What is calculus and why do you care?
1.1-1.6, Appendix A, B, C Review of precalculus:
functions, polynomials, rational functions, absolute value, trigonometry, exponentials, inverse functions, logarithms.
|HW1 on WebAssign, Due Wed. 1/31 at 9am.
Here is a collection of sample precalculus questions you should be able to do, courtesy Andrew Klampert. (Not to hand in-- here are the solutions).
If you need more review of trigonometry, you might find these chapters from David Kahn's Trig book helpful.
|Here is a single precalculus review lecture
If you need more detail on anything, there are lots of videos from MAT123 to help review precalculus topics.
|1/29||2.1 The tangent and velocity problems
2.2 The limit of a function
2.3 Calculating Limits
|HW2 on WebAssign, Due Wed. 2/7 at 9am.
Paper homework "Cardiac" due in recitation during the week of 2/5
|Here is a 15-minute introduction to limits video, and an optional video giving a definition of limits.
Lecture:Tangents, velocity, and limits
Lecture:Limits and Limits involving infinity
|2/5||2.5 Limits involving infinity
|HW3 on WebAssign, Due Wed. 2/14 at 9am.
Paper homework "Lim" due in recitation during the week of 2/12
|Lecture:Limits and Continuity|
|2/12||2.6 Derivatives and rates of change.
2.7 The derivative as a function
|HW4a on WebAssign, Due Mon. 2/19 at 9am.
Also, the second half of the assignment, HW4b on WebAssign, due on Thursday morning that week (Thu. 2/22)
|A short video on the definition of the derivative.
Lecture:The definition of the derivative
|2/19||midterm 1 Monday, 2/19 8:45pm covers 2.1-2.6
here is more information about the exam
2.8 What does f' say about f?
|Lecture:The derivative as a function, and the relation of f' and f|
|2/26||3.1 Derivatives of polynomials and exponentials
3.2 The product and quotient rules
|A short video on exponentials
Lecture:Derivatives of polynomials (the power rule)
Lecture:The product and quotient rules
|3/5||3.3 Derivatives of trigonometric functions
3.4 The chain rule
|Watch the idea of the chain rule video.
Optionally, you can watch a two-part video from YouTube on proving the chain rule: first, a wrong proof that gives the right idea, followed by one that fixes the proof.
Lecture:The Chain Rule
Lecture:Derivatives of trigonometric functions
|3/12||Spring Break||This is not the kind of spring break you want.|
|3/19||3.5 Implicit differentiation
3.6 Inverse trigonometric functions and their derivatives
3.7 Derivatives of logarithmic functions
Lecture:Derivative of logarithm and applications
|3/26||3.7 Logarithmic differentiation
midterm 2 Thursday, 3/29 8:45pm covers chapter 3
|Lecture:Derivatives of inverse trig, logarithmic differentiation
Lecture:more related rates, local max/min
|4/2||3.9 Linear approximations and differentials
4.1 Related rates
4.2 Maximum and Minimum values
|Lecture:Max/Min and curve sketching
Lecture:Midterm II review
4.3,4.4 Curve sketching
|Lecture:Linear Approximations and differentials
Lecture:Derivatives and the shape of curves
|4/16||4.6 Optimization problems||Lecture:Optimization word problems
Lecture:more optimization, some review
|4/23||Part I of final in Frey 109.
4.5 L'Hospital's rule
4.7 Newton's method
|Lecture:l'Hopital's rule, Newton's method
|Lecture:some review for final
Wednesday, May 11, 8:00-10:45am
|Lecture:Final Review Session|