Sept. 6 - 10

* Course Introduction (slides)

* section 1.1: definition of a function, domain + range (inequalities and interval notation), graphs, VLT, piecewise functions (ex. absolute value), symmetry (skip for now), increasing/decreasing functions

* section 1.2: calalog of essential functions (important properties + shapes of graphs)

* Familiarize yourself with the course website, record test dates, print lecture notes for this week.

* Review your lecture notes from Week 1 thoroughly (see Note 1 below). If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 1.1: # 3, 7, 9, 11, 13, 15, 17, 19, 29, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63. (See Note 2 below); section 1.2: # 1, 3, 5, 7, 9, 11.

* Work on Assignment 1 in Childsmath. (See Note 3 below). Assignment 1 will be due on Tuesday September 14, 2021, 11:59pm. Start Assignment 2 in Childsmath.

** Note 1: Before beginning homework and/or assignments, I highly recommend reviewing your lecture notes and studying the examples we did during lecture. Try to talk yourself through the lecture notes and explain the concepts in your own words (imagine that you are teaching it to someone else). Then, redo some of the examples on scrap paper and see how well you do by yourself. This might take 2+ hours to really go through the lecture notes in detail. Once you've done that, then you should be ready to work on the assignments and textbook exercises on your own (and if you've studied your notes well, you'll move quickly through these!).

** Note 2: Working on practice problems regularly (ideally after each lecture) is essential to developing skills and confidence in mathematics. While you may feel that you understand just by watching me solve a few problems during lecture (and that's great!), you'll need a deeper level of understanding and sufficient practice with a wide variety of problems to solve questions independently on a test or exam. These practice problems are not to be handed in for credit.

** Note 3: Childsmath is an online assessment system which was developed by Dr. Aaron Childs in our department. In Math 1F03, we will use this system for our assignments, tests, and final exam. You can practice entering answers symbolically by accessing the SystemTutorial, under the Open Resources heading. (This is also available under our course as Assignment 0.) Collectively, these assignments will be worth 15% of your final grade.

* section 1.3: transformations of functions, combinations of functions

* section 1.4: exponential functions: definition, domain + range, graphs, important properties, laws of exponents, transformations of graphs, solving exponential equations

* section 1.5: inverse functions: one-to-one functions, HLT, definition + properties of an inverse function, cancellations equations, finding the inverse of a function, graphing f-inverse from the graph of f; logarithmic functions (definition, domain + range, graphs, cancellation equations, laws of logs, transformations of graphs, solving logarithmic equations), skip inverse trig functions

* Review your lecture notes from Week 2 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 1.3: #1, 3, 5, 9-25 odd, 33, 37, 39, 55, 57; section 1.4: # 1, 3, 5 (desmos), 7 (desmos), 9-13, 15, 17; section 1.5: # 1-19 odd, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 53, 55, 57, 59, 61, 63, 67.

* Work on Assignment 2 in Childsmath. Assignment 2 will be due on Tuesday September 21, 2021, 11:59pm. Start Assignment 3 in Childsmath.

* section 1.4: exponential functions: definition, domain + range, graphs, important properties, laws of exponents, transformations of graphs, solving exponential equations

* section 1.5: inverse functions: one-to-one functions, HLT, definition + properties of an inverse function, cancellations equations, finding the inverse of a function, graphing f-inverse from the graph of f; logarithmic functions (definition, domain + range, graphs, cancellation equations, laws of logs, transformations of graphs, solving logarithmic equations), skip inverse trig functions

* section 2.2: limit of a function: definition (difference between value of a function AT some x-value and value of a function NEAR some x-value), one-sided limits, determining limits from the graph of a function, estimating limits using a table of values, infinite limits + vertical asymptotes

* Review your lecture notes from Week 3 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 1.4: # 1, 3, 5 (desmos), 7 (desmos), 9-13, 15, 17; section 1.5: # 1-19 odd, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 53, 55, 57, 59, 61, 63, 67; section 2.2: # 1-11 odd, 15, 17, 19, 29-37 odd, 41.

* Finish Assignment 2 in Childsmath. Assignment 2 will be due on Friday, September 24, 2021, 11:59pm. Work on Assignment 3 in Childsmath.

* section 2.2: limit of a function: definition (difference between value of a function AT some x-value and value of a function NEAR some x-value), one-sided limits, determining limits from the graph of a function, estimating limits using a table of values, infinite limits + vertical asymptotes

* section 2.3: limit laws: in evaluating limits algebraically (lots of computations in this section), we use limit laws, the direct substitution property, and the fact that we can replace a function f(x) with its simplified version g(x) and use g(x) to compute the limit (when this limit exists)

* section 2.5: continuity: definitions (continuity at a point, discontinuities (removable, infinite, jump), continuity on an interval), functions that are continuous on their domains, combinations + compositions of continuous functions

* Review your lecture notes from Week 4 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 2.2: # 1-11 odd, 15, 17, 19, 29-37 odd, 41; section 2.3: #1, 7, 11, 13, 15, 17, 21, 23, 25, 27, 29, 45, 51; section 2.5: # 1, 3, 5, 7, 19, 21, 23, 25 (for part b, create a piecewise formula like you see in question 24), 27, 29, 31, 35, 37, 41.

* Finish Assignment 3 in Childsmath. Assignment 3 will be due on Friday, October 1, 2021, 11:59pm. Work on Assignment 4 in Childsmath.

* section 2.6: limits at infinity; horizontal asymptotes: definition of a limit "at" infinity, definition of a HA, calculating limits at infinity (simplifying tricks), infinite limits at infinity (looking at the "end behaviour" of functions)

* section 2.1 + 2.7: rates of change, the derivative: define the slope of a tangent line to a curve as the limit of slopes of secant lines, average rate of change = slope of a secant line, instantaneous rate of change = slope of a tangent line = derivative

* section 2.8: the derivative as a function: define the derivative function f'(x), calculate f'(x) using the definition, graph f'(x) by analyzing the graph of f(x), determine when a function f(x) is not differentiable at a number a

* Review your lecture notes from Week 5 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 2.6: #1, 3, 5, 7, 15, 17, 19, 21, 23, 25, 27, 29, 33, 47, 49, 51; section 2.7: # 1, 3, 5, 7, 17, 19, 21, 23, 27, 29, 33, 43, 45; section 2.8: # 1, 3, 5, 7, 9, 11, 21, 23, 27, 29, 31, 41, 43, 59.

* Finish Assignment 4 in Childsmath. Assignment 4 is due on Friday, October 8, 2021, 11:59pm. Work on Assignment 5 in Childsmath.

Test 1: October 19th

* section 2.1 + 2.7: rates of change, the derivative: define the slope of a tangent line to a curve as the limit of slopes of secant lines, average rate of change = slope of a secant line, instantaneous rate of change = slope of a tangent line = derivative

* section 2.8: the derivative as a function: define the derivative function f'(x), calculate f'(x) using the definition, graph f'(x) by analyzing the graph of f(x), determine when a function f(x) is not differentiable at a number a

* Review your lecture notes from Week 6 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 2.7: # 1, 3, 5, 7, 17, 19, 21, 23, 27, 29, 33, 43, 45; section 2.8: # 1, 3, 5, 7, 9, 11, 21, 23, 27, 29, 31, 41, 43, 59.

* Finish Assignment 5 in Childsmath. Assignment 5 is due on Friday, October 29, 2021, 11:59pm. Start Assignment 6 in Childsmath.

* section 3.1: derivatives of polynomials and exponential functions: learn rules which allow us to quickly calculate the derivatives of these functions... all rules are proved using the definition of the derivative (from section 2.8) so it is very important that you use this original definition whenever a question states that you calculate the derivative "from first principles" or "using the definition".... if it does NOT state this, then you may use the short cuts.

*section 3.2: the product and quotient rules: how to differentiate f(x)g(x) and f(x)/g(x) (two formulas you will need to memorize)

* section 3.3: derivatives of trigonometric functions: how to differentiate sinx, cosx, tanx... how to differentiate the reciprocal trig functions

* Review your lecture notes from Week 7 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 3.1: # 3-33 odd, 37, 38, 39, 59, 61, 75, 77; section 3.2: # 3-27 odd, 35, 45, 47, 49, 51; section 3.3: # 1, 5, 7, 11, 13, 15, 19, 21, 23, 27, 29, 39.

* Finish Assignment 6 in Childsmath. Assignment 6 is due on Friday, November 5, 2021, 11:59pm. Start Assignment 7 in Childsmath.

* section 3.4: the chain rule: how to differentiate a composition of functions f(g(x))... plan to spend extra time studying this section... it is the hardest of all of the rules and appears in most questions!

* section 3.6: derivatives of logarithmic functions: how to differentiate y=log_a x and y=lnx and how to combine these new rules with our old ones (chain rule, product rule, etc.)

* section 4.1: maximum and minimum values: define local and global extreme values of a function, define and find critical numbers of a function, fermat's theorem, EVT, find absolute max/min on a closed interval

* Review your lecture notes from Week 8 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 3.4: #1-29 odd, 39, 41, 57, 59, 65, 67, 69, 71, 73; section 3.6: # 3 - 13 odd, 23, 25, 27, 33, 35, 37, 39; section 4.1: # 1-43 odd, 47, 51, 53, 57, 59.

* Finish Assignment 7 in Childsmath. Assignment 7 is due on Friday, November 12, 2021, 11:59pm. Start Assignment 8 in Childsmath.

* section 4.3: how derivatives affect the shape of a graph: f' tells us where f is increasing and decreasing, the first derivative test can classify critical points as local maxima, minima, or neither, the second derivative test can also do this, when it applies... the second derivative is also used to tell us the concavity of f and where it has inflection points (if any), we can use this information to start sketching graphs of complicated functions

* section 4.5: curve sketching: using the tools of calculus, we can gather all the important information about a function and sketch a graph that displays the most important features of the function... we focus on sketching polynomial and rational functions

* Review your lecture notes from Week 9 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 4.3: #1, 5, 6, 7, 8, 9, 11, 13, 17, 21, 23, 25, 27, 29, 31, 33, [37, 39, 41 - you have a question on test 2 similar in style to these!], 45, 47, 55, 59; section 4.5: # 1-19 odd.

* Finish Assignment 7 in Childsmath. Assignment 7 is due on Friday, November 12, 2021, 11:59pm. Work on Assignment 8 in Childsmath. Start Assignment 9 in Childsmath.

* section 4.5: curve sketching: using the tools of calculus, we can gather all the important information about a function and sketch a graph that displays the most important features of the function... we focus on sketching polynomial and rational functions

* section 12.2: vectors: definition of vector quantities and some examples + terminology. geometric and algebraic representations of vectors, combinations of vectors (add, subtract, multiply by a number), calculating magnitudes of vectors, finding and drawing vectors in 2D and 3D, basis vectors, unit vectors, properties of vectors

* Review your lecture notes from Week 10 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 4.5: # 1-19 odd; section 12.2: #1-25 odd.

* Finish Assignment 8 in Childsmath. Assignment 8 is due on Friday, November 19, 2021, 11:59pm. Work on Assignment 9 in Childsmath.

Test 2: November 23rd

* section 12.3: the dot product: a special type of multiplication defined between two vectors that results in a number... this number can be used to determine the angle between two vectors

* section 12.4: the cross product: another special type of multiplication between two vectors that results in a third vector perpendicular to the other two

* Review your lecture notes from Week 11 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 12.3: #1-25 odd; section 12.4: #1-7 odd, 13, 14, 15, 16, 17, 19, 27, 28.

* Finish Assignment 9 in Childsmath. Work on Assignment 10 in Childsmath.

* section 12.5: equations of lines and planes: find vector, parametric, and symmetric equations of lines... determine the scalar equation of a plane

* Finishing course material; Review

* Review your lecture notes from Week 12 thoroughly. If you need more explanation on a particular topic, please refer to the appropriate sections in your textbook.

* Work on suggested practice problems from the textbook: section 12.5: # 3-15 odd, 23-35 odd.

* Finish Assignment 9 in Childsmath. Assignment 9 is due on Friday, December 3, 2021, 11:59pm. Work on Assignment 10 in Childsmath.

* Finishing course material; Review

Last Day of Classes: Wednesday, December 8th