MATH 165 - Calculus of a Single Variable I

Syllabus

General Course Description:

Coordinate Geometry, Limits and their properties, continuity, differentiation and applications of differentiation, integration and applications of integration.

Prerequisites:

A grade of C or better in GE-115 College Algebra and GE-118 Precalculus, or placement by Mathematics Placement Test.  Specific prerequisite competencies for the course:  Upon the start of the course, the student should be able to perform the tasks listed below -
  1. Ability to recognize and solve problems
    1. Use mathematics and technological tools to solve "real world" problems that arise in social sciences, biological sciences, physical sciences, and other mathematical sciences
  2. Algebra and algebraic structures
    1. Understand the concepts of variable, expression, equation, inequality, and the properties of integers, rational numbers, real and complex numbers
    2. Analyze tables and graphs to identify properties and relationship
    3. Solve linear and non-linear equations and inequalities and systems using concrete, formal and informal methods
    4. Have knowledge of diverse examples of functions arising from a variety of problem situations and investigate the properties of these functions through appropriate technologies, including graphing utilities and graphing calculators
    5. Demonstrate a through knowledge of the trigonometric functions, their properties, graphs, and applications
Specific Competencies in the Course:

Through the use of problem solving during the class time, homework, library assignments and tests, the student will be guided to develop mastery of the basic concepts of differential and integral calculus of functions of single variable. Upon completion of the course, the student should:
  1. understand the basic concepts of calculus: limit, derivative, and integral and their applications.
    1. Use graphs, tables, and formal methods to evaluate limits involving elementary functions such as polynomial, rational, trigonometric, exponential, and logarithm functions
    2. Be able to prove whether a function is continuous
    3. Demonstrate an understanding of limit definition of derivatives and definite integrals
    4. Know the relationship between differentiability and continuity
  2. have the ability to differentiate and integrate elementary functions and the ability to apply these processes in solving problems
    1. Use the rules for differentiating and integrating elementary functions
    2. Apply derivatives to find tangents to curves
    3. Solve maximum-minimum and related rates problems
    4. Solve motion problems involving velocity and acceleration in one or two dimensions
    5. Use graphs to understand and analyze properties of functions and their relationships to concepts of calculus
    6. Use the concepts from calculus to sketch and analyze graphs of elementary and piecewise functions
    7. Apply integration to find areas under curves and distances in motion problems.
  3. have the knowledge of the capabilities and limitations of computers and calculators
    1. Use calculators to estimate derivatives, integrals, and solutions to equations
    2. Use computers and graphing calculators to explore mathematical concepts
  4. have an understanding of the historical development of mathematics, the universality of mathematics and its applications in today's world
    1. Posses a knowledge of the modern applications of mathematics to problems in science, in the social sciences, and business.
After completing this course, students should be able to apply the above competencies and concepts to solve problems in their appropriate fields of application.

Methods of Presentation:

Apply innovative technologies and critical thinking that give rise to interactive instructional approaches permitting focus on problem solving and encourage generalization wherever possible; using lecture method, transparencies, computer, and individual and group assignments.

Materials to be used in the Course:

Textbook with its CD-Rom giving Calculator and MS Excel instructions, a scientific calculator, the student's own Resource Manual, and Media Material