Calculus - All Sections (WI25)
MATH 3 CALCULUS
Course Info:
- Lectures: Monday, Wednesday, Friday
Section 1: block 11 (11:30 am - 12:35 pm ET)
Section 2: block 12 (12:50 pm - 1:55 pm ET)
Section 3: block 10 (10:10 am - 11:15 am ET)
Section 4: block 2 (2:10 pm - 3:15 pm ET) - X-period: Recitation
Section 1: Tuesday (12:15 pm - 1:05 pm ET)
Section 2: Tuesday (1:20 pm - 2:10 pm ET)
Section 3: Thursday (12:15 pm - 1:05 pm ET)
Section 4: Thursday (1:20 pm - 2:10 pm ET) - Room: Kemeny 006
- Instructor Information:
Instructor Section Office E-mail Office Hours Alena Erchenko 1 and 2 Kemeny 331 alena.erchenko@dartmouth.edu Mon 2 - 3 pm,
Tue 9 - 10 am,
by appointmentLuke Askew 3 Kemeny 243 luke.a.askew.gr@dartmouth.edu Mon 11:15 - 12:15
Tu 11am - 12pm
by appointment
Ahmad Reza Haj Saeedi Sadegh 4 Kemeny 310 ahmadreza.hajsaeedisadegh@dartmouth.edu Mon 10-11 am,
Tue 10-11 am,
by appointment
- TA for X-hours for all sections:
Alejandro Basilio Galvan Perez-Ilzarbe
Office: Kemeny 222
E-mail: alejandro.b.galvan.gr@dartmouth.edu
Office Hours: Wednesday 9-10am in Kemeny 229 or by appointment. - Recommended Texts: Strang, Gilbert ; Herman, Ed "Jed", OpenStax, Volume 1 and Volume 2.
- Tutorials: Tuesday 7-9:30pm and Thursday 7-9pm in Kemeny 008.
- Peer Tutorials: Register here on Group Tutoring site!
Julia’s Peer Tutoring sessions are as follows:
- Mondays, 9:00-10:00pm in Dartmouth Hall 001
- Wednesdays, 8:00-9:00pm in Silsby 213
- Sunday DROP-INs from 4:00-5:00pm in Dartmouth Hall 001
Schuni’s FGO Tutoring sessions will run:
- Mondays, 8:00-9:00pm in Berry 178B (in the Academic Skills Center)
- Wednesdays, 7:00-8:00pm in Berry 178B
- Thursdays, 7:00-8:00pm in Berry 178B
- DEE (Dartmouth Emerging Engineers) Tutorials:
Sundays, Mondays, Tuesdays, Wednesdays, Thursdays
Drop-in between 7-10 pm in ECSC B05 (underneath the stairs)
- Grading: Grades will be based on weekly homework (20%), weekly quizzes (25%), midterm (25%) and final (30%). Your lowest homework and quiz scores will be dropped.
Homework:
Homework is due on Gradescope on the day indicated below before 4 pm ET. Late submissions will not be accepted. Please upload your solutions by following the instructions in this video. Feel free to submit handwritten or work typeset in LaTeX (Overleaf is a great resource and tool for the latter). If you are skipping a problem, it is easier for the grader if you write "Skip" and upload that as your solution to the problem. You are more than welcome to work with others on the homework problems. However, the solutions should be written up on your own and reflect your understanding.
Due Date | Homework | Solution |
1/8 | Homework 0 | N/A |
1/15 | Homework 1 | Solution |
1/22 | Homework 2 | Solution |
1/29 | Homework 3 | Solution |
2/12 | Homework 4 | Solution |
2/19 | Homework 5 |
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2/26 | Homework 6 | Solution |
3/5 | Homework 7 | Solution |
Quizzes:
There will be weekly in-class quizzes on Fridays for 15-20 mins at the beginning of the class. The quizzes will be covering the material of the week before.
Date | Practice Quiz | Quiz | Solution |
1/17 | Practice Quiz 1 - Solution | Quiz 1 Section 1 Quiz 1 Section 2 Quiz 1 Section 3 Quiz 1 Section 4 |
Solution (Section 1)
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1/24 | Practice Quiz 2 - Solution | Quiz 2 Section 1 Quiz 2 Section 2 Quiz 2 Section 3 Quiz 2 Section 4 |
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1/31 | Practice Quiz 3 - Solution | Quiz 3 Section 1 Quiz 3 Section 2 Quiz 3 Section 3 Quiz 3 Section 4 |
Solution (Section 1) |
2/14 | Practice Quiz 4 - Solution | Quiz 4 Section 1 Quiz 4 Section 2 Quiz 4 Section 3 Quiz 4 Section 4 |
Solution (Section 1) Solution (Section 2) Solution (Section 4) |
2/21 | Practice Quiz 5 - Solution | Quiz 5 Section 1 Quiz 5 Section 2 Quiz 5 Section 3 Quiz 5 Section 4 |
Solution (Section 1) |
2/28 | Practice Quiz 6 - Solution | Quiz 6 Section 1 Quiz 6 Section 2 Quiz 6 Section 3 Quiz 6 Section 4 |
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3/7 | Practice Quiz 7 - Solution | Quiz 7 Section 1 Quiz 7 Section 2 Quiz 7 Section 3 Quiz 7 Section 4 |
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Schedule:
The specific topics covered in each class are tentative and will be updated as the term progresses. Moreover, the notes posted for each lecture may contain slightly more content than the lecture and may bleed a bit into the next lecture. Let me know if you find any errors.
Week | Date | Topic | OpenStax references | Activity | Lecture Notes |
Week 1
(January 6-10) |
Monday | Review of functions: functions as models, domain, range, increasing/decreasing functions, bounded functions, even/odd | Chapter 1, Sections 1.1 | Lecture 1 (Sections 1 and 2) | |
Wednesday | Periodic, composition. Polynomial functions | Chapter 1, Sections 1.1-1.2 | Homework 0 due | Lecture 2 (Sections 1 and 2) | |
Friday |
Power, exponential, and trigonometric functions and inverses
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Chapter 1, Sections 1.3-1.5 |
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X-hour (Tuesday/Thursday) | Recitation | Worksheet_1 - Solutions | |||
Week 2
(January 13-17) |
Monday |
Limits and limit laws - idea and ways to find.
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Chapter 2, Sections 2.2-2.3
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Wednesday |
Limits (continue).
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Chapter 2, Section 2.4 |
Homework 1 due |
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Friday | Tangent lines and velocity. Rates of Change. The derivative as a function. | Chapter 3, Sections 3.1-3.2, 3.4 | 15-mins quiz 1 on Week 1 material |
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X-hour (Tuesday/Thursday) |
Recitation |
Worksheet_2 - Solutions | |||
Week 3
(January 20-24) |
Monday |
NO CLASS. |
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Wednesday |
Differentiation rules: product, quotient, and chain rules |
Chapter 3, Sections 3.3 and 3.6 |
Homework 2 due |
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Friday | Derivatives of power, exponential, and trigonometric functions | Chapter 3, Sections 3.5, 3.9 | 15-mins quiz 2 on Week 2 material |
Lecture 8 (Sections 1 and 2) | |
X-hour (Tuesday/Thursday) | Recitation | Worksheet_3 - Solutions | |||
Week 4
(January 27-31) |
Monday | Implicit differentiation and inverses | Chapter 3, Sections 3.7-3.8 | Lecture 9 (Section 1 and 2) | |
Wednesday | Related rates and linear approximation | Chapter 4, Sections 4.1-4.2 | Homework 3 due | Lecture 10 (Section 1 and 2) | |
Friday | Review | 15-mins quiz 4 on Week 3 material |
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X-hour (Tuesday/Thursday) | Recitation | Worksheet_4 - Solutions | |||
Week 5
(February 3-7) |
Monday | Finding extremes : maximums and minimums | Chapter 4, Section 4.3 | Evening Midterm Exam on Weeks 1-4 material (6:30pm-8:30pm in Kemeny 008) | Lecture 11 (Section 1 and 2) |
Wednesday | Mean value theorem and L'Hopitals rule | Chapter 4, Sections 4.4 and 4.8 |
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Friday | The derivative and the shape of graphs. | Chapter 4, Section 4.5 | Lecture 13 (Section 1 and 2) | ||
X-hour (Tuesday/Thursday) | Recitation | Worksheet_5 - Solutions | |||
Week 6
(February 10-14) |
Monday | Curve sketching. | Chapter 4, Section 4.5-4.6 | Lecture 14 (Section 1 and 2) | |
Wednesday | Optimization. | Chapter 4, Section 4.7 |
Homework 4 due | Lecture 15 (Section 1 and 2) | |
Friday | Antiderivatives. | Chapter 4, Section 4.10 |
15-mins quiz 4 on Week 5 material |
Lecture 16 (Section 1 and 2) | |
X-hour (Tuesday/Thursday) | Recitation | Worksheet_6 - Solutions | |||
Week 7
(February 17-21) |
Monday | Areas and distances |
Chapter 5, Section 5.1 | Lecture 17 (Section 1 and 2) | |
Wednesday | The definite integral | Chapter 5, Section 5.2 | Homework 5 due | Lecture 18 (Section 1 and 2) | |
Friday | Fundamental theorem of Calculus | Chapter 5, Section 5.3 | 15-mins quiz 5 on Week 6 material |
Lecture 19 (Section 1 and 2) | |
X-hour (Tuesday/Thursday) | Recitation | Worksheet 7 - Solutions | |||
Week 8
(February 24-28) |
Monday | Integration formulas and the net change theorem | Chapter 5, Section 5.4 | Lecture 20 (Section 1 and 2) | |
Wednesday | Integration by substitution | Chapter 5, Section 5.5 | Homework 6 due | Lecture 21 (Section 1 and 2) | |
Friday | Integration by parts | OpenStax Volume 2, Chapter 3, Section 3.1 | 15-mins quiz 6 on Week 7 material |
Lecture 22 (Section 1 and 2) | |
X-hour (Tuesday/Thursday) | Recitation | Worksheet 8 - Solutions | |||
Week 9
(March 3-7) |
Monday | Areas between curves. Volumes | Chapter 6, Sections 6.1-6.3 | Lecture 23 (Section 1 and 2) | |
Wednesday | Physical applications. Moments and center of mass. Exponential Growth and Decay. | Chapter 6, Section 6.5-6.6, Chapter 6, Section 6.8 | Homework 7 due | Lecture 24 (Section 1 and 2) | |
Friday | Review | 15-mins quiz 7 on Week 8 material |
Lecture 25 (Section 1 and 2) | ||
X-hour (Tuesday/Thursday) | Recitation | Worksheet 9 - Solutions | |||
Final Exam (March 11) | Tuesday - 8-11am | Final Exam covers Week 1-9 material |
Course Catalogue Description:
This course is an introduction to single variable calculus aimed at students who have seen some calculus before, either before matriculation or in MATH 1. MATH 3 begins by revisiting the core topics in MATH 1 - convergence, limits, and derivatives - in greater depth before moving to applications of differentiation such as related rates, finding extreme values, and optimization. The course then turns to integration theory, introducing the integral via Riemann sums, the fundamental theorem of calculus, and basic techniques of integration.
Learning Outcomes:
By the end of this course, you should be able to:
1. Describe what continuity of a function is using graphic, numerical, and algebraic tools.
2. Understand what derivatives and integrals represent.
3. Differentiate and integrate functions of single variable.
4. Sketch a graph of a function by analyzing its properties.
5. Set up mathematical statements from the word problems and given data.
6. Develop a sense how mathematics can be used in various fields.
Additional Pages:
- Academic Honor Principle
- Expectations
- Student Accessibility Needs
- Mental Health
- Title IX
- Religious Observances
- Additional Support for your Learning
- Guidelines on using Generative Artificial Intelligence (GenAI) for Coursework
Additional Resources:
- Interactive book Ximera
- YouTube Channel by Grant Sanderson: 3Blue1Brown, The essense of Calculus
- It is highly recommended to solve as many exercises from the textbook or other resources as you have time for. This will be more useful than rereading your class notes or textbook as it will often force you to go back to look at the material anyway. The only way to truly learn mathematics is through practice. Feel free to ask your instructor about your solutions.
- There are many other textbooks and online materials that you can consult. If you have questions on whether a particular one might be useful, do not hesitate to reach out.