SUFE/UMM Calculus
Section Numbers refer to textbook: Stewart Calculus Early Transcendentals Single Variable, 5th Edition
I have tried to eliminate all references to Mathematica, the computer algebra system we use at UMM, but there may still be some problems in the examples that refer to Mathematica in the solution.
The Handout I use at the end of the course for partial derivatives and a first look at multivariable calculus relies heavily on Mathematica. I left it (and the associated Mathematica file) on the webpage in case someone wanted to look at it.
I use the readings as part of a weekly journal series in which students email me their thoughts on the readings for a minimal contribution to the final grade.
| Lecture Topic | Reading/Journal | Examples/Problems |
|---|---|---|
| 1.1 Four Ways to Represent a Function | examples Lecture Notes Functional Notation |
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| 1.2 Mathematical Models: Catalog of Essential Functions | examples The Twelve Basic Functions |
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| 1.3 New Functions from Old Functions | examples | |
| 1.4 Graphing Calculators and Computers | ||
| 1.5 Exponential Functions | examples | |
| 1.6 Inverse Functions and Logarithms | Give me a short description of how you have prepared for the upcoming Test. | examples |
| 2.1 The Tangent and Velocity Problems | examples Animation of Secant Approaching Tangent |
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| 2.2 The Limit of a Function | examples | |
| 2.3 Calculating Limits Using the Limit Laws | Read the short article about Karl Weierstrass. Do not worry about the mathematical details (pointwise, uniform convergence, etc). What is your reaction the the knowledge that Cauchy (a brilliant mathematician) gave a "famously incorrect proof" in one of his books? | examples |
| 2.4 Precise Definition of Limit | ||
| 2.5 Continuity |
examples | |
| 2.6 Limits at Infinity; Horizontal Asymptotes | examples | |
| 2.7 Tangents, Velocities and Other Rates of Change | examples Graphical picture of derivative |
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| 2.8 Derivatives 2.9 The Derivative as a Function |
Read the article on the History of Differentiation (there is more to the article, but you just need to read the history part). | examples A function with a sharp corner |
| 3.1 Derivatives of Polynomials and Exponential Functions | examples Notes: Derivative Proofs |
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| 3.2 The Product and Quotient Rules | examples Examples from the lecture |
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| 3.3 Rates of Change in Natural and Social Sciences | Read the article on Applications of Calculus (there is more to the article, but you just need to read the applications part). Which application would you want to learn more about, and why? | examples |
| 3.4 Derivatives of Trigonometric Functions | examples Trigonometry Review |
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| 3.5 The Chain Rule | examples Chain Rule: Graphical Interpretation Derivative Calculator on Web |
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| 3.6 Implicit Differentiation | examples | |
| 3.7 Higher Derivatives | ||
| 3.8 Derivatives of Logarithmic Functions | examples | |
| 3.10 Related Rates | Examples from the lecture examples |
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| 3.11 Linear Approximation and Differentials | Pick a topic related to math or the course that you would like to talk about. | examples |
| 4.1 Maximum and Minimum Values | examples | |
| 4.2 The Mean Value Theorem | ||
| 4.3 How Derivatives Affect the Shape of a Graph | Check out the website Wolfram Alpha. Use it to find the local minimum of 3x^3- 2x^2-4 (you can just type your question into the box at the top of the page), and then play around with a bit to see what it can do. What is the local min you found? What do you think of Wolfram Alpha? | examples |
| 4.4 Indeterminate Forms and l'Hospital's Rule | Read the article on Guillaume de l'Hôpital. What do you think of his deal with Johann Bernoulli? | examples Application in Biology (paragraph three in Model Implications) |
| 4.5 Summary of Curve Sketching | ||
| 4.6 Graphing with Calculators and Calculus | ||
| 4.7 Optimization | examples Examples from lecture |
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| 4.8 Applications to Business and Economics | ||
| 4.9 Newton's Method | ||
| 4.10 Antiderivatives | Read the History of Calculus, and offer a few short comments on content of the reading. | examples |
| 5.1 Areas and Distances | examples | |
| 5.2 The Definite Integral | examples | |
| 5.3 The Fundamental Theorem of Calculus | examples | |
| 5.4 Indefinite Integrals and the Net Change Theorem | examples How to Remember the Basic Integrals Examples from the lecture Animations of Position and Velocity |
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| 5.5 The Substitution Rule | Pick a topic related to math or the course that you would like to talk about. | examples Examples from the lecture |
| 10.1 Curves Defined by Parametric Equations 10.2 Tangents and Areas |
examples | |
| Handout: Surfaces & Traces MMA file |
MMA (Surfaces and traces) | |
| Handout: Space Curves & Contour Plots |
Software using Surface Intersection Weather Pattern Contour Plots Topographical Maps |
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| Handout: Partial Derivatives | tangent line animations | |
| Handout: Extrema |