Big Sandy Community and Technical College. Course Syllabus

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Big Sandy Community and Technical College Course Syllabus PS Number: 54562 Semester: Fall Year: 2015 Faculty Name: Randy Watts Title: Professor Course Prefix and Number: MAT 175 Course Credit Hours:

1 Big Sandy Community and Technical College Course Syllabus PS Number: Semester: Fall Year: 2015 Faculty Name: Randy Watts Title: Professor Course Prefix and Number: MAT 175 Course Credit Hours: 5 Course Prerequisites: Course Title: ((MT 150 and MT 155) or equivalent with grades of 'C' or higher) or Math ACTE score of 27 or higher or Consent of Instructor Calculus I Catalog Course Description: Examines one-variable calculus including limits, differentiation and integration of algebraic, trigonometric, exponential, logarithmic, hyperbolic, and inverse trigonometric functions with applications. Instructor Contact Information: Campus Location: Pikeville Building & Room: N319 Office Hours: See attached schedule. Office Phone Number: Alternate Number: ext Best Times to Call: Pikeville Campus office hours KCTCS randall.watts@kctcs.edu Special Instructions: Supervisor Contact Information: Name: Patsy Jackson Campus Location: Prestonsburg Building & Room: Campbell (C120H) Office Phone Number: or ext KCTCS patsy.jackson@kctcs.edu

2 Text and Supplies: Thomas Calculus 13 th edition. You are also required to have an access code to MyMathLab. This can be purchased bundled with the text or separately. You will need a scientific calculator. KCTCS General Education Competencies Students should prepare for twenty-first century challenges by gaining: A. Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts. B. Intellectual and practical skills, including inquiry and analysis critical and creative thinking written and oral communication quantitative literacy information literacy teamwork and problem solving Students will be evaluated in this course by their performance on competency based questions on the final exam. C. Personal and social responsibility, including civic knowledge and engagement (local and global) intercultural knowledge and competence ethical reasoning and action foundations and skills for lifelong learning D. Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized skills. Course Specific Competencies (Student Outcomes): Student achieving a passing grade will be able to demonstrate proficiency in the following areas, to a degree commensurate with the grade received. 1. Approximate limits graphically and numerically and evaluate limits analytically. 2. List the conditions for the continuity of a function at a point and determine the intervals of continuity of a function. 3. Evaluate infinite limits and limits at infinity. 4. Define the derivative of a function and evaluate the derivative of a function using the definition.

3 5. Evaluate the derivative of a function using differentiation rules for algebraic and trigonometric functions as well as product, quotient, and chain rules. 6. Use the derivative of a function to find the equation of the line tangent to the graph of the function at a given point. 7. Sketch the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph. 8. Use implicit differentiation to find the equation of the line tangent to the graph of an equation at a given point. 9. Use derivatives to solve application problems including problems involving related rates and optimization. 10. Define the differential and use differentials to approximate function values. 11. Use Riemann sums to find the area under a curve. 12. Find indefinite and definite integrals of a function using integration rules for algebraic and trigonometric functions. 13. Find definite and indefinite integrals using substitution. 14. Find the average value of a function on an interval. 15. Use definite integrals to find the area under a curve and the area between two curves. 16. Find derivatives of exponential, logarithmic, inverse trigonometric, hyperbolic, and inverse hyperbolic functions. 17. Find integrals of exponential and logarithmic functions. 18. Find integrals using inverse trigonometric and inverse hyperbolic functions. Lab Competencies (Student Outcomes): (Enter N/A if this does not apply.) N/A Course Outline: I. Limits A. Finding limits graphically B. Approximating limits numerically C. Finding limits analytically D. δ-ε proofs E. One-sided limits F. Continuity G. Removeable/nonremoveable discontinuities H. Infinite limits (f(x) ± ) I. Limits as x ± J. Horizontal asymptotes K. Indeterminate forms/l'hôpital's Rule L. Vertical asymptotes II. Differentiation A. Definition of the derivative B. Finding derivatives using the definition C. Finding the tangent line to the graph of a function D. Basic differentiation rules for algebraic and trigonometric functions, product and quotient rules, chain rule E. Implicit differentiation F. Finding the tangent line to a graph III. Applications of Differentiation A. Related rate applications B. Rolle's Theorem

4 IV. C. Mean Value Theorem D. Finding critical numbers E. First derivative test/increasing/decreasing F. Finding relative maxima and minima G. Concavity and inflection points H. Second derivative test I. Curve sketching J. Optimization applications K. Differentials L. Newton's method for approximating zeros Integration A. Riemann sums/finding area using a limit B. Fundamental theorem of calculus C. Finding the average value of a function D. Properties of definite integrals E. Integration using substitution F. Area between two curves V. Transcendental Functions A. Differentiation of ln x B. Differentiation using ex C. Differentiation using ax and logax D. Differentiation of inverse trigonometric functions, hyperbolic functions, and inverse hyperbolic functions E. Integration using ln x F. Integration using ex G. Integration using ax and logax H. Integration using inverse trigonometric functions I. Integration using hyperbolic functions J. Integration using inverse hyperbolic functions Course Structure: A typical class will consist of minutes of answering questions on assigned homework from the previous class. The rest of the class will consist mainly of lecturing on the new material with as many examples as possible. Students are encouraged to ask questions during lectures. Homework will be assigned at the end of each section. Working homework problems is essential for success on exams. Students are expected to read in the text the sections covered in class. Technology/Media Component: Students must purchase an access code to MyMathLab, a website associated with the text book. A scientific calculator is also required. Service-Learning: N/A Course Requirements and Evaluation: Your grade will be determined by four unit exams(including the final exam) each worth 20% of your final grade. Homework, in MyMathLab, will count as 20% of your grade. Occasional quizzes may be given and if so will count as extra credit. Grading Policy:

5 The scale below shows the relationship between your semester percent average and the letter grade you will receive. A = B = C = D = E = 0-59 Attendance Policy: Students are strongly encouraged not to miss any classes. Students are responsible for all announcements made in class such as homework assignments and exam dates. Missed Exam Policy: If a student misses class during a regular scheduled exam the grade of zero will be assigned for that exam unless he or she can show that the absence was the result of sickness, a family emergency, or some other event completely beyond their control. Late Assignment Policy: All homework and exams must be completed by the deadline given to receive credit. Withdrawal Policy: A student may officially withdraw from this class from now through the last day of classes before finals week. Additional information can be found at the following site:

Math Techniques of Calculus I Penn State University Summer Session 2017

Math Techniques of Calculus I Penn State University Summer Session 2017 Math 110 - Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg E-mail: sxz38@psu.edu Office phone: 814-865-4291 Office Hours: