MATH 2413 - Calculus and Analytic Geometry I

Spring 2006 Semester

(Required)

Catalog Data 2006-2008:        

MATH 2413: 

Calculus and Analytic Geometry I. Credit 4.  Functions, limits, derivatives of algebraic, trigonometric, exponential and logarithmic functions, curve sketching, related rates, maximum and minimum problems, definite and indefinite integrals with applications. 

Prerequisite:  MATH    2312 or its equivalent.

Textbook:                 James Stewart, Calculus (Early Transcendentals), 5th edition, Brooks/Cole; Harris and Lopez, Discovering Calculus with Maple, 2^nd edition

Coordinator:                Michael Laidacker, Associate Professor of Mathematics

Course Objective:         

MATH 2413 is the first in a series of three calculus courses.  The main goal of this course is to introduce the derivative and integral, along with the basic applications of each.

Prerequisites by Topic:              Four years of high school mathematics

Topics:

  1.       Exponential Functions

  2.       Logarithm Functions

  3.       Tangent and velocity problems

  4.       Limit of a function

  5.       Calculating limits using limit laws

  6.       Precise definition of a limit

  7.       Continuity

  8.       Limits at infinity; horizontal asymptotes

  9.       Tangents, velocities, and rates of change

10.       Derivatives

11.       The derivative as a function

12.       Derivatives of Polynomials and Exponentials

13.       Product and Quotient Rules

14.       Derivatives of Trigonometric Functions

15.       The Chain Rule

16.       Implicit differentiation

17.       Higher Derivatives

18.       Derivatives of Logarithmic Functions

19.       Hyperbolic Functions

20.       Related rates

21.       Linear approximations and differentials

22.       Maximum and minimum values

23.       The mean value theorem

24        How derivatives affect the shape of a graph      

25.       Indeterminate forms and L’Hospital’s rule

26.       Optimization problems

27.       Newton’s method

29.       Antiderivatives

29.       Areas and distances

30.       The definite integral

31.       The fundamental theorem of calculus

32.       Indefinite integrals and the net change theorem

33.       The Substitution Rule

34.       Areas between curves

35.       Volumes

36.       Volumes by cylindrical shells

37.       Work

Laboratory projects:

8 lab sessions: Getting started, functions and limits, differentiation, application of the derivative, integration, applications of the definite integral, logarithmic, exponential, inverse trig and hyperbolic functions

Schedule:      Three 50-minute lectures per week.  One 50-minute lab.  Four 50-minute exams and a 2-hour final.