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CALCULUS I
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Class Hours: 4.0 |
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Credit Hours: 4.0 |
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Laboratory Hours: 0.0 |
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Date Revised: Fall 2008 |
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Catalog Course Description: |
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Single variable calculus for students majoring in science, mathematics, engineering, and computer science. Limits and differentiation of polynomial, rational, trigonometric, exponential and logarithmic functions and their applications. ACT math score of at least 26 is recommended. |
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Entry Level Standards: |
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A thorough knowledge of algebraic and trigonometric functions is necessary for entrance to this course. |
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Prerequisites: |
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High school algebra I and algebra II and geometry and trigonometry and satisfactory placement test scores; or Math 1730; or MATH 1710 and 1720. |
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Textbook(s) and Other Reference Materials Basic to the Course: |
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Calculus: Early Transcendentals
by Jon Rogawski,, First Edition, W.H. Freeman and Company, 2008 References: Calculus: Early Transcendentals
by James Stewart, Sixth Edition, Thomson
Learning, 2008 Calculus: Early Transcendentals
by Larson, Hostetler, and Edwards, Fourth Edition, Houghton Mifflin Company, 2007 Technology Requirement. |
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I. Week/Unit/Topic Basis: |
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Week |
Topic |
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1 |
Introduction, Precalculus Review, Limits, Rates of Change and Tangent Lines |
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2 |
Limits (Numerically and Graphically), Limit Laws, Limits and Continuity |
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3 |
Continuity, Evaluating Limits Algebraically, Trigonometric Limits |
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4 |
Intermediate Value Theorem, Formal Definition of a Limit, Derivative Definition, |
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5 |
The Derivative as a Function, Review, Exam 1 |
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6 |
Product and Quotient Rules, Rates of Change, Higher Derivatives |
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7 |
Trigonometric Functions, Chain Rule |
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8 |
Implicit Differentiation, Related Rates |
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9 |
Derivatives of Inverse, Exponential, and Logarithmic Functions |
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10 |
Review, Exam 2, Linear Approximation |
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11 |
Extreme Value Theorem, Mean Value Theorem and Monotonicity |
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12 |
The Shape of a Graph, Graph Sketching and Asymptotes |
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13 |
Applied Optimization, L’Hopital’s Rule |
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14 |
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15 |
Final Exam |
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II. Course Objectives*: |
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A. |
Become familiar with all descriptive aspects of a function. VI. 1-6 |
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B. |
Understand the concept of and be able to evaluate a limit of a function. VI. 1-6 |
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C. |
Be able to calculate derivatives of algebraic and transcendental functions. VI. 1-6 |
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D. |
Pose real and technical problems mathematically. VI. 1-6 |
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E |
Apply limits and derivatives to solve real and technical problems. VI. 1-6 |
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F. |
Interpret and communicate mathematical problems and their solutions into clearly written English. VI. 1-6 |
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*Roman numerals after course objectives reference TBR’s general education goals. |
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III. Instructional Processes*: |
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Students will: |
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1. |
Use graphing calculator and/or computer software. Technological Literacy Outcome |
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2. |
Actively explore real world problems through projects such as B'ezier curves to aid in computer aided design. Mathematics Outcome |
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3. |
Translate analytical information into graphical representations. Mathematics Outcome |
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4. |
Use multiple approaches such as physical, numerical, graphical, symbolic and verbal to solve application problems in physics, biology, engineering, and computer science. Transitional Strategy, .Mathematics Outcome |
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5. |
Use the tools of calculus to study the phenomenon of change between different variables. .Mathematics Outcome |
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*Strategies and outcomes listed after instructional processes reference TBR goals for strengthening general education knowledge and skills, connecting coursework to experiences beyond the classroom, and encouraging students to take active and responsible roles in the educational process. |
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IV. Expectations for Student Performance*: |
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Upon successful completion of this course, the student should be able to: |
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1. |
Determine what a function is and work comfortably with functional notation. A |
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2. |
Evaluate limits and derivatives of algebraic and transcendental functions using analytic, numerical and graphing techniques. Evaluate the derivative of a function using the (limit) definition. B, C |
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3. |
Graph a function using the concepts of symmetry, domain, shifting and stretching, along with information gathered from limits, the function's derivative and the aid of a graphing calculator and/or computer software. A, E |
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4. |
Recognize a continuous function. Classify the different types of discontinuities using analytical and graphical means. B |
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5. |
Use derivatives to solve problems such as distance - velocity - acceleration, related rate and optimization problems. E |
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6. |
Read and interpret graphs, limits and derivatives which are used in applied settings and communicate that analysis in writing. F |
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Work with technology and special projects involving real world data which enhances the conceptual understanding and usefulness of mathematics. D, F |
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*Letters after performance expectations reference the course objectives listed above. |
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V. Evaluation: |
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A. Testing Procedures: |
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Students are evaluated on the basis of tests, projects, homework, quizzes, and a comprehensive final exam. A minimum of four major tests are recommended. |
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B. Laboratory Expectations: As assigned by instructor |
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C. Field Work: As assigned by instructor |
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D. Other Evaluation Methods: As assigned by instructor |
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E. Grading Scale: |
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93% -
100% A |
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VI. Policies: |
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A. Attendance Policy: |
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B. Academic Dishonesty: |
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Individual instructors must
distribute their policy on academic dishonesty during the first week of
class. In addition to other possible
disciplinary sanctions that may be imposed as a result of academic
misconduct, the instructor has the authority to assign either (1) an F or a
zero for the assignment or (2) an F for the course. |
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C. Accommodations for Disabilities: |
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If you need accommodations
because of a disability, if you have emergency medical information to share,
or if you need special arrangements in case the building must be evacuated,
please inform the instructor immediately. Please see the instructor privately
after class or in his/her office. Students must present a current
accommodation plan from a staff member in Services for Students with
Disabilities (SSWD) in order to receive accommodations in this course.
Services for Students with Disabilities may be contacted by going to Goins 127 or 131 or by phone: 694-6751(Voice/TTY) or
539-7153. |
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D. Cell Phones: |
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Cell phones are to be
either turned off or put on vibrate mode while in class. Instructor discretion as to penalty. |
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