Introduction to limits and differential/integral calculus with a wide variety of applications. Students interested in intensive use of mathematics should take MATH 021. Credit not given for more than one of the courses MATH 019, MATH 021 unless followed by MATH 022. See MATH 023. Prerequisite: MATH 009 or MATH 010, or sufficiently strong background in secondary school algebra and geometry.
Open to Degree and CDE students
Fundamentals of Calculus I is the first course in our two-course applied calculus sequence. The follow-up course is Math 020 --- Fundamentals of Calculus II. Fundamentals of Calculus I is an introduction to the calculus of functions of one variable. This will include an understanding of the concepts of limits, continuity, the definition of the derivative, the Fundamental Theorem of Calculus, techniques and applications of differentiation, basic integration including substitution, and assorted applications of integration. This basically covers chapters 2 – 5 of the textbook given below. Topics will be presented with a level of depth and rigor appropriate for students pursuing degrees in business, economics, social and life sciences. Please speak to the Department of Mathematics and Statistics if you are unsure if you are taking the correct calculus course.
Textbook: Calculus for Business, Economics, Life Sciences and Social Sciences, 14th Edition, Barnett. Please note that you will need the MyLab Math Supplement that comes packaged with the textbook. You may wish to only purchase the MyLab access code which includes an eBook or electronic version of the textbook. The UVM Bookstore offers both options. If you choose to purchase just the access code and eBook (this is what most students do) you can also buy it directly from the Pearson website, www.pearson.com/mylab. You will need a scientific or graphing calculator for this course. Learning Objectives: After completing this course, the student will be able to: • Understand what a limit is and to calculate limits using a variety of methods • Determine the intervals where a function is continuous • Understand that the derivative is the limit of the difference quotient as the difference in the x values approaches 0; and be able to demonstrate this graphically • Compute the derivative using the difference quotient (algebraic method) • Compute the derivative of polynomial function using the Power Rule • Find derivatives of exponential and logarithmic functions • Find derivatives of products, quotients and composite functions • Use implicit differentiation for equations that cannot be solved for y • Solve related rate problems • Find local extrema using the first derivative • Use the first and second derivative to determine where a function is increasing or decreasing and where a function is concave up or concave down • Sketch graphs of a variety of functions using curve-sketching techniques • Solve optimization problems • Find antiderivatives of basic functions • Determine the area under a curve using the definite integral • Understand the Fundamental Theorem of Calculus and how it relates differentiation and integration • Use the Fundamental Theorem of Calculus to solve problems
MyLab math homework: 20% Quizzes: 25% Midterms: 30% (15% each) Final exam: 25%
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