SUMMER 2018/1000 MTH 141 Calculus I

Text:  Hughes-Hallet,et. al., Calculus, 7th Edition
Prerequisites: MTH 111 or equivalent
Calculators: A graphing calculator is required.

Instructor: Dr. M. Kulenovic
Lippitt 202D
Ph. 44436
e-mail: mkulenovic@ uri.edu

Office hours: MTWTh: 1-2 p.m.

web page: www.math.uri.edu/~kulenm

Summer Tutoring

Interesting Calculus mathlets !

Course Information

Introduction

This is the first calculus course for students of engineering, mathematics, science and other areas of study that require a strong mathematical background. In MTH 141 we shall explore in depth the idea of rate of change of a function and its applications to problems in physics, geometry, chemistry and biology. We will approach new ideas and problems from algebraic, graphical, and numerical points of view.

How to Succeed in MTH141 - Summer session

• Spend about 10 hours per week, outside of class, working problems, reading the text, and working on Projects. Sometime during the first week of class, set up your weekly schedule so that specific days and times are reserved for working out math problems.
• Buy a notebook where you will write solutions to all the recommended problems.
• Save all quizzes, handouts, and any other work. Use them to prepare yourself for tests.
• Establish a group of fellow students to work with.
• Come to class every time!  Skipping class, even only a couple of times, will translate into a lower course grade.

Goals and Objectives.

The goals are to have you develop symbol manipulation skills, mathematical modeling skills, skills in the use of technology to treat mathematical problems that involve the concepts of rate of change and derivative, an understanding of the language of calculus, and an appreciation for the uses of calculus in the sciences.

Learning Outcomes  At the end of the course the student should be able to:

• (Limits and continuity) Evaluate limits analytically, graphically, and numerically, and use limits to investigate properties of functions such as continuity and existence of asymptotes.  Investigate continuity properties of functions.
• (Derivatives) Define and evaluate the derivative at a point as a limit using limits, numerical, graphical methods. Investigate differentiability of a function at a point using limits, numerical, or graphical methods.
• (Computing derivatives algebraically) Compute first and higher order derivatives algebraically by applying theorems.  Compute derivatives of functions defined implicitly.
• (Using Derivatives) Apply differentiation to investigate velocity, acceleration, related rates, monotonicity, optimization problems, linear approximation, limits (L’Hopital’s rule), and functions defined parametrically.  Apply theorems about continuous and differentiable functions (Extreme Value Theorem, Mean Value Theorem, Rolle's Theorem, the Racetrack Principle).
• (Integration) Use Riemann sums to approximate integrals. Use the First and Second Fundamental Theorem of Calculus to compute integrals of simple functions, and apply them to total change. Use integrals to compute area of planar regions bounded by simple functions.
• (Modeling, Approximation, Technology use) Use calculus and technology to investigate mathematical models and determine their applicability. Use technology to study accuracy of approximations, perform numerical and symbolic calculations, and produce graphical representations of functions to investigate their properties.

The course grade will be computed as follows:

MTH 141/1000 (Session 1)

Course grade = (25 E1 + 25 E2  + 30 FE + 10 MP + 10 CW)/100

Key: E1 = Exam 1, E2 = Exam 2, FE = Final Exam, MP = Mathematica Projects, CW = Class Work.  Class Work includes quizzes.

Mathematica   Information

We will use the software Mathematica in this course. The Mathematica software is available in most computer labs at URI Mathematica is a powerful computer algebra system that can perform the most complicated calculations and draw spectacular graphics at the touch of the button. Knowledge of software like Mathematica should help you in your future professional career as well as in understanding material in calculus.

Our work with Mathematica will be organized into 2 Mathematica Worksheets which will be part of SAKAI package of the course. You will be able to download the worksheets from SAKAI web page at any of the URI computer labs or to your home computer if you have a personal copy of Mathematica. Student Edition of Mathematica is readily available at bookstores and over the Internet and is free for students at URI. There will be help with Mathematica available at one of the URI computer labs. The hours and names of people who will be helping you will be posted on this page as soon as they are scheduled.

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