# Mathematics 169

MATH 169: Calculus I with Integrated Precalculus II (GE)

Prerequisites: One of the following: A grade of C or better in MATH 168 or permission of the Department of Mathematics and Statistics. Students with credit for MATH 126 Business Calculus or another college level calculus course are encouraged to contact the Department of Mathematics and Statistics for permission.

Credit hours: (3)

The sequence MATH 168 : 169 covers the topics covered in MATH 171  but also includes topics from algebra and trigonometry that MATH 171 assumes as prerequisite. MATH 169 covers indefinite and definite integrals, the area of under a curve, and the Fundamental Theorem of Calculus for functions covered in MATH 168. The course also covers limits, differentiation, and integration of trigonometric functions, the inverse trigonometric functions, and L’Hopital’s Rule.

Note(s): General Education and Scientific and Quantitative Reasoning designated course.  Students may not receive credit for both MATH 169 and either MATH 171 or MATH 151.

Detailed Description of Course

The following topics will be covered for algebraic functions:

1.L'Hopital's Rule

2.Antidifferentiation and the indefinite integral

3.Sigma notation, Riemann sums, area under a curve, and the definite integral

4.The Fundamental Theorem of Calculus

5.Antidifferentiation with substitution

6.Average value of a function

7.Trigonometric functions

a.Definitions on right triangles and on the unit circle

b.Trigonometric equations

i.Recognizing and applying identities

ii.Simplifying trigonometric expressions

iii.Solving trigonometric equations

c.Graphs of trigonometric functions

i.Period and amplitude

ii.Phase shifts, reflections, symmetries, and transformations

d.Inverse trigonometric functions

e.Applications of trigonometry, such as polar coordinates

f.Limits, derivatives, and integrals of trigonometric and inverse trigonometric functions

8.Conics

9.Complex numbers

Detailed Description of Conduct of Course

Instructors will use a combination of lectures, group work and computer laboratory sessions. Some may require students to present homework problems to the rest of the class on a regular basis. Software packages and graphing utilities will be used on solving problems and as illustrative aids.

Student Goals and Objectives of the Course

Students are expected to learn the basic principles of Calculus and Analytic Geometry and to demonstrate the use of these principles in problem solving. In addition to paper and pencil problem solving, students will use appropriate graphing calculator and computer algebra system technology.

Students will be able to:
1) Interpret relationships among numeric, symbolic and graphical information as applied to the real world
2) Solve problems using numeric, symbolic and graphical information.

Assessment Measures

Graded tasks may include tests, quizzes, homework exercises, papers, class participation and attendance. Students will be required to demonstrate literacy in the use of mathematical software packages and/or graphing calculators as effective tools in problem solving.

Other Course Information

This course is primarily intended for freshman and sophomore students, especially those majoring in mathematics, computer science, the natural sciences, psychology, or economics who need to take Calculus I but are not placed into MATH 171. Students may not receive credit for both MATH 169 and either MATH 171 or MATH 151.

Review and Approval

November 2, 2017

March 01, 2021