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Calculus 1(A)
University of Toronto St. George
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PROFESSORS

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TBA

Mihai Nica

Melissa Lee Emory

Dimitri Chouchkov

Mayes-Tang S.

Richards L.

LeBlanc E.

Zerouali A.

Thaddeus Janisse

C Su

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Class Notes

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MAT135H1 Lecture Notes - Lecture 1: Inverse Function

Read sections 1. 1 -1. 5, appendix d from the textbook. An assignment that assigns a real number, and another real number, f ( ) Therefore, we input a

MAT135H1 Lecture Notes - Lecture 2: Quotient Rule, Power Rule, Product Rule

Mat135 - lecture 2 - exponentials and logarithms. Read sections 1. 1 -1. 5, appendix d from the textbook. Exponential functions follow the form f ( ) =

MAT135H1 Lecture Notes - Lecture 3: Pythagorean Theorem

Read sections 1. 1 -1. 5, appendix d from the textbook. Let ( , ) be a point on the circle of radius r associated with angle . All angles will be in ra

MAT135H1 Lecture Notes - Fall 2018 Lecture 4 - The Tangent, The Tangent, Drag (physics)

Mat135 - lecture 4 - the tangent and velocity. Read sections 2. 1 -2. 3 from the textbook. The objective is finding the v (instantaneous) Assume that t

MAT135H1 Lecture Notes - Fall 2018 Lecture 5 - ǀXam language, ǀXam language

Mat135 - lecture 5 - the limit of a function. Q: using the above graph of f , find the following limits, if they exist lim x 1 lim x 2 lim x 4 lim x 5

MAT135H1 Lecture 6: MAT135 - Lecture 6 - Calculating Limits using Limit Laws

Mat135 - lecture 6 - calculating limits using limit laws. Assume lim x a lim x a f ( ) , c = c lim x a g ( ) exist. 1 be a positive integer and c . G (

MAT135H1 Lecture Notes - Lecture 7: Intermediate Value Theorem, Trigonometric Functions, Asymptote

Mat135 - lecture 7 - infinite limits and continuity. Read sections 2. 5 -2. 6 from the textbook. If f ( ) > 0 near (but not equal to) a , f ( ) grows a

MAT135H1 Lecture 8: MAT135H1 - Lecture 8 - Limits and Rate of change (2)

MAT135H1 Lecture Notes - Lecture 8: Asymptote, Coefficient

Read sections 2. 5 -2. 6 from the textbook. Instead of considering the limits where f ( ) limits where (end behaviour of f ( )) , we now focus on looki

MAT135H1 Lecture 8: MAT135H1 - Lecture 8 - Limits and Rate of change (1)

MAT135H1 Lecture 9: MAT135H1 - Lecture 9 - One-sided limits and limits at infinity (2)

MAT135H1 Lecture 9: MAT135H1 - Lecture 9 - One-sided limits and limits at infinity (1)

MAT135H1 Lecture Notes - Lecture 9: Difference Quotient

Mat135 - lecture 9 - derivatives and rates of change. Read sections 2. 7 -2. 8 from the textbook. For = f (), the slope of the tangent line at ( a , f

MAT135H1 Lecture Notes - Lecture 10: Difference Quotient

Mat135 - lecture 10 - the derivative as a function. Read sections 2. 7 -2. 8 from the textbook. F "() = lim h 0 f (+ h ) - f () / h. If f "() exists, w

MAT135H1 Lecture Notes - Lecture 11: Power Rule, Natural Number

MAT135H1 Lecture Notes - Lecture 12: Quotient Rule, Product Rule

Mat135 - lecture 12 - product and quotient rules. Read sections 3. 1 -3. 3 from the textbook. If f and g are differentiable at then d dx ( f ( ) G ( ))

MAT135H1 Lecture Notes - Lecture 13: Quotient Rule, List Of Trigonometric Identities

Mat135 - lecture 13 - derivatives of trigonometric functions. Read sections 3. 1 -3. 3 from the textbook. 0 sin / = 1 ( cos - 1 / ) = 0. Calculate lim

MAT135H1 Lecture 15: MAT135 - Lecture 14 - Chain Rule

Read sections 3. 4, 3. 5, and 1. 5 from the textbook. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u

MAT135H1 Lecture 16: MAT135 - Lecture 16 - Chain Rule Part Two

Mat135 - lecture 16 - chain rule part two. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u ) is differ

MAT135H1 Lecture 17: MAT135 - Lecture 17 - Chain Rule Part Three

Mat135 - lecture 17 - chain rule part three. Suppose g is differentiable at and f is differentiable at g ( ). In leibniz notation, if = f ( u ) is diff

MAT135H1 Lecture Notes - Lecture 18: Implicit Function, Unit Circle

Read sections 3. 5 and 1. 5 from the textbook. So far, we"ve considered tangent lines of graphs and curves of a particular form: In the above, is expli

MAT135H1 Lecture Notes - Lecture 19: Minute And Second Of Arc, Inverse Trigonometric Functions

Mat135 - lecture 19 - inverse trigonometric functions. Read sections 3. 5 and 1. 5 from the textbook. Recall that a function f has an inverse if and on

MAT135H1 Lecture Notes - Lecture 20: Implicit Function

Mat135 - lecture 20 - derivatives of logarithmic functions. Read sections 3. 6 and 3. 7 from the textbook. Recall that d dx e = e . Using implicit diff

MAT135H1 Lecture Notes - Lecture 21: Logarithmic Differentiation

Mat135 - lecture 20 - derivatives of logarithmic functions. Read sections 3. 6 and 3. 7 from the textbook. As you can see, it is very messy. You need l

MAT135H1 Lecture Notes - Lecture 22: Marginal Cost

Mat135 - lecture 22 - rates of change. Read sections 3. 6 and 3. 7 from the textbook. Recall the idea of interpreting derivatives as rates of change. L

MAT135H1 Lecture 23: MAT135 - Lecture 23 - Exponential Growth and Decay

MAT135H1 Lecture Notes - Lecture 24: Implicit Function, Pythagorean Theorem

MAT135H1 Lecture Notes - Lecture 25: Implicit Function, Searchlight, Pythagorean Theorem

Mat135 - lecture 25 - related rates part two. Read sections 3. 8 and 3. 9 from the textbook. The main steps to most related rates problems: Differentia

MAT135H1 Lecture Notes - Lecture 29: Maxima And Minima, Minimax, Cubic Function

Mat135 - lecture 29 - maximum and minimum values. We will begin to address it in this lecture and finish it next class. Given a function f on a domain

MAT135H1 Lecture Notes - Lecture 30: Mean Value Theorem, Constant Function

MAT135H1 Lecture 31: MAT135 - Lecture 31 - Intervals of Increase & Decrease

MAT135H1 Lecture Notes - Lecture 32: Maxima And Minima

MAT135H1 Lecture Notes - Lecture 33: Inflection Point, Inflection

MAT135H1 Lecture Notes - Lecture 34: Minimax, Maxima And Minima

Mat135 - lecture 34 - identifying local extrema. However, if f "( c ) = 0 and f ( c ) = 0 then we know need to assume the following case: C could be a

MAT135H1 Lecture 35: MAT135 - Lecture 35 - Indeterminate Forms and L'Hopital's Rule

MAT135H1 Lecture Notes - Lecture 36: Asymptote

MAT135H1 Lecture Notes - Lecture 37: Asymptote, Even And Odd Functions, Inflection

MAT135H1 Lecture 38: MAT135 - Lecture 38 - Optimization

MAT135H1 Lecture Notes - Lecture 39: Antiderivative