This webpage is a repository mirroring OWL for students in section 001 who cannot access it yet.
Feel free to reach me at pudanshi (at) uwo (dot) ca. Prefix the subject of your email by "CALC 1000A: "
I host office hours in my office (MC 275 K) and at the Math-Physics Accelerator Help Centre, room PAB 26, in the Physics and Astronomy Building on
Tuesdays: 08:30 am to 10:30 am in MC 275 K
Wednesdays, Thursdays: 3:30 pm to 4:30 pm in PAB 26, Math-Physics Accelerator Help Centre.
Please email me to schedule an appointment if you cannot attend any office hours.
We meet in MC 110 from 08:30 am to 09:30 am every Monday, Wednesday, Thursday and Friday.
Sept. 5: Introduction and review.
ToDo
Read the course outline and attempt the suggested problems for Section 1.1 and 59-87 (odd) from Section 1.2.
Review Week 1 and trigonometry from C | Review the Pre-Calculus section of your textbook.
WebAssign, Gradescope and iClicker: Please read the course outline first. We will not use WebAssign or Gradescope before the next week and will not use iClicker for grading until the following week. Any other questions should be taken up with our course coordinator, James Uren.
Sept. 9: Sections 1.2.5-1.2.9 and 1.3. For those interested, here's a handout detailing some range computations I skimmed in class.
Sept. 11: Section 1.3 (review) and Section 1.4.1-1.4.4. Here's a handout featuring examples of the transformation sequence of graphs.
Sept. 12: Section 1.4. A handout with some worked-out problems for Sections 1.3, 1.4
Sept. 13: Section 1.5: Logarithms and Exponential functions. **Hyperbolic functions are not covered in this course.**
ToDo
Familiarize yourself with trigonometric identities.
Solve the suggested problems for Sections 1.3, 1.4, 1.5 and Chapter Review.
Review basic laws of exponents, logarithms, and inverse trigonometric functions, paying particular attention to the range and domains.
iClicker: Here's the link for our section.
WebAssign: Please attempt Quiz 0 to get a hang of WebAssign.
Sept. 16: Quiz 1 (Sept. 16, 00:00 hrs till Sept. 22, 23:59 hrs) goes live. We review Chapter 1.
Sept. 18: Section 2.2 and Limit Laws.
Sept. 19: Section 2.3
Sept. 20: Section 2.3 and Squeeze Theorem
ToDo
Using iClicker.
Quiz 1. Due: Sept. 22, 23:59 hrs.
Notice the updated office hours from this week onwards.
Sept. 23: Squeeze Theorem, Continuous Functions and Intermediate Value Theorem (time permitting).
Sept. 25: Problem-solving on discontinuities
Sept. 26: Composite function theorem and the Intermediate Value Theorem
Sept. 27: Horizontal asymptotes reveal the long-term behaviour of a function (compared with derivatives, which reveal instantaneous behaviour). We compute some limits at infinity. Here are the notes for today's lecture.
ToDo
Suggested problems.
Revise the limits at infinity: solve problems.
Sept. 30: No class as we observe the National Day for Truth and Reconciliation.
Oct. 2: Derivative of a function at a point, derivatives as functions, the idea of differentiability, comparison between differentiability and continuity, three examples of continuous functions that are not differentiable (corners, vertical tangents, and others). This covers sections 3.1-3.2 of our text. Here are today's lecture notes.
Oct. 3: We discussed differentiability and the rules of differentiations. I have included explanations for iClicker questions as well as for in-class questions. Here are today's notes.
Oct. 4: We revised some differentiable functions. We looked at different rules that help us compute derivatives for differentiable functions more quickly than the first principles; notably, we looked at the proof of the product rule. I have included the proof for the quotient rule. For those interested I have included a (very short, ~ 4-5 lines) combinatorial proof for the binomial theorem. We also looked at derivatives of trigonometric functions, and higher derivatives, with some examples. Here are today's notes.
ToDo
Revise 3.1 and brush up on high-school derivative formulae.
Solve suggested problems.
This week's goal is to master the chain rule. This rule will help us compute the derivatives of inverses and implicit differentiation, effectively wrapping up derivatives.
Oct. 7: Today, we had a gentle introduction to the chain rule. Keep practicing exercises below Section 3.6 till you master the technique. Here are today's notes.
Oct. 9: We wrapped up the chain rule with some computations. Notes for today's lecture.
Oct. 10: Today, we started working on the inverse function theorem. Please go over the notes and reach out if you have questions. I have also included some solved examples and some fun exercises.
Oct. 11: We looked at the derivatives of inverse trigonometric functions today. Notice how derivatives of inverse trigonometric functions are not trigonometric/inverse trigonometric functions but are algebraic.
ToDo
Start revising for midterm.
Go over the textbook sections covered so far, and reach out if you have any difficulties.
We will cover implicit differentiation from Oct. 21 onwards.
Reading week.
We wrap up chapter 3 this week.
Oct. 21: We introduced implicit differentiation. Here are the notes for today's lecture.
Oct. 22: We solved some problems regarding implicit differentiation. The notes will contain some more solved problems to cement the understanding.
Oct. 23: We look at logarithmic differentiation through the lens of implicit differentiation. Here are today's notes.
Oct. 25: We practice some more logarithmic differentiation problems. Here are the notes.
ToDo
Go over implicit differentiation.
Try to use logarithmic differentiation whenever you feel it might ease your computations, for instance, whenever possible to simplify the product or quotient.
This week, we start applying the concepts we have learned to physical phenomena. This marks the start of Chapter 4.
Oct. 28: We introduce related rates. The only way to master related rates is through practice, lots of it. Solve problems from Section 4.1 of your text. Here are today's notes.
Oct. 30: We solve some problems from 4.1 to understand better how to mathematically model a physical phenomenon and reinterpret the mathematical results in real-life terms. Here are today's notes.
Oct. 31: No new material today. Midterm review and doubt-clearing session.
Nov. 1: We discuss the extrema of a function. Using examples, we examine the distinction between absolute, local and endpoint extrema. Here are today's notes. (had a small typo in the definition of local extrema)
ToDo
Practice what you have learnt so far. Meet me during office hours to clear any doubts.
Midterm on Nov. 1 from 7 pm to 9 pm.
This week focuses on understanding the extreme values of functions and applying the techniques learnt to optimization problems arising in real-life scenarios. Time permitting, we might be able to discuss L'Hôpital's rules and indeterminate forms as well.
Nov. 4: Revise absolute extrema, local extrema and endpoint extrema prior to the lecture. Today we talked about local extrema, critical points and Fermat's theorem. Here are the notes.
Nov. 6: Revise the notion of critical points. We will talk about derivatives and how they influence the shape of a graph, along with derivative tests.
Nov. 7:
Nov. 8:
ToDo
Visit me during office hours to discuss any doubts regarding the critical points, the distinction between absolute, local and endpoint extrema.