Math 21A: Calculus
Winter Quarter, 2012
Section A, M W F, 04:10PM -- 05:00PM, YOUNG 198

Please read the mathematics placement REQUIREMENTS to enroll in and to stay enrolled in Math 21A.

Textbook: Thomas' Calculus: Early Transcendentals, 12th Edition by Weir and Hass (Addison-Welsey; $144.67 via Amazon.com)

Final Grade

• A+ >= 360
• A  >=302
• A- >= 290
• B+ >= 276
• B  >= 250
• B- >= 241
• C+ >= 228
• C  >= 207
• C- >= 191
• D+ >= 182
• D  >= 170
• D- >=159

Instructor

Teaching Assistants

Course Grade

The course grade will be based on (weights in parentheses):
Quizzes (12%)
Midterm 1 (25%)
Midterm 2 (25%)
Final (38%)

Quizzes

There will be four or five quizes (probably four). Your lowest score will be dropped. Quizzes will be held in discussion section. There will be no make-up quizes nor alternative times for quizzes. The quiz dates are: January 19th, January 26th, February 16th, February 23rd, and March 15th. If there are only four quizzes one date will not be used.

• Quiz 3 solution
• Quiz 4 solution

Exams

There will be two midterms and the final. There will be no make-up exams nor alternative times for exams. A missed exam is zero points.

If there is an official reason that would prevent you from attending a midterm you must contact me before the midterm takes place, and you must receive a response from me excusing you from the midterm. If I excuse you your course grade would be determined by your performance on the other midterm and the final. If you miss a midterm for unforeseen reasons, contact me in person as soon as possible. You must take the final to pass the course. Missing the final will result in a failing grade for the course.

Calulators are not allowed to be used during any exam.

Fairness Policies

Midterms

Calulators are not allowed to be used during any exam. All that is allowed are writing instruments.

Midterm I

• Midterm1: Friday, 2/3/2012, during class
• First midterm office hours (tentatively): Monday 2:45-3:45, Wednesday 5:15-7:15
• Material covered
  • Chapter 2, Parts of sections 3.1 and 3.2, (Your background - Chapter 1 and algebra should be strong)
  • Limit definition, Calculate limits, Sandwich Theorem, Possible epsilon delta proof, Continuity, IVT, aymptotes (horizontal, oblique, vertical), Plot functions (know domain, range).
  • From sections 3.1 and 3.2 know the limit definition of the derivative, how the derivative corresponds to the slope of a curve and the instantaneous rate of change of a function. Be able to get an equation for the tangent line at a point on the curve or identify points on the curve that have a slope equal to a given value.
  • For this exam you will not have to graph nor identify the graph of the derivative of a function from a graph of the function.
  • The theorm about differentiability implying continuity will not be covered on this midterm
• This practice midterm is longer than the midterm is going to be. It has some typical problems.
• Practice midterm solution.
  • Correction to problem 5 is here
• Midterm1 solution

Midterm II

• Midterm2: Friday, 3/2/2011, during class
• Second midterm office hours (tentatively): Monday 5:15-6:15, Wednesday 2:45-3:45, 5:15-6:15
• Material covered
  • Emphasis is on chapter 3, Sections 3.1-3.10
  • Prior knowledge: you should know how to get the sin, cos, tan, csc, sec, cot of angles 0, pi/6, pi/4, pi/3, pi/2 and the angles related to them around the unit circle, From these you can get the inverse trig functions of the related ratios.
  • Also see the practice problems
  • The limit definition of the derivative. Tangents and Normal lines.
  • How the graph of the derivative relates to the original function.
  • Differentiation Rules. The chain rule. (A problem calculating derivatives using these)
  • The derivative as a rate of change: Position function problem. Relation between the position velocity and acceleration.
  • Derivative of the trigonemtric functions.
  • Implicit Differentiation. There will be a problem incorporating this.
  • If f has a derivative at x=c then f is continuous at x=c.
  • Derivatives of inverse functions, logs, and exponential functions.
  • Logarithmic diferentiation.
    • The derivatives of the six inverse trig function: You really only need to know 3 as the other 3 you just multiply by a negative sign. You will need to know how to get the other three from the three we derived in class. You should know d/dx(tan^{-1}x). I will give you d/dx(sec^{-1}x) and d/dx(sin^{-1}x) on the exam.
  • Related rates
• Here are some typical problems practice midterm. With solution here. Note problem 10 is from section 3.4 not 3.5.
• Midterm2 solution
• Curve guide: A~>=71; B~>=54; C~>=40; D~>=32

Final

The final room has been assigned. It is in room 198 Young. The same room we have lecture in.

The final date is set: Friday, March 23th, 10:30 a.m.- 12:30 p.m.. There will be no alternate time for the final. If you can't make the scheduled time, please reconsider taking this course. There will not be any alternate final.

Calulators are not allowed to be used during the final.

• The final is cumulative but weighted on the new material. To do the new material you need old skills.
  • Obviously, you will have to calculate derivatives but you are not limited to calculating them by the limit definition like on Midterm 1.
  • You clearly need to determine asymptotic behavior to do detailed graphing
  • There will be indeterminate forms like on midterm1, but now you may use LHOPS rule if it applies.
• Final Topics (This may be updated without notice)
  • Some additional problems to look at and Final topics are found here
  • Detaied graphing
  • Applied optimization
  • Related Rates
  • Limits: especially Indeterminate Forms and LHOPS rule.
  • MVT, corollary 1, corollary 2,
  • local extrema, absolute extrema, first derivative test, second derivative test.
  • Linearizations \ Differentials
  • Newton's Method

Students with Disabilities

Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC). Faculty are authorized to provide only the accommodations requested by the SDC. If you have any questions, please contact the SDC at 530/752-3184 or sdc@ucdavis.edu.

Lecture Summary

• 1/9: Completed 2.1 and reviewed log and exponential functions. Please reiew sections 1.1-1.6. We will reiew some of this material as we need it. Algerbra skills are very important for calculus. So is the ability to manipulate exponential and log functions.
• 1/11: Covered 2.2 up through the squeeze theorem.
• 1/13:
  • Used the squeeze theorem to prove two limits involving trignometric functions
  • A review of what we have done so far in section 2.3 is here
• 1/18:
  • Finished 2.3
  • Started 2.4 on one sided limits; proved an important trigonemtric limit using one sided limits.
• 1/20:
  • Reviewed chapter 1: Functions, Inverse functions, tricks to graphing functions, showed logs and exponentials are inverses to one another
  • Finished 2.4, Read this to help you with problems 21-42 in section 2.4.
  • Started 2.6
• 1/23
  • Finished 2.6
  • Started 2.5
• 2/6
  • Started 3.3
  • Derivative and/or formulas for a constant, power rule, sum/difference rule, exponentials, product rule, quotient rule.
  • Finished 3.3 higher order derivatives
  • Started 3.4 velocity, acceleration, jerks; no economic applications yet.
• 2/15
  • Finished the chain rule 3.6
  • Started implicit differentiation 3.7
• 2/26
  • Section 3.11
• 2/28
  • Section 4.1
• 3/2 Midterm 2
• 3/5
  • Section 4.2
• 3/7
  • Section 4.3
• 3/9
  • Handed back exams
  • Covered Section 4.4 up to detailed graphing
• 3/12
  • Finished up detailed graphing
  • Covered section 4.5 up to the top of page 257
• 3/14
  • Finished indeterminate forms section 4.5
  • Covered applied optimization problems, did 3 examples.
  • Finished a problem on applied optimization
  • Discussed Newton's Method

Homework

This list will be added to after just about every lecture, but will not be collected.

Homework solutions will be posted at the course webpage roughly one week after being assigned. During this time you are to work all the problems. The best way to do well on the exams and to learn math is for you to work many problems for yourself. It is your responsibility to do so and to check that you are doing so correctly. If you need help please ask the ta's or myself. It is a good idea to work additional problems than just those below.

• Sec. 2.1   1,3,5,9,13,19,21 solution
• Sec. 2.2   1,2,3,5,6,16,18,21,22(done in class),24,28,31,33,37,40,53,64,65,80,81,82 solution
• Sec. 2.3   1,3,5,8,9,11,13,31,33,37,38,45 solution
• Sec. 2.3   19,37,39,42,43 solution
• Sec. 2.4   1,3,5,7,9,14,15,18,22,25,27,29,33,40,42,43,48 solution
• Sec. 2.6   4,7,12,16,22,24,31,35,42,44,45,50,52,55,57,61,63,68,73,76,81,83,86,101 solution
• Sec. 2.5   5-10,15,17,21,27,29,31,35,37,41,43,46,48,53,54,55,56,59,60 solution
• Sec. 3.1   13,15,21,22,23-27,29 solution
• Sec. 3.2   2,4,6,9,10,12,13,16,22,25,27-30,37,39,41 solution
• Sec. 3.3   15,16,17,19,22,23,25,26,27,30,32,34,36,38,39,53,55,57,60,63,64,68,70,72,77 solution
• Sec. 3.3   10,12,43,47,49,51,60; Sec. 3.4   1,3,5,7,9,12,15,16,17,19,21,22,28,29,30 solution
• Sec. 3.5   4,9,11,14,17,21,26,31,33,35,37,39,43,45,49,53,58,61 solution
• Sec. 3.6   1,7,11,13,15,22,23,27,29,31,33,37,39,41,43,47,49,53,57,61,67,69,71,77,85,87,97,99 solution
• Sec. 3.7   2,5,8,11,14,15,18,22,23,27,30,33,35,39,42,44,46,50,52 solution
• Sec. 3.8   1,4,5,7,9,13,15,20,24,28,30,33,38,40,44,50,51,54,59,65,69,76,79,84,89,93,96,99 solution
  • Number 24 in the solution has a print error it should be 8x^7(ln x)^4+4x^7(ln x)^3
• Sec. 3.9   1,3,6,7,8,9,11,15,17,19,21,23,25,27,29,31,33,35,39,41,44,45,47,49,55 solution
• Sec. 3.10   10,14,20,21,22,23,24,25,27,32,33,34,44 solution
• Sec. 3.11   1,3,6,15,16bde,17,44,50,51,52,53,54,56,57,60,61 solution
• Sec. 4.1   1,3,4,15,18,23,25,31,33,37,39,43,44,48,50,55,60,62,66,68,74,76,83,85 solution
• Sec. 4.2   1,2,5,6,9,11,16,22,34,39,40,41,42,51,52,65 solution
• Sec. 4.3   1,3,5,8,9,10,14,20,29,33,35,39,41,43,52,53,55,59,61,63,65,67,74; solution
• Review chapter 1, section 1.1 if you have not already, we also covered this in lecture (symmetries)
• Review chapter 2, section 2.6 if you need to do so (asymptotic behavior)
• Review vertical tangents on the bottom of page 125 and the top of page 126, if you need to do so
• Sec. 4.4   Review what we covered on Friday and be prepared for detaied graphing. 2,6
• Sec. 4.4   10,17,21,23,29,30,33,41,56,58,92,98 solution
  • I labelled all pts in the plots as well as stating what the points are before the plots. This makes the figures very busy. I did this so it would be easier for you to see what points are which. In the figures, points labelled with inf are inflection points.
• Sec. 4.5   7,10,13,15,16,18,20,21,24,25,27,30,32,33,35,40,45,46,53,56,57,58,59,79 solution
• Sec. 4.6   1,2,4,7,9a,11,12,14,18,19,20a,32,38,57 solution1 (part1), solution2 (part2)
  • For the sake of time you can forget about doing problem 18 from scratch, It was to motivate to you the usefulness of numerical method's. After you do the calculus step, you need to find solutions to the equation tan(x/2)=2/x or some other form of the first derivative set equal to zero. One way to a solution is Newton's method which we learned today. But, for now consider yourself motivated and just look at my solution. Of course, you could also use the root finder function on your calculator or computer. But, that's not as much fun.
• Sec. 4.7   2,3,5,25,22