Instructor: Dr. James MacLaurin What: Math 1310-001 Email: maclaurin@math.utah.edu Lecture when and where: M,W,F 08:05 AM-09:25 AM AEB-320 Course website: check the Canvas course page in your CIS (you're in it now!) Office phone: 801 585 0000 Office: LCB 313 James’s office hours: 9:45-11:45 Every Monday Final Exam time & place: Monday April 30th, 8-10 am, AEB-320 The textbook: Calculus: Concepts and contexts, fourth edition, by James Stewart (ISBN- 978-0495557425) The work The work you will complete in Math 1310 comprises weekly homework and quizzes, weekly lab assignments, three midterm exams, and a comprehensive final exam. Homework will be turned in on Friday, and quizzes will typically be given every Friday except during exam days and holidays. The instructor will may adjust the due dates when needed. The two lowest homework and quiz scores will be dropped. Assignment weightings, point values, and grading rubrics are given to the right of this document, but could be slightly changed by instructor discretion. Details about the content of each assignment type are as follows: Homework: Roughly three to four textbook sections are due every Monday from lectures covering through the preceding week to Friday. If you click on a homework assignment, you will see listings of problems, about three of which will be randomly selected for grading by the grader. Three of a student's lowest homework scores will be dropped. Homework will only be accepted in class, no electronic copies. No late homework will be accepted. Quizzes: A quiz will be given most Friday’s, usually online. The link can be accessed via Canvas. The quiz will cover relevant topics covered in the week's lectures and in the lab section group work. The lowest two quiz scores will be dropped. Midterm exams: Three 50-minute midterm exams will be given on select Fridays. A practice exam and knowledge checklist will be posted roughly a week prior to the midterm that will cover the same material. Final exam: A two-hour comprehensive exam will be given covering the entire content of the course. As with the midterms, a practice final will be posted a week prior. Lab: Every Thursday students will meet for their laboratory section. These lab days will be spent working on more challenging homework problems. Students will work in groups, with facilitation by the Teaching Assistant. The goal of these problems is to give students a deeper understanding of how the mathematics is applied, with the goal of concept learning, and improving problem solving fluency---the skill of orchestrating many methods and skills, and interpretation of results, in order to achieve an stated objective. The lowest lab score will be dropped. Letter grades are determined as follows: If X is your percentage grade, then {X ≥ 93% ⇒ A, X ≥ 90% ⇒ A−, X ≥ 87% ⇒ B+, X ≥ 83% ⇒ B ,X ≥ 80% ⇒ B− ,X ≥ 77% ⇒ C+ , X ≥ 73% ⇒ C, X≥70%⇒C−, X≥67%⇒D+, X≥63%⇒D, X≥60%⇒D−, X<60%⇒E}. Letter grade assignments can be changed at the discretion of the instructor. The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations. All information in this course can be made available in alternative format with prior notification to the Center for Disability Services. Course learning objectives The tools and skills Students will understand how to transform functions into other functions through x- and y- translations and rescaling, re-parameterizations, and function composition. Students will also know the properties of special classes of functions including logarithms, exponential functions, polynomials, and rational functions; and know how to obtain function inverses f^{-1}(y)=x when they exist. Students will master the concept of a limiting value of a function f(x)=y when x approaches a value c, know when limits exists, utilize limit laws, how the property of continuity of a function at c relates to its limiting value, how asymptotic behavior can be described by limits, and how limiting values can be specified even when the f(c) is not defined. Students will understand how to use limits to compute the derivative of a function f' that describe or rate of change of a function f. Students will be able to utilize derivatives to model how two related quantities change with respect to each other, including motion of objects by in terms of velocity and acceleration. Students will also learn the methods of differentiation for different classes of functions including exponential and logarithmic functions, trigonometric and inverse trigonometric functions, power functions, and compositions, sums, products, and quotients of functions, as well as differentiating functions that are only implicitly defined by an equation. Students will also be able to utilize the derivative in applied contexts, including function approximation, and how the average slope of a function relates to the derivative through the mean value theorem. If two quantities are related by an equation, students will be able to obtain the derivative of one quantity by knowing the derivative of the other. Students will know how to utilize linear approximations to perform numerical/algorithmic equation solving via Newton's method. Also, students will be able to utilize the derivative to find maximum, minimum, or otherwise "optimal" input values for equations important in science, business, and engineering. Students will understand the definition of the integral of a function as the limiting value of an increasingly large average of function values. They will be able to relate the integral to anti-differentiation, when appropriate, through the fundamental theorem of calculus. Students will also be able to relate the integral to the area under the function's curve, know how to approximate the integral by a finite sum, and how to integrate over infinite-length domains. Specific integration techniques will also be mastered, including substitution, integration-by-parts, and partial fractions. Finally, students will understand the key concept underlying integration, that it computes the net accumulation of a quantity through summation of the change in the quantity amount per unit of time or space, over an specified interval of time or space. Problem solving fluency: In addition to topical content, students will also gain experience and further mastery of complete problem solving fluency. Students will be able to read and interpret problem objectives, be able to select and execute appropriate methods to achieve the aforementioned objectives, and be able to interpret and communicate results. Week by week guide: Week 1: 1.3, 1.5-6 Functions, Compositions, Exponential Function, Logarithms, Inverse Functions Week 2: 1.7, 2.1-2 Parametric Curves, Tangent and Velocity, Limits Week 3: 2.3-2.5 Limit Laws, Continuity, Limits at Infinity, Labor day--no class on Monday Week 4: 2.6-7 Derivatives and Rates of Change, Derivative as a Function, Midterm 1 Week 5: 2.8,3.1-2 Functions and Their Derivatives, Derivatives of Polynomials and Exponential Functions, Product and Quotient Rules Week 6: 3.3-5 Derivatives of Trig Functions, Chain Rule, Implicit Differentiation Week 7: 3.6-8 Inverse Trig Functions, Log Functions and their Derivatives, Scientific Applications Spring Break---between week 7 & 8 Week 8: 3.9, 4.1 Linear Approximation and Differentials, Related Rates, Midterm 2 Week 9: 4.2-4 Max and Min Values, Derivatives and Shapes of Curves, Graphing Week 10: 4.5-7 l'Hopital's Rule, Optimization, Newton's Method Week 11: 4.8, 5.1-2 Antiderivatives, Areas and Distances, The Definite Integral Week 12: 5.3-4 Evaluating Definite Integrals, Fundamental Theorem of Calculus, Midterm 3 Week 13: 5.5-6 Substitution Rule, Integration by Parts, Thanksgiving--no class Thursday-Friday Week 14: 5.7, 5.9-10: Other Integration Techniques, Approximate Integration, Improper Integrals Week 15: Review. Class meetings end after Thursday--no Friday class