This is an official section page for MATH184:105.All policies, general grading scheme, additional mathematical problems, policies, etc. may be found in the course website. Note that the course website is a main source of the course-related information. Section-specific information can be found in syllabus and through announcements (see below).
Announcements. Final exam is scheduled for December 11th at noon. Location is ESB 1013.
During the exam period, you may use the following source of support:
Review session notes. Practice exam: the set of problems was created based on the previous exams and may or may not be similar to the current exam. Also note that the number of problems is reduced, so you should be able to solve it in 1 hour, so not all the topics of this course are checked in this set of proble,s.
Mon Dec 9th 11:00am-01:00pm LSK 303C.
Tue Dec 10th 12:00pm-13:30pm LSK303D.
Review problems (will be posted soon.) To prepare to the exam, I recommend to solve as many problems as possible. Please try to solve suggested problems from the weekly goals listed on the course website. Here you can find more problems.
Limits and continuity.
Answers to suggested problems. Many thanks to Dr. Radhika Ganapat for providing answers.
Midterm 2 will be held at MCML 166 on Thursday, November 7th at 6:40-7:40pm.
You may get Midterm 2 back on of the following days/times.
In case you want to dispute your grade, please make a short write-up why you consider your grade should be increased. You may dispute your grade at least day after you get your Midterm back.
I posted some stats about the midterms at the bottom of the page.
Lecture notes. Note that examples in lecture notes may be different from the examples in class.
Lecture 1 - September 5. Concepts of business, the problem about oPad (to be finished during the next class).
Lecture 2 - September 10. We finished oPad problem, talked about functions and inverse functions, exponents and logarithms and limit, right-hand and left-hand limit. Note that in your textbook the sided limits are called right-hand and left-hand limits.
Lecture 3 - September 12. Velocity, rate of change, tangent line, estimating limits from a table, finding limits from a graph.
Lecture 4 - Septermber 17. Techniques for computing limits.
Lecture 5 - September 19. Continuity at a point.
Lecture 6 -September 24. Continuity on an interval, the Intermediate Value Theorem, introduction to derivatives,
Lecture 7- September 26. Rules for derivative: constant, power, sum rules, product rule, quotient rule. The Euler's number e and the function e^x. The reason why conditions for product rule and quotient rule are important.
Lecture 8. Graphs of derivatives, other techniques for computing limits. Derivative of exponential and logarithmic functions, derivatives of trigonometric functions.
Lecture 10. Derivatives for computing velocity and acceleration. Higher order derivatives. Marginal cost, profit, revenue. Introduction to implicit differentiation.
Lecture 11. Review
Lecture 12. Implicit differentiation. Normal line. The derivative of the logarithm. Logarithmic differentiation.
Lecture 13. Tangent lines for self-intersecting curves and implicit differentiation. Related rates of change and elasticity. Example.
Lecture 14. Related rates of change, linear growth and exponential growth. Related rates, example with the balloon. Example with the hourglass.
Lecture 15 was substituted by Dr. Sujatha Ramdorai. Scan of lecture notes of Tess. Thanks a lot to her!
Lecture 16. Intervals of increase and decrease. Examples. First derivative test.
Lecture 17. Concavity, inflection points. Sketching.
Review notes. Implicit differentiation, continuous compounding, rate of change. Solution to the example with the hourglass. Relative rate of change: walking around the lake. Elasticity example.
Lecture 18. Infinite limits, vertical asymptotes, limits as x tends to infinity, horizontal asymptotes. Useful formulas. Quiz was written today. Quiz with solution.
Lecture 19. Sketching with vertical asymptotes. Extra example for sketching. Optimization problems: fence along the straight river, the closest point. Steps for optimization.
Lecture 20. More optimization problems: box with the open top, concentration of bacteria, maximizing revenue, maximizing profit.
Lecture 21. Optimization returns ;) way to UBC problem, cone with maximal surface area. Introduction to linear approximation: how the tangent lines help to approximate.
Lecture 22. (Nov 19th) Continued: linear approximation. Linear approximation example for business problem. Error bounds for the constant approximation.
Lecture 23. Error bound for linear approximation: absolute value of the error. Example with square root. Overestimate or underestimate. Example with e.
Introduction to quadratic approximation: establishing properties of linear approximation.
Lecture 24. Example of computing error bounds. Quadratic approximation. Example. Does quadratic approximation always provide better estimate than linear approximation? Taylor polynomial. Using Taylor polynomials to estimate the value of e.
Lecture 25. Stat. Example of linear approximation, error bounds. Taylor polynomials for sin(x) and cos(x). Inverse trigonometric functions. Exam-writing tips. Various feedback.
Homeworks and solutions.
1. Do not worry if you are not able to understand the problem, it may be because homework is posted in advance, before the corresponding material was covered in the class. You may try to solve other questions.
2. Homework requires some thinking and deep understanding of material. Keep working!
3. Note that number in square brackets is the maximal number of points for this question, e.g.,  means that you can get at most 2 points for this problem.
Homework 3. Due Oct 3 3:30pm. Solutions. Problem 1 and 2, problem 3, problem 4 may be checked using the Wolfram Alpha, problem 5, problem 6, problem 7, problem 8,9 and 10 , problem 11 and 12
Homework 6. Due Oct 31 3:30pm. Some solutions are still missing! Problem 3. Problem 5. Problem 6. General approach to problem 6. Problem 7.
Comments. 1. If you asked to find horizontal asymptotes, you have to consider *both* limits lim_(x->infinity) f(x) AND lim_(x->-infinity) f(x).
2. In related rates problems you have to justify that the critical point you found is a point of absolute maximum or minimum on the appropriate interval.
3. Do not forget to state that the length of the segment of line should be positive. That applied to sides of the triangle, rectangular, box, radius of the circle, etc.
Homework 8. Due Nov 21 3:30pm.
Homework 9. Due Nov 28 3:30pm.
Need help? You may use the following resources:
Deviation shows how different the grades are from their average.
Example 1. Everybody get 25 out of 50. Then, average and mean will be 25, and since all grades are the same as the average, deviation is 0.
Example 2. Half of students get 0 out of 50, and half of students got 50 out of 50. Mean and average are 25 (as in example 1), but all grades are far away from the average, so deviation is high.
High deviation = lots of excellent grades and lots of bad grades
Low deviation = majority of grades are close to average
For both midterms the deviation is huge.