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California State Polytechnic University, Pomona

Mathematics Department, Syllabus



Mat 115

Calculus and Analytic Geometry II

Dr. V. M. Smith, Office 8-205, phone: (909) 869-3465


. . . . . . email: vmsmith@CSUPomona.edu

 

Please visit Quarter Schedule for
current Class Info and Office Hours

Pre-requisites: minimum grade of "C" in Mat 114 or equivalent (preferably within the last two quarters).

Course is open to all students satisfying the given pre-requisites.

There are no audits.

Text: Stewart. Calculus Early Transcendentals, 4th Edition, Brooks/Cole 1999.

Student Study Guide, Journey through Calculus CD and the manual for your particular calculator are highly recommended.

Chapters 5 through 8 in this text. Activities from the other materials and supplemenetary hand-outs will be covered in class as individual or group work and/or assigned as homework.


Mat 115 is the second course in the mathematics department's single variable calculus sequence. Mat 114 covers differential calculus (Chpt 1-4), Mat 115 covers integral calculus (Chpt 5-8) and Mat 116 covers parametric equations, polar coordinates, infinite sequences and series. Mat 214 and 215 cover vector and multi-variable calculus.

Expanded Description of the Course:

1. Investigations of integrals including
 

A. Fundamental Theorem of Calculus

B. Interpretation of as the total change of a function

C. Techniques of integration

   

 i.) Antiderivatives (by defiition as inverse function)

ii.) Riemann sums, trapezoidal rule, etc.

iii.) Trigonometric substitution

iv.) Transcendental and Partial Fractions

v.) Tables

2. Applications of integration to find solutions to real world problems
 

A.) Area, distance and volume (by shells, washers, etc.)

B.) Principle and interest

C.) Work, etc.

Expected Outcomes: Students will apply limits to infinite sums of rectangles to understand the definition of an integral. They will be able to integrate algebraic, trigonometric, exponential, logarithmetic, inverse trig functions, and approximate an integral value for table defined functions. They will be able to apply integral calculus in solving problems real world problems.

Materials required:

i. A graphing calculator with the capabilities of the TI-85 or better

ii. Graph paper (~3/8" units) and a set of colored pencils or crayons

iii. A loose-leaf notebook or other binder in which to keep all aspects of your quarter's work including homework, lecture notes, etc. You turn your notebook in with your final and you may be asked to discuss it and/or an overview of all your work at any time during the quarter.

Project: An Internet project investigating different web sites and preparing a mathematics class lesson plan or hypothetical industrial or science application that involves the calculus principles studied. Due date and other details will be given in class.

Comment for precredential secondary teachers:

you may satisfy the project requirement by attending

the CMC Mathematics Conference if Fall Quarter in Palm Springs, or

the CEEMaST Conference if Spring Quarter at Cal Poly

Conference dates for this year are as follows:

Fall Qtr CMC in Palm Springs, November 3-4, 2000

CEEMaST Spr Quarter - 1st Sat, May 2001

Graphing Calculator Work:

You are responsible for knowing how to program and use your graphing calculator to illustrate the different calculus concepts covered in the text, class and other assigned work. Calculator exercises are to be worked individually, by pair/share and in groups as assigned throughout the quarter.


Supplementary Reading Assignments augment the presentation of the course material covered in the text , in class, and homework assignments.

 

The aim for all tests, quizzes and activities, etc. is to help you learn the material and make positive progress on your journey as a life-long learner. You are responsible for all work assigned whether or not it is specifically discussed in class or whether or not you were in attendance. No make-up scores are recorded for any work turned in late.

Your course letter grade is determined holistically by your ability to use and explain both orally and in writing the concepts covered by the end of the quarter. Statements of my Grading Policy, Class Conduct and Procedures, Model of a Good Learner and Model of a Good Teacher are on the web. You are to read these and may download them from my web site at www.CSUPomona.edu/~VMSmith. Any adventure into mathematics is challenging at times; however, it is always exciting and rewarding for those who persevere (and yes, the pun is intended).

Improvement in reading, writing and problem solving requires time and commitment; you must budget your time accordingly. You need to allow for an absolute MINIMUM of two hours-concentrated study out of class for each hour we have in class.

Further comments:

As with all courses in mathematics, we look for patterns, apply them to solve problems, and use manipulatives to present a "hands-on" learning environment. Graphing calculators make our activities exciting as well as instructive. A main goal of this class is to improve our mathematical processing (critical thinking) skills so we can use throughout our journey as life-long learners. We strive to become more proficient in seeing mathematics as a process rather than a set of memorized rules with the goal of arriving at exact answers to arithmetic problems.

We build our understanding of integral calculus by becoming comfortable working with all types of functions, polynomial, transcendental, those defined only by their graphs or tables. We continue our friendship with limits and ise them exhaustively. In doing so, we become more knowledgeable about the meaning of the total rate of change and will use this information to solve real world problems.
  

For statements of my

Grading Policy, Class Conduct and Procedures, Model of a Good Student or

Model of a Good Teacher

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