COURSE SYLLABUS

 

Ohio Northern University

College of Arts and Sciences

Department of Mathematics

 

 

                                                                                                Effective Date: Winter 05-06

 

Course:  MATH 158               Name:  Calculus with Pre-Calculus 2

 

Credit hours: 5                        Lecture hours/week: 5             Lab hours/week :0

 

Instructor: Raiti, Hunt

 

Usual student level: Freshman

 

Course required of students in:  Successful completion of this course is an alternate for MATH 163, which is required by students in Mathematics, Computer Science, Engineering, Physics, and Chemistry.

 

Course frequency per year:  Two sections winter quarter

 

Average enrollment per year: 50

 

This course has a prerequisite: MATH 157

 

This course is a prerequisite for:  MATH 164  or MATH 159

 

Catalogue Description:

A continuation of MATH 157.  Continued review of algebra and trigonometry.  Extrema, curve plotting, Mean Value Theorem, applications of the derivative.  Introduction to definite and indefinite integrals and the Fundamental Theorem of Calculus.   MATH 157 and MATH 158 together cover the entire content of MATH 163 and the pre-calculus preparation necessary for MATH 163.  In addition, integration is introduced in MATH 158 so that concurrent enrollment in PHYS 231 and MATH 158 during winter quarter is possible.  Prerequisite:  MATH 157

 

Course Objectives: To give the students the necessary differential calculus tools, concepts, and methods to work in engineering, science and mathematics.  To give the students a brief introduction to integral calculus so that concurrent enrollment in PHYS 231 is possible.

 

Textbook: Calculus, 5th edition, by James Stewart

 

 

 

 

Combined Syllabus

MATH 157/MATH 158/MATH 159

Fall/Winter/Spring

 

NOTE:  This syllabus assumes five credit hours for each  quarter.

 

Essentially, this is just the syllabus for Math 163 and Math 164 combined. However, the order of the topics is rearranged so that students will have a solid introduction to integrals and the Fundamental Theorem of Calculus before the end of the third week of winter quarter so that they can take Physics I during winter quarter.  In addition, extra time is allotted for additional pre-calculus and algebra review as needed.

 

MATH 157          Calculus with Pre-Calculus 1            Fall Quarter

 

1.  FUNCTIONS AND MODELS

            1.1       Four ways to represent a function (with Appendices A,B)

            1.2       Mathematical models (with Appendices C,D

            1.3       New functions from old functions

            Also:    Review of algebra topics such as factoring and exponents as needed.

 

2.  LIMITS AND THE RATE OF CHANGE

            2.2       The limit of a function

            2.3       Calculating limits using limit laws

            2.4       The precise definition of a limit (optional)

            2.5       Continuity

            2.6       Tangents and Velocities

 

3.  DERIVATIVES

 

            3.1       Derivatives

            3.2       The Derivative as a function

            3.3       Differentiation Formula

            3.5       Derivatives of Trig functions

            3.6       Chain Rule

            (The rest of Chapter 3 will be covered in the second quarter)

 

4. APPLICATIONS OF DIFFERENTIATION

 

            4.1       Maximal and Minimal Values

            4.2       The Mean Value Theorem

            (4.3-4.9 will be covered in MATH 158)

            4.10     Antiderivatives

 

NOTE:  There is room on this syllabus for about 16 days of extra pre-calculus and algebra review as needed (compare to the time allotted for the above topics on the standard Math 163 syllabus)

 

 

 

MATH 158          Calculus with Pre-Calculus 2            Winter Quarter 

 

NOTE: Sections 5.1-5.4 need to be covered by the third week of classes for the benefit of students taking Physics I concurrently with this course.

 

5.  INTEGRALS

            5.1       Areas and distances + Sigma Notation (Appendix E)

            5.2       The definite integral

            5.3       The Fundamental Theorem of Calculus

            5.4       Indefinite integrals and the total change theorem

           

3.  DERIVATIVES

          3.7       Implicit Differentiation

            3.8       Higher Derivatives

            3.9       Related Rates

            3.10     Differentials

 

4.  APPLICATION OF DIFFERENTIATION

            4.3       How derivatives affect the shape of a graph

            4.4       Limits at infinity; horizontal asymptotes

            4.5       Summary of curve sketching

            4.6       Graphing with calculators (if not incorporated into previous sections)

            4.7       Optimization problems

            4.8       Applications to Economics (Optional)

            4.9       Newton’s Method (Optional)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MATH 159          Calculus with Pre-Calculus 3            Spring Quarter

 

5.  INTEGRALS

            Review of 5.1-5.4

            5.5       The substitution rule

 

6.  APPLICATIONS OF INTEGRATION

            6.1       Areas between graphs

            6.2       Volumes

            6.3       Volumes by cylindrical shells

            6.5       Average value of a function (optional)

 

7.  INVERSE FUNCTIONS

            7.1       Inverse functions

            7.2       The Natural Logarithmic Function

            7.3       The Natural Exponential Function

            7.4       General Log and Exp functions

 

            NOTE:  Extended time and supplementary problems will most likely

                        be needed for 7.1-7.4

           

            7.5       Inverse trigonometric functions

            7.6       Hyperbolic functions

            7.7       Indeterminate forms and L’Hospital’s Rule

           

8. TECHNIQUE OF INTEGRATION

            8.1       Integrations by parts

            8.2       Trigonometric Integrals

            8.3       Trigonometric Substitution

            8.4       Partial Fractions

            8.5       Strategy for integration

            8.6       Using tables and computer algebra systems (optional)

            8.8       Improper integrals