RANGER COLLEGE

Master Syllabus

Math 2413 Calculus I

2010-11

Prepared by: Dr. John Gresham

EMAIL: jgresham@rangercollege.edu

CATALOG COURSE DESCRIPTION: Theory of limits, variables, functions, differentiation of elementary functions and applications, transcendental functions and applications, maxima and minima, differentials, Mean Value Theorem, integration, Fundamental Theorem of Calculus. Use of computer technology and lab assignments will be required in this course.

PREREQUISITES: Completion of college algebra (Math 1314) and trigonometry (Math 1316) or the equivalent.

TEXT: Calculus, 6th ed. by Stewart

OTHER REQUIRED MATERIALS: graphing calculator (TI-83, -84, or -86 strongly recommended), graph paper.

COURSE CREDIT: 4 semester hours—3 lecture hours, 2 lab hours per week

INSTRUCTIONAL METHODS: Lecture supplemented by graphing calculator and computer presentations.

EXEMPLARY OBJECTIVES SUPPORTED BY THIS COURSE

M1. To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world problems

M2. To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically

M3. To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments

M4. To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results

M5. To interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them

M6. To recognize the limitations of mathematical and statistical models

M7. To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines

CALCULUS I COURSE OBJECTIVES: To be able to demonstrate these skills in writing:

1. Finding limits of functions (M2, M3, M5).

2. Determining continuity of a function and types of discontinuities (M2, M3, M5)

3. Finding derivatives of functions (M2, M5)

4. Solving application problems involving differentiation (M1, M4, M5, M6, M7)

5. Finding antiderivatives and definite integrals (M2)

TEACHING METHOD: Class lecture, supervised problem-solving, cooperative learning lab projects

COURSE CALENDAR for Calculus I

Suggested Timetable (subject to change) The assignment list for each section will be given as the section is covered. A comprehensive assignment list may also be linked on the math department web page.

Class Section Topic

1 Ch 1 Review functions, graphs, and graphing calculators

2 2.1 Tangent & velocity problems

2.2 Limit of a function

3 2.3 Calculating limits using limit laws

4 2.4 Precise definition of limit

2.5 Continuity

5 3.1 Derivatives and rates of change

6 3.2 Derivative as a function

7 3.3 Differentiation formulas

8 Test #1

9 3.4 Derivatives of trig functions

10 3.5 Chain rule

3.6 Implicit differentiation

11 3.7 Rates of Change

3.8 Related rates

12 3.9 Linear approximations and Differentials

13 4.1 Maximum and minimum values

14 4.2 Mean Value Theorem

4.3 How derivatives affect the shape of a graph

15 4.4 Limits at infinity; horizontal asymptotes

16 Test #2

17 4.5 Curve sketching

4.6 Graphing with calculus and graphing calculators

18 4.7 Optimization problems

19 4.8 Newton's method

20 4.9 Antiderivatives

21 5.1 Areas and distances

22 5.2 Definite integral

23 5.3 Fundamental Theorem of Calculus

24 Test #3

25 5.4 Indefinite integrals and the Net Change Theorem

5.5 Substitution rule

26 6.1 Areas between curves

27 6.2 Volume

6.3 Volume by cylindrical shells

28 6.4 Work

6.5 Average value of a function

29 Test #4

30 Review

Final Exam Time of final to be announced