## Prof. James Bagrow | |

Email: | james.bagrow [at] uvm.edu |

Lectures: | MWF 8:30–9:20, T 8:30–9:45 in Perkins 102 |

Office Hours: | M 10–11am, W 1–2pm, or by appointment |

Office: | Farrell Hall 212 ( Map to my office) |

Textbook: | CALCULUS 7E Early Transcendentals |

**2014-01-08**: This course is now over. PDF material has been removed so links below to these files will be broken.

- The
**course syllabus**. Be sure to check this out. - We’ll be using WebAssign for homework assignments. (Quick start guide.)
- You can get Mathematica through UVM for free! You can also use the labs in Votey or Perkins if they are available.
- Some useful Mathematica tutorials.
- Help sessions are available.
- There is a one-credit "Calculus I Companion" that meets Thursdays 8:30–9:45. [MATH 095L course website]

- A Mathematica review was given December 3, 2013.

- Final Exam (Monday, December 9, 2013): Practice Final Solutions Topics on Final
- Test 2 (Friday, Nov. 15 and Monday, Nov. 18, 2013):
[Practice Test]
[Practice Solutions]
**[Test Solutions]** - Test 1 (Friday, Oct. 4, 2013):
[Practice Test]
[Practice Solutions]
**[Test Solutions]**

**12/4:**You've made it, congratulations! Indefinite integrals. Applications of integrals. The net change theorem Integration by substitution (aka u-substitution aka change of variables).**Good luck on the final, study hard!**[Notes]**12/3:**Proof of FTC1 Introduction and proof of FTC2. Examples using the FTC to solve integrals. Introduction to Mathematica. [Notes] [Mathematica Notes]**12/2:**Welcome back from break, we're in the home stretch. Properties of definite integrals. Geometric shortcuts for evaluating definite integrals.**The Fundamental Theorem of Calculus (FTC), part I**. [Notes]**11/22:**Terminology for the definite integral. Definite integrals for non-positive functions. Evaluating the Riemann sum and the definite integral. [Notes]**11/20:**The area problem and the distance problem. Definition of the definite integral. [Notes]**11/19:**Review/**Postmortem**of Exam 2.**11/18:**Exam 2.**11/15:**Exam 2.**11/13:**Chapter 5 -**integral calculus!**Finding the area under a curve using approximating rectangles. [Notes]**11/12:**More antiderivatives. Rectilinear (straight line) motion. [Notes]**11/11:**Antiderivatives. [Notes]**11/8:**Quiz 8 review. Newton's Method. [Notes]**11/6:**Optimization problems. [Notes]**11/5:**Applying L'Hospital's Rule to indeterminate products, differences, and powers by rewriting them. [Notes] [Quiz 8]**11/4:**Second derivatives and the shape of a graph. Indeterminate forms and L'Hospital's Rule. [Notes]**11/1:**Proving the Mean Value Theorem using Rolle's Theorem. How derivatives affect the shape of a graph. Increasing/Decreasing Test. First derivative Test. [Notes]**10/30:**Finding maxima and minima using derivatives. Rolle's Theorem and The Mean Value Theorem. [Notes]**10/29:**Absolute and local maximum and minimum values. Extreme value theorem. [Notes] [Quiz 7]**10/28:**Linear approximations and linearization. Estimating linearization uncertainty using**differentials**. [Notes]**10/25:**Continuously compounded interest. Related rates. [Notes]**10/23:**Quiz 6 review only.**10/22:**Relative growth rates in exponential growth (and decay). Population growth and radioactive decay. [Notes] [Quiz 6]**10/21:**More examples of rates of change in the sciences. Start into exponential growth and decay. [Notes]**10/18:**Examples of rates of change in physics and chemistry. [Notes]**10/16:**Derivatives of logarithmic functions. Exploiting logs to save work:**logarithmic differentiation**. Proving the power rule. Caution: lots of similar-looking functions. [Notes]**10/15:**Examples showing different uses of implicit differentiation. Derivatives of inverse trigonometric functions. [Notes] [Quiz 5]**10/14:**Proof of the chain rule. Implicit differentiation. [Notes]**10/11:**The**chain rule**: derivatives of composite functions. [Notes]**10/9:**Finished Test 1 review. Derivatives of**trigonometric functions**. [Notes]**10/8:**Derivation and examples of**quotient rule**for derivatives. Test 1 review. No weekly quiz. [Notes]**10/7:**Review of derivative rules so far. Derivation and example of the**product rule**. [Notes]**10/4:**Exam 1.**10/2:**Computing derivatives of exponential functions. Exponentials are their own derivatives. Natural exponential function is very *cough* natural. [Notes]**10/1:**Computing derivatives the "easy" way. Power rule for derivatives of power functions, constant multiple rule, sum and difference rules. [Notes]**9/30:**Other notations for the derivative. Differentiability, when are functions differentiable, when do they fail to be differentiable, higher derivatives. [Notes]**9/27:**Understanding derivatives for quantities beyond position and time (not just velocity). Treating the derivative as a new function of itself. Sketching the derivative by examining the original function. The domains of functions compared with the domains of their derivatives. [Notes]**9/25:**Quiz 4 review. Derivatives and rates of change continued. Notation for derivative of a function, examples of computing derivatives. Average rate of change of a general quantity*y*with respect to another quantity*x*, take limit to get instantaneous rate of change of*y*with respect to*x*. [Notes]**9/24:**Derivatives and rates of change. Tangent line is limit of secant lines, now we can take limits directly, no more tables of numbers. [Notes] [Quiz 4]**9/23:**Infinite limits at infinity. Examples, examples, and more examples. Sketching a function by looking at its behavior near its roots and near positive and negative infinity. [Notes]**9/20:**Finding limits at infinity, horizontal/vertical asymptotes, algebraic tricks to avoid indeterminate forms. [Notes]**9/18:**Quiz 3 review. Using the IVT. Limits at infinity, horizontal asymptotes. [Notes]**9/17:**Polynomials and rational functions are continuous, what types of functions are continuous, evaluating nasty limits by exploiting continuity, continuity and function composition. The Intermediate Value Theorem (IVT).~~Using the IVT~~. [Notes] [Quiz 3a] [Quiz 3b]**9/16:**Sec 2.5: Continuity, continuous and discontinuous functions, limits of continunous functions, continuity on an interval, functions that are continuous on the left and on the right,~~polynomials and rational functions are continuous~~. [Notes]**9/13:**Sec 2.4: The precise definition of a limit, proving a limit, one-sided limits, infinite limits. [Notes]**9/11:**Quiz 2 review, using the squeeze theorem (Sec 2.3).~~Sec 2.4: The precise definition of a limit, proving a limit.~~[Notes]**9/10:**Example limit calculations, the squeeze theorem. [Notes] [Quiz 2]**9/9:**Infinite limits and calculating limits quickly using limit laws. [Notes]**9/6:**The velocity problem. The limit of a function. When limits exist or do not exist. One-sided limits. [Notes] [Mathematica]**9/4:**Quiz 1 review, Sec. 2.1 - Tangent lines,~~the velocity problem~~. [Notes]**9/3:**Sec. 1.6 - More logarithms, natural log, graphing logs. Inverse trig functions. [Notes] [Quiz 1]**8/30:**Sec. 1.6 - Inverse functions and (some) logarithms. Horizontal line test, one-to-one functions, graphing inverse functions, recipe to find inverse functions, logarithmic function is the inverse of the exponential function. [Notes]**8/28:**Sec. 1.5 - Exponential functions. [Notes]**8/27:**Sec. 1.2 - Modeling, types of functions, even/odd functions. [Notes] [Mathematica]**8/26:**Welcome to Calc I, syllabus, course info, tips and advice. Sec. 1.1 - Functions: representations, domain/range, vertical line test,~~even/odd functions~~, piecewise functions. [Notes]