# Fall 2013 ### 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.

## Labs

• A Mathematica review was given December 3, 2013.

## Lectures

• 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]