
Textbook: James Stewart, Calculus, 5th Edition, Brooks-Cole Publishers (International Edition),
Link
to publisher's description
Prerequisites: None. The course is an introductory math course for freshman students.
Last Taught: Fall Term 2010
Background and Goals: The sequence Applied Calculus Vv156-255-256 is an introduction to basic calculus. It differs from the Honors Math sequence in that new concepts are often introduced and extended from concrete examples, remaining closely aligned to applications. Most theorems are stated rigorously and motivated from examples, but complicated proofs and abstract generalizations are often omitted. The emphasis is on applying mathematical results to concrete problems.
The present course covers the calculus of functions of a single real variable.
Key Words: Elements of logic; set theory; properties of real and complex numbers; sequences, convergence, completeness of metric spaces; functions, convergence and continuity; the derivative and applications; normed vector spaces; series and power series; transcendental functions; the regulated and Riemann integrals and applications; the Lebesgue integral (as time permits).
Detailed Content:This course basically follows the presentation of the material in Stewart's book. Many concepts are not rigorously proved, and some theorems are not discussed in detail or omitted. Instead, more time is given to practical calculations and applications. The subjects covered include: real and complex numbers, sequences, functions, limits, continuity, the derivative and Riemann integral, series and power series as well as plane curves. A brief introduction to first-order differential equations concludes the course.
Alternatives: Vv186 (Honors Mathematics II) is a more theoretical course, which covers much of the same material.
Subsequent Courses: Vv255 (Applied Calculus III) is the natural sequel.
Overview:
| Week | Lecture Subject | Textbook Chapter | Date |
|---|---|---|---|
| 1 | Fundamentals and Complex Numbers | App. A-E,G 1 |
7-9-2010 9-9-2010 |
| 2 | Basic Properties of Functions | 11.1, 2.1-2.4, 2.6, 2.7 |
14-9-2010 16-9-2010 |
| 3 | Sequences and Limits | 11.1, 2.1-2.4, 2.6, 2.7 |
21-09-2010 25-09-2010 |
| 4 | Limits and Landau Symbols | 2.5, 2.8, 2.9, 3.1-3.6 | 28-09-2010 30-09-2010 |
| 6 | Continuity The Derivative |
3.8-3.11 |
19-10-2010 21-10-2010 |
| 7 | First Midterm Exam Applications of Differentiation |
4 | 26-10-2010 28-10-2010 |
| 8 | The Riemann Integral | 5, 6 | 2-11-2010 4-11-2010 |
| 9 | Techniques of Integration | 7 | 9-11-2010 11-11-2010 |
| 10 | Applications of Integration | 8 | 16-11-2010 18-11-2010 |
| 11 | Plane Curves Second Midterm Exam |
8.1, 10 |
23-11-2010 25-11-2010 |
| 12 | Plane Curves | 8.1, 10 | 30-11-2010 2-12-2010 |
| 13 | Series | 11 | 7-12-2010 9-12-2010 |
| 14 | Differential Equations | 9 | 14-12-2010 16-12-2010 |
| 15 | Mathematical Movie Final Exam |
21-12-2010 23-12-2010 |
Assignments (2010 version; PDF files):
(There will always be minor modifications from one iteration of the course to the next; if you are presently taking the course, your assignments may differ from these.)