Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

# Calculus - Analytic Geometry I

Spring 2012

Hi, here is some information about my course Calculus I (CRN: 13292, MAC 2311-005). We meet Monday, Wednesday, Thursday, and Friday, 10:00 - 10:50 a.m. in ED 113.

The origins of calculus go back at least 2500 years to the ancient Greeks, who found areas using the "method of exhaustion". Limits arise not only when finding areas of a region, but also when computing the slope of a tangent line to a curve, the velocity of a car, or the sum of an infinite series. In each case, one quantity is computed as the limit of other, easily calculated quantities. Sir Isaac Newton invented his version of calculus in order to explain the motion of the planets around the sun. Today calculus is used in calculating the orbits of satellites and spacecraft, in predicting population sizes, in estimating how fast coffee prices rise, in forecasting weather, in measuring the cardiac output of the heart, in calculating life insurance premiums, and in a great variety of other areas. We will explore some of the uses of calculus in this course.

Textbook and Topics

We will use the Calculus Online Textbook: Calculus by Gilbert Strang, Massachusetts Institute of Technology, Wellesley-Cambridge Press. The book is MIT open courseware, available online under the Creative Commons Licence:

Calculus book

For pdfs of the sections, and for additional materials have a look at the page:

Strang, Calculus

To warm up for the course, have a look at the videos!

We are going to cover the following chapters:

 Chapter 2 Strang-Chapter 2 Derivatives(3 weeks) The Derivative of a Function, Powers and Polynomials, The Slope and the Tangent Line, Derivative of the Sine and Cosine, The Product and Quotient and Power Rules, Limits, Continuous Functions Chapter 3 Strang-Chapter 3 Applications of the Derivative(3 weeks) Linear Approximation, Maximum and Minimum Problems, Second Derivatives: Minimum vs. Maximum, Graphs, The Mean Value Theorem and l'HÃ´pital's Rule Midterm Exam on 2/24 The 50 minute exam will be about the material covered so far. We will discuss in class what day will be ideal for all of us. Chapter 4 Strang-Chapter 4 The Chain Rule(2 weeks) Derivatives by the Chain Rule, Implicit Differentiation and Related Rates, Inverse Functions and Their Derivatives, Inverses of Trigonometric Functions Chapter 5 Strang-Chapter 5 Integrals(3 weeks) The Idea of an Integral, Antiderivatives, Summation vs. Integration, Indefinite Integrals and Substitutions, The Definite Integral, Properties of the Integral and the Average Value, The Fundamental Theorem and Its Consequences Excursion to Computer Lab We will visit the computer lab to explore how computer algebra (Maple) can be used to compute functions and derivatives, and to assist us in graphing. You can earn extra credit for using Maple to solve Calculus problems. Chapter 6 Strang-Chapter 6 Exponentials and Logarithms(2 weeks) The Exponential ex, Growth and Decay in Science and Economics, Logarithms, Hyperbolic Functions

Objectives

• Ability to compute limits, derivatives, and simple integrals using a structured approach,
• use calculus concepts to plot functions and to discuss their graphs,
• apply calculus techniques to a variety of math, science and engineering problems, and
• gain familiarity with graphing and calculus tools in computer algebra systems like maple.

Tutoring

There is free math tutoring available in the Math Learning Center in GS 211. The tutor for our course is Olga Y Shukina, her hours are MWF 1 - 4 p.m. and Thursdays, 11-12 a.m.

This course is supported by SI, a free, peer-led study group program designed to assist all enrolled students in gaining a better understanding of course material through guided outside group work. Our SI leader is Sujinun "Ning" Ovathanasin, her hours are M 2-2:50 p.m., W 11-12:50, R 11-11:50 a.m. in PS 113.

Credit

Homework:  I will assign homework problems every week. The problems will not be graded, but some may show up on a quiz. Homework problems.

Quizzes:  We will have a quiz every Friday; the ten best quizzes count for 40 % of the grade. No calculators can be used during the quiz.

Extra Credit:  You can obtain extra credit counting towards your quiz grade for assignments done on a computer algebra system, for example Maple.

Midterm Exam:  The midterm exam on 2/24 has covered Chapter 2 and Sections 3.1 - 3.4. It will count for 20 % of the grade.

Final Exam: The final exam is comprehensive and will count for 40 % of your grade. It has been scheduled for Sunday, April 29, 4:00 - 6:30 p.m. in SO 250. There are 10 problems on the exam, the 8 best answers count. Please bring a picture id (Owl card or drivers licence)!

Further Information

For the Code of Academic Integrity, Religious Accommodation and my grading scale please visit Infos for all my courses.

Contact Me

Office hours:  MWRF, 11 a.m. - noon in SE 230.