SHAW UNIVERSITY

COURSE OUTLINE

 

MAT 201 CALCULUS-I

Instructor: Dr. K.P. Satagopan

Office Hours: MWF: 2-4 PM

T-TH: 1-3 P.M

Office: Graphics #6

Phone: 546-8379

e-mail: sat@shawu.edu

TEXT: CALCULUS, Finney / Thomas, Addison-Wesley, 1991

General Description:

This is the first Calculus course out of a sequence of three. This course is intended for all Science, Math

Education and Business majors. The pre-requisite is MAT -115 -Pre-Calculus or equivalent.

It deals with functions, operations on functions, limits, continuity, derivatives and integrals. It also shows

applications of these mathematical techniques to various other scientific areas and real life problems.

Graphing calculators and the Computer Algebra System MAPLE will be used for problem solving and projects.

COURSE OBJECTIVES:

After completing this course, the students should be able to do the following:

· Find the domain, range of a given function and find if it is 1-1 onto or neither, find the inverse of a function. (NCATE 9.4)

· Sketch the graphs of elementary functions, the absolute value functions, step functions, etc. (NCATE 3.7)

· Evaluate the one-sided limit and the limit of polynomials, rational functions, trigonometric and exponential functions. (NCATE 2.1)

· Evaluate limits involving infinity.

· Verify if a given function is continuous or not at a given point, in an interval. Approximate roots of polynomials using the properties of continuous functions. Find the derivative of a function by the definition, and by product, quotient Rule. (NCATR 2.2,3.0 and 3.1)

· Know the relationship between differentiability and continuity of functions. (NCATES 2.3)

· Differentiate composite functions, implicit functions.

· Find the equations of the tangent and normal to a curve by using derivatives. (NCATE 3.3)

· Find the rate of change by using derivatives. (NCATE 3.4)

· Solve word problems using the techniques of derivatives. (NCATE 1.0)

· Solve motion problems involving velocity, acceleration. (NCATE 3.5). Sketch the graph of a given function by using derivatives to get some properties of the graph. (NCATE 3.7)

· Find where it is increasing/decreasing for a given function without drawing the graph.

· Find the maximum or minimum values of a given function. (NCATE 3.4). Solve word problems using maximum, minimum values of functions. Find anti-derivatives of a given function.

· Construct some simple mathematical models.

· Understand the relationship among limits, derivatives and integrals. (NCATE 2.0)

· Demonstrate an awareness that the process ofintegratio1l. is a,..1imiting process. (NCATE 2.2)

· Evaluate the definite and indefinite integrals o~ functions using substitutions and other techniques. (NCATE 3.0, 3.2)

· Solve motion problems involving velocity, acceleration etc., using integration. (NCATE 3.5)

CHAPTERS AND TOPICS:

Chapter 1- Review: Slopes and Equations of Lines- Functions and their Graphs-

Circles and Parabolas- Trigonometric Functions and Their Graphs- Absolute values.

Chapter 2- Limits and Continuity: Limits- Sandwich Theorem- Limits involving Infinity- Continuous Functions.

Chapter 3 -Derivatives- Slopes, Tangent Lines and Derivatives- Differentiation Rules- Velocity, Speed and Other Rates of Change- Derivatives of Trig. Functions-, the Chain Rule- Implicit Differentiation- Linear Approximations and Differentials- Newton's Method.

Chapter 4- Applications of Derivatives: Related Rates of Change- Maxima, Minima and M. V. T; Curve Sketching; Optimization; Anti- derivatives;. Modeling.

Chapter 5 -Integration: Calculus and Area- Formulas for Finite sums- Definite Integrals- The Fundamental Theorems of Integral Calculus- Indefinite Integrals- Integration by Substitution-Running the chain Rule. Backward- Numerical Integration- A brief introduction to Logarithmic and Exponential functions..

GRADING:

Quiz/Homework - 30% of the final grade

Tests: 40% of the final grade

Final Exam. 30% of the final grade

ATTENDANCE POLICY:

More than 4 unexcused absences may result in an "F" in the course. You are responsible for the classes you

missed and for the information passed out during your absence.