## Rose-Hulman - Department of Mathematics - Course Syllabus MA112 - Calculus II - 2010-11

 Description & Prerequisites Course Goals Texts and Other Materials Course Topics Course Policies Links last posted to site: 08/19/10

Parts of the web page to be completed or determined by the instructor are in green.

### Catalogue Description and Prerequisites

MA 112 Calculus II 5R-0L-5C F,W,S Pre: MA 111 or 102 Techniques of integration, numerical integration, applications of integration. L'Hopital's rule and improper integrals. Separable first order differential equations, applications of separable first order differential equations. Series of constants, power series, Taylor polynomials, Taylor and McLaurin series.

Prerequisite: All of the topics in MA111 will be assumed.

### Course Goals

1. Introduce students to integral calculus (including elementary first order differential equations); see topics 1, 2 and 3 below in Topics Covered below for specific topics.
2. Introduce students to the application of the integral calculus and differential equations in science and engineering; see topics 2 and 3 below in Topics Covered
3. Introduction students to series of constants and functions, and the notions of approximation and convergence
4. Develop student mathematical modeling and problem solving skills.
5. Develop student ability to use a computer algebra system (CAS) to aid in the analysis of quantitative problems.  This includes (but is certainly not limited to) mastery of the commands listed in Performance Standards below.
6. Develop student ability to communicate mathematically.
7. Introduce applications of mathematics, especially to science and engineering.

### Textbook and other required materials

Textbook: Thomas' Calculus - Early Transcendentals Twelfth Edition - Weir, Hass
Supplement: Just in Time - bundled with text.
DE Problem supplement: 2004-05 version from Angel
Computer Usage: Maple14 must be available on your laptop

### Course Topics

Note: The Fall quarter class is predomiantly Advanced Placement Freshman. However, some time will be spent reviewing some topics and getting up to speed in Maple. Student taking the course later in the will have already been instructed in Maple in a prior course.

1. Integration---Basic Theory and Techniques
• Riemann sums (review for Fall quarter freshman as needed)
• Anti-derivatives for xn , exp(x), 1/x, sin(x), cos(x), sec2 (x), 1/(x2+1), 1/sqrt(1-x2), cosh(x), and sinh(x)
• Linearity of integration
• Integration by substitution
• Integration by parts
• Integration by partial fraction decomposition
• Other integration techniques
• L'Hopital's rule (may be taught in Calc I, review as needed)
• Improper integrals
• Numerical approximation using Trapezoidal and Simpson's rule

•
2. Applications of Integration
• Area
• Displacement and distance travelled
• Volumes of revolution (disk/shells)
• Arc length, surface area of revolution
• Work from force, potential energy

3. Differential Equations
• Definition, order, linearity
• Separation of variables for separable first order equations.
• Application to exponential growth and decay, population growth (logistic equation), Newton's law of cooling, salt tank problems, falling bodies (with and without air resistance.)
4. Series
• Series of constants
• convergence
• ratio test, integral test
• power series
• Taylor polynomials
• Taylor and Mclaurin series of basic functions

### Course Requirements and Policies

The following policies and requirements will apply to all sections and classes:

#### Computer Policy

A summary of the computer policy page:

Students will be expected to demonstrate a minimal level of competency with a relevant computer algebra system. The computer algebra system will be an integral part of the course and will be used regularly in class work, in homework assignments and during quizzes/exams. Students will also be expected to demonstrate the ability to perform certain elementary computations by hand. (See Performance Standards below.)

#### Performance Standards

With regard to be "by hands" computational skills, each student should

1. Know all derivative rules listed in the MA 111 syllabus plus cosh(x), and sinh(x).
2. Know anti-derivatives for xn, exp(x), 1/x, sin(x), cos(x), sec2 (x), 1/(x2+1), 1/sqrt(1-x2), cosh(x), and sinh(x) with respect to x, and linear combinations of these functions.
3. Be able to use integration by parts, u-substitution, and partial fraction decomposition to evaluate simple integrals.
4. Be able to solve simple separable first order ODE's

These by-hands skills may be tested using in class quizzes.

With regard to basic Maple commands, by the end of MA 112 every student should be able to:

1. Use all Maple commands expected in MA 111.
2. Use the int command to compute anti-derivatives.
3. Use evalf with the Int command to approximate integrals numerically.

#### Final Exam Policy

The following is an extract from the final exam policy page. Consult the policy page for complete details.

The final exam will consist of two parts. The first part will be "by hands" (paper, pencil). No computing devices (calculators/computers) will be allowed during the first part of the final exam. This part of the exam will cover both computational fundamentals as well as some conceptual interpretation, though the level of difficulty and depth of conceptual interpretation must take into account that this part of the exam will be shorter than the second part of the exam.  The laptop, starting with a blank Maple work sheet, and a calculator, may be used during the second part of the exam. No "cheat sheets", prepared Maple worksheets or prepared program on the calculator may be used. The second part of the exams will cover all skills: concepts, calculation, modeling, problem solving, and interpretation.