MATH 16B (SECTION 002), Remote, 12:10-1 p.m. MWF
MATH 16B (SECTION 003), Remote, 2:10-3 p.m. MWF
Instructor: Dr. D. A. Kouba
Last Updated: March 13, 2021
Text: CALCULUS, An Applied Approach (7th edition) by Larson and Edwards
Office: 3135 MSB
EXAM DATES :
- EXAM 1-- MONDAY, January 25, 2021
- EXAM 2-- FRIDAY, February 19, 2021
- EXAM 3-- MONDAY, March 8, 2021
- FINAL EXAM 2:10 pm Class-- WEDNESDAY, March 17, 2021, 8-10 a.m.
- FINAL EXAM 12:10 pm Class-- THURSDAY, March 18, 2021, 3:30-5:30 p.m.
Here is a Schedule of lectures.
Here are copies of Handouts 1-12 .
Here are Supplementary Class Handouts .
Here are Trigonometry Review Sheets including graphs, exact values, and identities.
Here are Differentiation Rules from Math 16A.
Here is a List of Logarithm and Exponential Rules .
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Here are Practice Exam 1 and Solutions .... and another .... Practice Exam 1 and Solutions
Here are Practice Exam 2 and Solutions .... and another .... Practice Exam 2 and Solutions
Here are Practice Exam 3 and Solutions .... and another .... Practice Exam 3 and Solutions
Here are Practice Final Exam and Solutions .
___________________________________________________________________________________________________________
Click here for additional optional PRACTICE PROBLEMS with SOLUTIONS found at
THE CALCULUS PAGE , a website which I created.
Here are some
TIPS for doing well on my exams.
Here is the Course Syllabus
HERE ARE SOLUTIONS TO Winter Quarter 2021 EXAMS :
Exam 1 Solutions
Exam 2 Solutions
Exam 3 Solutions
Final Exam Solutions
Here are Math 16B . . . . . HOMEWORK Solutions
You can get help from Graduate TA's at the Virtual Calculus Room .
HERE ARE HOMEWORK ASSIGNMENTS, LECTURE NOTES, AND SHORT VIDEOS
SCANNED PROBLEMS for Sections 4.1-4.6
-- Here are detailed class notes covering Rules for Exponents and Exponential Functions . Here are detailed class notes covering Discrete and Continuous Compounding of Interest .
-- Here is a
video showing how to use Rules for Exponents to solve equations.
-- Here is a
video showing how to use the Discrete and Coninuous Compound Interest formulas..
- HW #1 ... Here is a handout on Exponent Rules and the Number e ..... Here are brief notes on Discrete and Continuous Compounding of Interest ... (Section 4.1) ... p. 262: 2, 4, 6, 8, 12-14, 18-24, 26, 27, 29, 32, 35, 37, 39, 40ab ..... and ..... Handout 1 . ..... and ..... SA1, SA4, SA7abc
- HW #2 ... Here is an Example of a naturally-occuring exponential function ... (Section 4.2) ... p. 270: 1, 4-6, 8, 12-18, 20, 21, 32, 36, 37, 39, 42, 44, 45 (where p is price x is units sold), 48, 53 (Solve all parts algebraically.) .... and ..... SA7d, SA7e SA8, SA17ab
-- Here are detailed class notes covering the Differentiation of Exponential Functions .
-- Here is a
video showing examples using the Derivatives of Exponential Functions.
- HW #3 ... (Section 4.3) ... p. 279: 2, 6, 9, 10, 12-14, 16, 17, 20, 23, 26, 27, 30, 32, 34, 39bc (Solve algebraically. Part c requires this formula: ln e^z = z.), 40, 42 ..... and ..... Handout 2
-- Here are detailed class notes covering Natural Logarithms .
-- Here is a
video showing how to use Natural Logarithms to solve equations.
- HW #4 ... Here are brief notes on differentiating the Natural Logarithm Function ... Here are brief notes explaining the formulas for differentiating Exponential Functions ... (Section 4.4) ... p. 287: 1, 7, 13-18, 20, 24, 25, 30, 39, 43, 46, 54, 57, 60, 62, 64, 67, 73, 79, 85-90 ..... and ..... These ..... and ..... SA2, SA7fghi, SA17cde
-- Here are detailed class notes covering the Differentiation of Logarithmic Functions .
-- Here is a
video showing examples of Derivatives of Logarithmic Functions.
- HW #5 ... (Section 4.5) ... There are many applications which use logarithms base 10. They include measuring the pH of a solution , determining sound intensity in decibels , and the use of the Richter scale for earthquakes, which is being supplemented and replaced by the moment magnitude scale ... p. 296: 4, 6, 7, 10, 11, 13, 14, 17, 20, 22, 23, 26, 27, 29, 31, 34, 37, 40, 41, 43, 46, 48, 49, 51, 52, 60, 61, 66, 67, 69, 72, 82bcd (Solve algebraically.) ..... and ..... Handout 3 ..... and ..... SA7j, SA14
-- Here are detailed class notes covering Exponential Growth/Decay .
-- Here is a
video showing examples of Exponential Growth and Decay.
-- Here is a
video showing an example using Half-Life.
- HW #6 ... Here is a Carbon Dating Problem and its Solution , which we will do in class ... (Section 4.6) ... p. 305: 1, 9, 11, 18, 19, 23ab, 40, 44, 46, 48 ..... and ..... and ..... Researchers in Siberia found a frozen
wolf/dog puppy , which was 18,000 years old. Use methods from class to estimate the amount of Carbon 14 remaining in the animal. The solution is here ..... and ..... SA3 ..... Here is a link with more information about the process of Carbon Dating .
SCANNED PROBLEMS for Sections 5.1, 5.2
-- Here are detailed class notes covering Antiderivatives and Gravity Problems .
-- Here is a
video showing examples of Antiderivatives.
-- Here is a
video showing an example of a Gravity Problem.
- HW #7 ... (Section 5.1) ... p. 326: 2, 5, 9, 12, 13, 15, 18, 22, 24, 25, 34, 36, 41, 44, 45, 49, 51, 54, 56, 57, 59, 60, 75-78 ..... and ..... Handout 4 ..... and ..... SA5ab ..... and ..... Gravity Problems
-- Here are detailed class notes covering Antiderivatives using U-Substitution .
-- Here is a
video showing examples of Antiderivatives using U-Substitution.
- HW #8 ... (Section 5.2) ... p. 335: 9, 12, 15, 18, 21, 24, 27, 32, 33, 41, 42, 47, 55, 59, 60 ..... and ..... SA6abc
EXAM 1 is Monday, January 25, 2021. It will cover handouts, lecture notes, and examples from class, homework assignments 1 through 8, and material from sections 4.1-4.6, 5.1, 5.2 in the book which was presented in lecture notes through Wednesday, January 20, 2021. Most of the exam questions will be homework-type, practice exam-type questions.
Let's do it ! !
TYPES OF QUESTIONS FOR EXAM 1 FOR WINTER 2021 (subject to unannounced changes)
- 4 -- Anti-Derivatives
- 4 -- True or False Questions
- 1 -- Implicit Differentiation
- 1 -- Gravity Problem
- 1 -- Discrete or Continuous Compounding of Interest
- 1 -- Exponential Growth/Decay
- 1 -- Extrema and/or Inflection Point Problem Using First and/or Second Derivatives
- 2 or 3 -- Others
HERE ARE SOME RULES FOR EXAM 1.
- 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
- 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
- 3.) You will be graded on proper use of derivative and integral notation.
- 4.) Put units on answers where units are appropriate.
- 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
THE GRADING SCALE FOR EXAM 1 FOR WINTER 2021 IS :
A ...... 110-125
B ...... 90-109
C ...... 60-89
D ...... 45-59
F ...... 0-44
SCANNED PROBLEMS for Section 8.5
-- Here are detailed class notes covering Antiderivatives of Trig Functions .
-- Here is a
video showing examples of Antiderivatives of Trig Functions.
- HW #9 ... (Section 8.5) ... Here is a sheet with Trig Derivatives (Memorize these.), Integrals (Memorize these.), and Identities (You need not memorize these.) ... and here are some Solved Examples ... p. 594: 1, 5-7, 10-12, 14, 16, 22, 26, 32-34 ..... and ... Handout 5 ..... and ..... SA9
SCANNED PROBLEMS for Sections 5.3-5.7
-- Here are detailed class notes covering Antiderivatives of Exponential Functions and Logarithmic Antiderivatives .
-- Here is a
video showing examples of Antiderivatives of Exponential Functions.
-- Here is a
video showing examples of Logarithmic Antiderivatives.
- HW #10 ... (Section 5.3) ... p. 342: 1, 3, 6, 10, 11, 14, 15, 20, 24-26, 30, 31, 34, 36, 38, 39, 41, 42, 44, 47, 49, 51-53, 57, 58, 63, 64 ..... and ..... SA10ab ..... and ..... (section 8.5) p. 594: 13, 15, 17, 19-21, 23-25, 27, 28, 30
-- Here are detailed class notes covering Definite Integrals , Average Value of a Function on Interval [a, b] , and Properties of Definite Integrals and Even/Odd Functions .
-- Here is a
video showing examples of Definite Integrals.
-- Here is a
video showing examples of the Average Value of a Function on Interval [a, b].
-- Here is a
video showing examples Properties of Definite Integrals and Even/Odd Functions.
- HW #11 ... (Section 5.4) ... Here are some Notes on Areas of Standard Geometric Shapes and associated Definite Integrals ... Here are some of the Properties of Definite Integrals and
Even/Odd Functions ... p. 353: 1, 3, 6, 7, 10, 11, 13, 15, 18, 19, 22, 23, 28, 31, 34, 37, 40, 44, 46, 50, 53, 54, 56, 58, 59, 63, 65, 67, 69, 70, 73, 74, 90, 91 ..... and ..... Handout 6 ..... and ..... SA10C
-- Here are detailed class notes covering the Area Between Curves using Vertical Cross-Sections and Horizontal Cross-Sections.
-- Here is a
video showing examples of Area Between Curves using Vertical Cross-Sections. Here is a video showing examples of Area Between Curves using Horizontal Cross-Sections..
- HW #12 ... (Section 5.5) ... p. 362: 2-4, 6, 8, 10, 12-15, 17, 19, 23, 26, 28, 29, 33, 35, 37, 40 ..... and ..... Handout 7
-- Here are detailed class notes covering the Midpoint Rule and Trapezoidal Rule . Here are detailed class notes covering elementary Applications of the Definite Integral .
-- Here is a
video showing examples of the Midpoint Rule and Trapezoidal Rule.
-- Here is a
video showing examples of elementary Applications of the Definite Integral.
- HW #13 ... (Section 5.6) ... Here are some Notes on estimating the value of a definite integral using the Midpoint Rule and the Trapezoidal Rule ... Here is an Example of M4 , the Midpoint Estimate with n=4, together with a measure of the Absolute Percentage Error ... Here is an Example of T5 , the Trapezoidal Estimate with n=5, together with a measure of the Absolute Percentage Error ... p. 369: 1, 3, 7, 12, 18, 19, 21, 23, 26, 31, 32 (Find T8 and M4.) ..... and ..... p. 362: 51, 52 (Assume N1(t)and N2(t) have units people/week, not people.) ...... and ..... Handout 8 ..... and ..... SA11
********* Here is Section 5.7 content from the textbook *********
-- Here are detailed class notes covering the Disc Method , where we use integration to find the Volume of a Solid of Revolution.
-- Here is a
video showing examples of the Disc Method about Horizontal Axes.
-- Here is a
video showing examples of the Disc Method about Vertical Axes.
- HW #14 ... (Section 5.7) ... p. 376: 1, 2, 6, 8, 10, 12, 14, 16, 25, 27, 30, 31 ..... and ..... Applications of Definite Integrals
- HW #15 ... (Section 5.7) ... Here is a Summary of how to find Volumes of Solids of Revolutions
... p. 376: 17, 18, 20, 22, 26, 28, 29 ..... and ..... Handout 9
SCANNED PROBLEMS for Sections 6.1, 6.2
-- Here are detailed class notes covering Standard U-Substitution, U-Substitution with a "BacK Substitution, and Power U-Substitution .
-- Here is a
video showing examples of U-Substitution with a "Back" Substitution.
-- Here is a
video showing examples of Power U-Substitution.
- HW #16 ... (Section 6.1) ... p. 394: 1, 4, 6, 7, 10, 11, 13, 16-20, 23, 27, 29, 31, 34, 35, 37, 40, 41, 44, 47, 58, 65 ..... and ..... Handout 10
-- Here are detailed class notes covering Integration by Parts .
-- Here is a
video showing examples of Integration by Parts.
- HW #17 ... (Section 6.2) ... Here is a derivation of the Integration by Parts formula ... p. 403: 2, 5, 7, 9, 11, 13, 16-19, 21, 22, 24, 27, 32, 33, 38, 40, 49, 51, 54b, 59, 61a
EXAM 2 is Friday, February 19, 2021. It will cover handouts, lecture notes, and examples from class, homework assignments 9 through 17, and material from sections 8.5, 5.3-5.7, 6.1, 6.2 in the book which was presented in lecture notes through Wednesday, February 17, 2021. Most of the exam questions will be homework-type, practice exam-type questions.
TYPES OF QUESTIONS FOR EXAM 2 FOR WINTER 2021 (subject to unannounced changes)
- 6-- Indefinite Integrals (Using any Method: formulas, trig identities, standard u-substitution, u-substitution with a back substitute, power u-substitution, and integration by parts (one time only for this exam))
- 1-- Midpoint or Trapezoidal Estimate
- 1 or 2-- Area of Region (Using dx or dy)
- 1-- Average Value of Function on Interval [a, b]
- 3-- Volume of Solid of Revolution (Around x-axis, y-axis, or any vertical or horizontal line)
- 1 or 2-- Others
HERE ARE SOME RULES FOR EXAM 2.
- 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
- 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
- 3.) You will be graded on proper use of derivative and integral notation.
- 4.) Put units on answers where units are appropriate.
- 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
THE GRADING SCALE FOR EXAM 2 FOR WINTER 2021 IS :
A ...... 110-125
B ...... 90-109
C ...... 60-89
D ...... 45-59
F ...... 0-44
SCANNED PROBLEMS for Sections 6.2-6.6
-- Here are detailed class notes covering Integration by Parts more than Once and Integration by Parts with a Twist .
-- Here is a
video showing examples of Integration by Parts More Than Once.
-- Here is a
video showing examples of Integration by Parts with a Twist.
- HW #18 ... (Section 6.2) ... p. 403: 3, 4, 19, 28, 29 ..... and ..... Handout 13
-- Here are detailed class notes covering Integration by Partial Fractions .
-- Here is a
video showing examples of Integration by Partial Fractions.
-- Here is a
video showing examples of Integration by Partial Fractions with Repeated Factors.
-- Here is a
video showing an example of Integration by Partial Fractions together with Polynomial Division.
- HW #19 ... (Section 6.3) ... p. 413: 2, 6, 8, 12, 13, 18, 20, 26, 29, 30, 35, 38, 42, 44, 53 ..... and ..... Handout 11
-- Here are detailed class notes covering Improper Integrals .
-- Here is a
video showing examples of Improper Integrals with +/- Infinity.
-- Here is a
video showing examples of Improper Integrals with Division by Zero.
-- Here is a
video showing an example of an Improper Integral with Partial Fractions.
- HW #20 ... (Section 6.6) ... Here is a worked out example of an Improper Integral using Partial Fractions ... p. 444: 1-10, 12, 14-16, 18, 19, 22-26, 29, 30 ..... and ..... more Improper Integrals ..... and ..... SA13
-- Here is an Integral Table and here are detailed class notes covering Integral Tables .
-- Here is a
video showing examples of Integration using Integral Tables.
- HW #21 ... (Section 6.4) ... p. 424: 14, 16, 20, 22, 34, 54, 56, 58, 60 ..... and ..... Handout 12
-- Here are detailed class notes covering Simpson's Rule and Absolute Error Formulas for the Midpoint, Trapezoidal, and Simpson's Rules .
-- Here is a
video showing examples of Absolute Errors for a specific values of n.
-- Here is a
video showing examples of Absolute Errors for unknown values of n.
- HW #22 ... (Section 6.5) ... This link briefly explains the Plausibility of Simpson's Rule and here is what Simpson's Rule with n=6 looks like ... Here are worked out examples using the Absolute Error Formulas for the Simpson's Rule, the Trapezoidal Rule, and the Midpoint Rule, Here is a detailed development and derivation of the Trapezoidal Rule Error Formula ... p. 433: 1, 4, 10, 14, 18, 20, 29, 31, 32, 36, 38, 48 ..... and .....
SA12
EXAM 3 is Monday, March 8, 2021. It will cover handouts, lecture notes, and examples from class, homework assignments 17 through 22, and material from sections 5.7 and 6.2-6.6 which was presented in lecture notes through Friday, March 5, 2021. Most of the exam questions will be homework-type, practice exam-type questions.
Bring it !
TYPES OF QUESTIONS FOR EXAM 3 FOR WINTER 2021 (subject to unannounced changes)
- 1-- Simpson's Rule Problem
- 1-- Absolute Error Problem for Trapezoidal Rule or Simpson's Rule
- 1-- Integration Table Problem
- 3-- Improper Integrals
- 4 or 5-- Indefinite Integrals (Using any method--formulas, standard u-substitution, u-substitution with a back substitute, power u-substitution, partial fractions, integration by parts, integration by parts more than once, integration by parts twice with a twist.)
- 1 -- Other
HERE ARE SOME RULES FOR EXAM 3.
- 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
- 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
- 3.) You will be graded on proper use of derivative and integral notation.
- 4.) Put units on answers where units are appropriate.
- 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
THE GRADING SCALE FOR EXAM 3 FOR WINTER 2020 IS :
A+ ...... 100-110
A ...... 90-99
A-/B+ ...... 85-89
B ...... 65-84
C ...... 40-64
D ...... 25-39
F ...... 0-24
SCANNED PROBLEMS for Sections 9.1-9.3
- HW #23 ... (Section 9.1) ... Here are introductory Notes and an Example on Discrete Probability, Expected Value, Variance, and Standard Deviation ... Here are two worked out Examples of Discrete Expected Value ...
p. 622: 1-7, 10, 11, 13, 22, 24, 25, 27, 29, 31, 32 ..... and .....
SA15
- HW #24 ... (Section 9.2) ... Here is the Definition of a Probability Density Function ... Here are Examples showing that a function is a Probability Density Function ... p. 631: 6, 9, 10, 13, 14, 16, 19, 22-25, 27, 28, 33 ..... and .....
SA16
- HW #25 ... This is an Example of using a Probability Density Function to compute Expected Value, Mean, Median, Variance, and Standard Deviation ... (Section 9.3) ... p. 641: (Also find median for problems 1, 4, 5, and 10) 1, 4, 5, 10, 11, 35, 42, 43
The FINAL EXAM is
2:10 pm Class-- Wednesday, March 17, 2021, 8-10 a.m.
12:10 pm Class-- Thursday, March 18, 2021, 3:30-5:30 p.m.
BRING A PICTURE ID TO THE EXAM
AND BE PREPARED TO SHOW IT TO KOUBA OR THE TEACHING ASSISTANTS !!
The final exam will cover handouts, lecture notes, and examples from class, homework assignments 1 through 25, and material from sections 4.1-4.6, 5.1-5.7, 6.1-6.6, 8.5, and 9.1-9.3. Use your three hour exams, 25 homework assignments, and the practice exams as a guide to your preparing for the final exam. Most of the exam questions will be homework-type, practice exam-type questions. There will be an OPTIONAL EXTRA CREDIT problem on the exam.
You can get there !
TYPES OF QUESTIONS FOR THE FINAL EXAM FOR WINTER 2021 (subject to unannounced changes)-- There will be no Midpoint, Trapezoidal, or Simpsone Rule Problems. There will be no Absolute Error Problems.
- 7 -- Indefinite Integrals Using Any Method
- 2 -- Volume of Solid of Revolution (Around x-axis, y-axis, vertical line, or horizontal line)
- 1 -- Find Area of Region (Using dx or dy)
- 1 -- Continuous or Discrete Compound Interest
- 1 -- Improper Integral
- 1 -- Exponential Growth/Decay
- 1 -- Probability Density Function (Mean, Median, Variance, Standard Deviation, Probability)
- 1 -- Discrete Probability
- 1 -- Other
HERE ARE SOME RULES FOR THE FINAL EXAM.
- 0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
- 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A
CALCULATOR ON THIS EXAM.
- 2.) You may NOT use L'Hopital's Rule to compute limits on this exam.
- 3.) You may NOT use shortcuts from the textbook for finding limits to infinity.
- 4.) You need NOT MEMORIZE trigonometry identities. A short list of identities will be provided on the front cover of the exam.
- 5.) Using only a calculator to determine the value of limits will receive little or no credit.
- 6.) You will be graded on proper use of limit notation.
- 7.) Put units on answers where units are appropriate.
- 8.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
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Your comments, questions, or suggestions can be sent via e-mail to Kouba by
clicking on the following address :
kouba@math.ucdavis.edu .