MAT 168 Calculus II
Textbook
Purchasing a textbook or an access code for online homework system is NOT required for this course. I have made links to some free online calculus books available here. These are all good books but I particularly recommend Michael Spivak's and also Gilbert Strang's. Some of the books were used generations ago but they are still wonderful books. In my opinion, they are much better than calculus textbooks we commonly use nowadays. In addition, my lecture notes will be provided as well. The links to my lectures can be found in the weekly course schedule below.
How to Study
Math is a hands-on subject. So it is not fully learned by reading or listening lectures but by doing it. Solve problems as many as you can. That is the best way to learn math. Even when you don't fully understand concepts, you have to start working on problems. While keep tackling problems, you will gradually have better understanding of concepts.
Topics
Class Meeting Times and Class Room
Office Hours
Calculator
Grading
WebWork Online Homework
Your username is your student ID with w in lower case like w12345. Your default password is same as your student ID with w also in lower case. Make sure you change your password after the first log-in. To see how to enter mathematical notations in WebWork click here. If you have a question or need a help while working on a WebWork homework question, you may use the link "Email instructor" to send me a message as seen here. You don't have to tell me what the problem is as the message would include a copy of the problem your are working.
Antiderivatives, Integration, Application of Integration, Integration Techniques
NA
No in-person office hours, instead virtual online office hours on Skype or MS Teams can be arranged by appointment
Use of a calculator is rarely required for the course and not certainly for your tests. In fact, you lose sense of numbers thus negatively affect your ability to learn mathematics if you mindlessly rely on calculators.
Online WebWork Homework Assignments (25%)+3 Tests and Final Exam (75%)=100%. You will be give two chances to take each test (except for Final Exam) and if you take a test twice, only the higher score will be on record. Note that I do NOT mean allowing retake of the same test but chances to take two different versions of each test. Final Exam is optional and if taken, its grade will replace the lowest exam grade with the assumption that your final exam grade is higher than your lowest exam grade. In the unfortunate event your final exam grade is lower than your lowest exam grade nothing happens i.e. no grade replacement will occur. In other words, you will not be punished for trying final exam.
Free Online/On-Campus Tutoring
Weekly Schedule
Click on linked topics to view lecture notes and watch lecture screencasts. Our class begins on Wednesday 1/17 and each week begins on Wednesday except for Final Exam Week.
| Antiderivatives | Antiderivatives Antiderivatives 2 |
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| Approximating areas under curves | Left-end point method Midpoint method Right-end point method Riemann sum |
Homework 1 (Antiderivatives) | 1/24: Last day to add/drop full term classes without academic or financial penalty. Last day to drop full term classes without grade of W. | |||
| Definite Integrals | Definite Integrals Definite Integrals 2 Definite Integrals 3 |
Homework 2 (Indefinite integrals & Riemann sums) | ||||
| Fundamental Theorem of Calculus Substitution Rule |
Fundamental Theorem of Calculus Fundamental Theorem of Calculus 2 Substitution |
Homework 3 (Fundamental theorem of calculus & Definite integrals) Homework 4 (Substitution) |
2/10-2/13: Mardi Gras break | |||
| Areas Between Curves Volumes by Disks |
Areas Between Curves Volumes by Disks |
Homework 5 (Areas between curves, Volumes by disks) | ||||
| Volumes by Disks Volumes by Washers |
Volumes by Disks Volumes by Washes |
Homework 5 (Areas between curves, Volumes by disks) Homework 6 (Volumes by washers, Volumes by cylindrical shells) |
TEST 1 (Homework 1 - Homework 4) is due on Friday 2/23. | |||
| Volumes by Washers Volumes by Cylindrical Shells |
Volumes by Cylindrical Shells Volumes by Cylindrical Shells 2 |
Homework 6 (Volumes by washers, Volumes by cylindrical shells) | ||||
| Arc Length Surfaces of Revolution |
Arc-Length Arc-Length 2 Surfaces of Revolution |
Homework 7 (Arc length) Homework 8 (Surfaces of revolution) |
3/10-3/17: Spring Break | |||
| Arc Length Surfaces of Revolution |
Arc-Length Arc-Length 2 Surfaces of Revolution |
Homework 7 (Arc length) Homework 8 (Surfaces of revolution) |
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| Integration by Parts | Integration by Parts Integration by Parts 2 Integration by Parts 3 Correction: In the last example, I forgot to multiply \(e^x(-\cos x)\) by \(-1\). The second part of the integral (22:35 mark) should \(+e^x\cos x\) and consequently the final answer should be \[\frac{1}{2}e^x\sin x+\frac{1}{2}e^x\cos x+C\] |
Homework 9 (Integration by parts) | TEST 2 (Homework 5 - Homework 8) is due on Friday 3/22. | |||
| Trigonometric Integrals | Trigonometric Integrals Correction: In the last exmaple, I used a wrong half-angle formula for \(\sin^22x\). The correct one is \[\sin^22x=\frac{1-\cos 4x}{2}\] Consequently, the final answer should be corrected to \[\frac{1}{16}\left(x-\frac{1}{4}\sin 4x+\frac{1}{3}\sin^32x\right)+C\] Trigonometric Integrals 2 Trigonometric Integrals 3 |
Homework 10 (Trigonometric integrals) | 3/29 Good Friday. | |||
| Trigonometric Substitutions | Trigonometric Substitution Trigonometric Substitution 2 |
Homework 11 (Trigonometric substitution) | 4/4: Last Day to Withdraw from the University and Receive a Grade of W (Request to withdraw should be submitted in SOAR by 5:00 pm.). | |||
| Partial Fractions | Partial Fractions Partial Fractions 2 Partial Fractions 3 |
Homework 12 (Partial fractions) | ||||
| Improper Integrals | Improper Integrals
mp4 format Quick Time format |
Homework 13 (Improper integrals) | ||||
| Review for TEST 3 | ||||||
| TEST 3 (Homework 9 - Homework 12) is due on Thursday 5/2. | FINAL EXAM | FINAL EXAM is due on Wednesday 5/8. |