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 appointment

    Luke 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

 

Solution

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)

Solution (Section 2)

 

Solution (Section 4)

1/24 Practice Quiz 2 - Solution Quiz 2 Section 1
Quiz 2 Section 2
Quiz 2 Section 3
Quiz 2 Section 4

Solution (Section 1)

Solution (Section 2)

Solution (Section 3)

Solution (Section 4)

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)
Solution (Section 2)
Solution (Section 3)
Solution (Section 4)

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)
Solution (Section 2)
Solution (Section 3)
Solution (Section 4)

2/28 Practice Quiz 6 - Solution Quiz 6 Section 1
Quiz 6 Section 2
Quiz 6 Section 3
Quiz 6 Section 4

 

Solution (Section 1)
Solution (Section 2)

3/7 Practice Quiz 7 - Solution Quiz 7 Section 1
Quiz 7 Section 2
Quiz 7 Section 3
Quiz 7 Section 4

 

Solution (Section 1)
Solution (Section 2)

 

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

 

Chapter 1, Sections 1.3-1.5

 

Lecture 3 (Sections 1 and 2)

X-hour (Tuesday/Thursday) Recitation Worksheet_1 - Solutions
Week 2
(January
13-17)
Monday

Limits and limit laws - idea and ways to find.

 

 

Chapter 2, Sections 2.2-2.3

 

 

Lecture 4 (Sections 1 and 2)

Wednesday

Limits (continue).
Continuity

 

 

Chapter 2, Section 2.4

Homework 1 due

 

Lecture 5 (Sections 1 and 2)

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

 

Lecture 6 (Sections 1 and 2)

X-hour (Tuesday/Thursday)

Recitation

Worksheet_2 - Solutions
Week 3
(January
20-24)
Monday

 

NO CLASS. 
Martin Luther King Jr. Day

 

 

Wednesday

 

Differentiation rules: product, quotient, and chain rules

 

Chapter 3, Sections 3.3 and 3.6

Homework 2 due

 

Lecture 7 (Sections 1 and 2)

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
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

 

Lecture 12 (Section 1 and 2)

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:

  1. Academic Honor Principle
  2. Expectations
  3. Student Accessibility Needs
  4. Mental Health
  5. Title IX
  6. Religious Observances
  7. Additional Support for your Learning
  8. 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.