MAT 167 Calculus I
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 are available online as well. The links to my lectures can be found in the weekly course schedule below. It includes mostly the notes of the material that I actually teach in this class. Those who are interested in learning more can find additional notes here.
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 on tackling problems, you will gradually have better understanding of concepts.
Topics
In this course we study Differential Calculus that includes the following 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.
Free Online/On-Campus Tutoring
Free Online/On-Campus Tutoring information for Spring 2024 can be found here.
Weekly Schedule
Functions and Limits, Derivatives, Applications of Differentiation
NA
Online office hours can be arranged on skype or MS Teams by appointment.
Use of a calculator is rarely required for the course. 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.
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.
| Some Important Formulas from College Algebra and Trigonometry for Freshmen Calculus The Limit of a Function: Limits of Functions, Examples of Non-Existing Limits, The Precise Definition of a Limit (Optional, only for those who are interested) Calculating Limits: How to Calculate Limits I (Do not worry about the proofs of \(\displaystyle\lim_{x\to a}x=a\) and \(\displaystyle\lim_{x\to a} c=c\) unless you are interested.) |
Limit of a Function How to Calculate Limits |
Homework 1 (Rules of limits - basic) | ||||
| Calculating Limits How to Calculate Limits II, How to Calculate Limits III Continuity: Continuity |
How to Calculate Limits 2 How to Calculate Limits 3 How to Calculate Limits 4 Continuity Continuity 2 |
Homework 2 (Evaluating limits - factoring) Homework 3 (Evaluating limits - rationalizing & trigonometric) Homework 4 (Continuity - concept of) |
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. | |||
| Limits Involving Infinity Limits involving Infinity and Asymptotes Derivatives and Rates of Change: Derivatives |
Limits involving Infinity and Asymptotes Limits involving Infinity and Asymptotes 2 Limits involving Infinity and Asymptotes 3 Limits involving Infinity and Asymptotes 4 Derivatives Derivatives 2 Derivatives 3 |
Homework 5 (Infinite limits and vertical asymptotes, Limits at Infinity, horizontal & oblique asymptotes) Homework 6 (Definition of the Derivative) |
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| The Derivative as a Function & Basic Differentiation Formulas: Basic Differentiation Formulas, Continuity versus Differentiability |
Basic Differentiation Formulas Continuity versus Differentiability |
Homework 7 (Derivatives of polynomial functions and power functions) | 2/10-2/13: Mardi Gras break | |||
| The Product and Quotient Rules: The Product and Quotient Rules Derivatives of Trigonometric Functions |
The Product and Quotient Rules Derivatives of Trigonometric Functions |
Homework 8 (The Product and Quotient Rules) | ||||
| The Chain Rule & Implicit Differentiation: The Chain Rule, Implicit Differentiation |
The Chain Rule Implicit Differentiation |
Homework 9 (The Chain Rule) | TEST 1 (Homework 1 - Homework 6) is due on Friday 2/23. | |||
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The Chain Rule & Implicit Differentiation (continued): Implicit Differentiation Derivatives of Logarithmic and Exponential Functions |
Implicit Differentiation 2 Derivatives of Logarithmic Functions and Exponential Functions |
Homework 10 (Implicit Differentiation, Logarithmic Differentiation) | ||||
| Related Rates | Related Rates: Example 1 Related Rates: Example 2 Related Rates: Example 3 Related Rates: Example 4 Related Rates: Example 5 |
Homework 11 (Related Rates) | 3/10-3/17: Spring Break | Related Rates | Related Rates: Example 1 Related Rates: Example 2 Related Rates: Example 3 Related Rates: Example 4 Related Rates: Example 5 |
Homework 11 (Related Rates) |
| Linear Approximations and Differentials |
Linear Approximation Linear Approximation 2 Differentials |
Homework 12 (Linear approximation and differentials) | TEST 2 (Homework 7 - Homework 11) is due on Friday 3/22. | |||
| Maximum and Minimum Values & The Mean Value Theorem: Maximum and Minimum Values, The Mean Value Theorem |
Maximum and Minimum Maximum and Minimum 2 Mean Value Theorem Correction: In the lecture, I said \(\frac{f(b)-f(a)}{b-a}\) can be considered as the average of \(f(x)\) on \([a,b]\). That is incorrect. The correct statement is that it can be considered as the average of \(f'(x)\) on \([a,b]\). For details, please refer to my lecture note. |
Homework 13 (Global extrema, Mean value theorem) | 3/29 Good Friday. | |||
| Derivatives and the Shapes of Graphs: The First and Second Derivative Tests |
The First Derivative Test The Second Derivative Test |
Homework 14 (Increasing/decreasing functions and local extrema, Concavity and points of inflection) | 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.). | |||
| Optimization Problems | Optimization Problems Optimization Problems 2 |
Homework 15 (Optimization) | ||||
| Inverse Trigonometric Functions and Their Derivatives | Inverse Trigonometric Functions and Their Derivatives mp4 format Quick Time format |
Homework 16 (Derivatives of inverse trigonometric functions) | ||||
| L'Hôpital's Rule | L'Hôpital's Rule mp4 format Quick Time format |
Homework 18 (Indeterminate Forms and L'Hôpital's Rule) | ||||
| TEST 3 | TEST 3 (Homework 12 - Homework 15) is due on Thursday 5/2. | |||||
| FINAL EXAM | FINAL EXAM is due on Wednesday 5/8. |