We meet Mondays, Wednesdays and Fridays in Buchanan A104 at 8am. GradesMaterials for December final preparationCourse objectives covered by the December final Skills important for the December final Past exams and their solutions. Course materialsTextbook - we will use chapters 0-3. The textbook is free! Lecture 1: coordinates and lines. Suggested exercises: section 0.2 - problems 1-6 Lecture 2: lines. Suggested exercises: section 0.2 - problems 13-18 Lecture 3 + notes: distances, circles. Suggested exercises: section 0.2 - problems 7-11, 19-22, 24-30. Lecture 4 + notes: functions, their domains and graphs. Suggested exercises: section 0.3 - problem 5, problems on domain of a function Lecture 5 + notes: graphs of functions, functions defined by cases, transformations of graphs. Notes include interval notation, which is used in webwork 1 (we'll go over it in class next time). Suggested exercises: section 0.3 - 7, 12a, 13a, 13c, 14, 20, 21; section 0.4 - 2, 3, 8a, 8c, 10, 11, 15a, 15b, 15c, 16a, 16b, 16c, 22 Lecture 6 + notes: transformations of graphs, interval notation, composition of functions, average velocity. Suggested exercises: section 0.4 - 5, 6, 8b, 14, 17, 25, 26, 27 Lecture 7 + notes: average velocity, instantaneous velocity, slopes of secant and tangent lines. Suggested exercises: section 1.0 - 1-4, 6, 7 Lecture 8 + notes: acceleration, rate of change, difference quotient. Suggested problems: section 1.0 - problems 5, 8, sketch the graphs of position, velocity and acceleration for a falling object, an object oscillating back and forth, a runner in a 100m running competition and a Skytrain train. Lecture 9 + notes: average rate of change of a function, instantaneous rate of change of a funciton, slope of the tangent to a graph of a function, limits. Suggested problems: section 1.1 - 1-6, 14-17, find the slope of the tangent line to the curve y=x ^{3} at point (x,x^{3}).Lecture 10 + notes: limits, limits of rational functions, one-sided limits. Suggested problems: section 1.2 - problems 7-8,9,16,20. Lecture 11 + notes: limits, "strange" functions", continuity. Suggested problems: section 1.2 - problem 11, section 0.4 - problems 31-32, section 1.3 - problems 1,2 Lecture 12 + notes: continuity, continuity of functions with piecewise definition, intermediate value theorem. Suggested problems: section 1.3 - problems 3a,b,f,h, 5, 6, 7a,b,d,e. Lecture 13 + notes: intermediate value theorem for finding solutions of equations, proofs using IVT. Suggested exercises: section 1.3 - problems 12-17,18,19,22,23. Lecture 14 + notes: more on intermediate value theorem, definition of derivative. No new suggested problems. Lecture 15 + notes: definition of derivative, examples of derivatives. Suggested problems: section 2.0, problems 1-4, 6, 7-10, 11, 12, 14, 15, section 2.1 problems 1, 2, 9, 10, 13, 14, 15, 16, 18. Lecture 16 + notes: examples of derivatives. No new suggested problems. Lecture 17 + notes: review (examples on range of a function, true/false questions) Lecture 18 + notes: derivative as a function, alternative way to compute derivatives, differentiability implies continuity. Suggested problems: section 2.0, problems 13, 16, 17, 18, section 2.1 problems 3-6, 7-8, 11-12, 19-20, 22-23, 24, 25, section 2.2, problems 1, 2 Lecture 19: derivative of x ^{n}, derivative of f+g. Suggested problems: section 2.2, problems 19, 20, 23, 24, 25, 28, 29, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51. Lecture 20 + notes: product rule - intuition behind and proof. Suggested problems: section 2.2, problems 7, 3-4 (don't do (f/g)' for now) Lecture 21 + notes: quotient rule. Suggested problems: section 2.2, problems 3-4, 18, 26. Lecture 22 + notes: sines and cosines. Suggested problem: find sine and cosine of the following angles: 30 ^{o}, 135^{o}, 225^{o}, 390^{o}, -60^{o}. Lecture 23 + notes: measuring angles in radians, graphs of sin and cos, properties of sin and cos. Suggested problems: convert 30 ^{o}, 135^{o}, 225^{o}, 390^{o}, -60^{o }to radians, sketch graphs of sin(x+π/3), cos(-2x), cos(3x+π).Lecture 24 + notes: derivatives of sine and cosine. Suggested problems: section 2.3, problems 12 a-c, 14 (the kinetic energy is defined in problem 13), 15, 24, 29, 30, 31, 32, 34. Lecture 25 + notes: the function 2 ^{x}, its graph and its derivative, rules for exponents.Lecture 26 + notes: the number e, e ^{x}, (e^{x})', differential equation f'(x)=rf(x), exponential growth models. Suggested problems: section 2.3, problems 19, 22, 33, 39, 42, 45, 46.Lecture 27 + notes: the natural logarithm, properties of ln, graph of ln. Suggested problems: section 2.5, problems 1, 2, 3, 4, 10, 12, 15, 16, 17, 26, 29, 33. Lecture 28 + notes: derivative of ln, the chain rule. Suggested problems: section 2.5, problems 5, 6, 9, 18, 19, 20, 21, 22, 23. Lecture 29 + notes: much more chain rule. Suggested problems: section 2.5, problems 24, 25, 31, 32, 33, 35, 38, 39, 40. Lecture 30 + notes: more on the chain rule. Lecture 31 + notes: logarithmic differentiation. Suggested problems: problems 1-12 Lecture 32 + notes: implicit differentiation. Suggested problems: problems 1-14 Lecture 33 + notes. Lecture 34 + notes. Lecture 35 + notes. HelpHelp from graduate students is available at the math learning center (but it is not course-specific) PASS study groups are facilitated by experienced undergraduate and graduate instructors and offer course-specific help. Students from our section are encouraged to go to Monday 9-10am, Monday 7-8pm, Wednesday 9-10am or Wednesday 7-8pm sessions. Khan Academy has excellent videos on topics relevant to our course HomeworksWebwork: online assignments Remarks for written assignments. The written assignments should be brought to the Friday lectures or scanned and emailed by 9am on Friday. Graded assignments are returned on Friday lectures of the week after they are submitted. Unclaimed assignments can be picked up at my office ESB4109 when I am there. Assignment 1.3 and its solutions. Assignment 2 and its solutions. Assignment 3 and its solutions Assignment 4 and its solutions. Assignment 5 and its solutions. Assignment 6 and its solutions. Assignment 7 and its solutions. Assignment 8 and its solutions. Assignment 9 and its solutions. Assignment 10 and its solutions. Skills modulesAlgebra skills module is posted on the Webwork and is due 9am on Friday September 13. Geometry skills module is posted on the Webwork and is due 9am on Friday September 27. Functions skills module will be posted on the Webwork and be due 9am on Friday October 11. WorkshopsPlease register in and attend one of the workshops. You should expect to work in small groups on problems assigned by the workshop instructor. This experience should help you with applying the concepts you learn about in the lectures to solving problems. ExamsMidterm 1 was on October 16, 6:00pm-7:30pm in HENN 200. December final is on December 11 at 12pm. Midterm 1 materialsPast midterm 1. Don't solve 3b. Solutions. Past midterm 2. Don't solve 4c, 5c. Solutions. Past midterm 3. Don't solve 6. Don't worry too much about the questions on inequalities. Past final. Solve 1b, 3, 4a, 7*. Review your homeworks (go over the posted solutions). Revisit suggested problems. Review the webworks. Grading scheme15% Webwork and assignments 5% Skills modules 15% Workshops 20% Midterms 20% December exam 25% April exam There will be no make-up exams. If you miss a midterm, please provide a doctor's or a coach's note within one week after the midterm date. |