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Schedule
PLEASE DO THE ASSIGNED READING FROM THE SYLLABUS BEFORE LECTURE.
- Week 1, August 22 August 26
Section 1.1 Four ways to represent a function
Section 1.2 Mathematical models: A catalog of essential functions
Appendix C Trigonometry
Section 1.4 Exponential functions
- Week 1 Topics. Students should be able to:
Understand the concept of function, and be familiar with all the elementary functions and their graphs.
Work with piecewise functions and functions defined by tables or graphs.
Understand how functions (and their graphs) change under composition with an affine function (i.e., translations).
Work with functions, and solve algebraic equations.
Use basic modeling ideas to solve word problems.
Write and use equations of lines given two points, point and slope, etc.
- Week 2, August 29 September 3
Section 1.5 Inverse functions and logarithms
Section 2.2 The limit of a function
Section 2.3 Calculating limits using the limit laws
Paper Homework 1 due in recitation. - Week 2 Topics. Students should be able to:
Understand the meaning of an inverse function.
Understand the horizontal line test.
Understand how the graph of an inverse function is related to the graph of the original function.
Understand the exponential and logarithmic functions, including the exponential rules and logarithm rules.
Calculate averate rates of change for functions defined by graphs or tables.
Be able to sketch secant lines to a graph, and to use the slopes of secant lines to estimate the slope of the tangent line at a point.
Understand the concept of the limit of a function for values of the input near a specified value (but not necessarily equal to that specified value).
Understand the precise definition of the limit of a function.
Understand one-sided limits.
Be able to estimate such limits by inspection of the graph.
Use the "algebra of limits" to calculate limits of functions (in the case where the limit is finite only).
Understand what it means for a limit not to exist.
Calculate limits using algebra (factoring, evaluation).
Understand the statement of the squeeze theorem, and its use.
- Week 3, September 5 September 9
Section 2.4 Continuity
Section 2.5 Limits involving infinity
Paper Homework 2 due in recitation.
No class on Septebmer 5. - Week 3 Topics. Students should be able to:
State and understand the definition of continuity at a point and ways that a function can fail to be continuous at a point.
Define continuity on an interval.
Understand the "algebra of continuous functions".
Understand the Intermediate Value Theorem, and use it to find roots of continuous functions via repeated approximation.
Understand the relationship between an unboundedly increasing or decreasing limit and the vertical asymptotes of the graph.
Understand the relationship between the value of a limit as the input "increases to infinity" or "decreases to negative infinity" and horizontal asymptotes of the graph.
- Week 4, September 12 September 16
Section 2.6 Derivatives and rates of change
Section 2.7 The derivative as a function, p. 146
Paper Homework 3 due in recitation. - Week 4 Topics. Students should be able to:
Understand the meaning of the tangent to a curve at a point.
Calculate the slope of a tangent as the limit of a difference quotient.
Calculate the derivative of a given function at a point.
Estimate a derivative from a table of values of the function.
Understand velocity as a rate of change, and the difference between average and instantaneous velocity.
Apply the mathematical notion of derivative to calculate the instantaneous rate of change of various quantities: displacement, velocity, population, revenue, etc.
Define the derivative function of a specified function.
Given the graph of a function, sketch the graph of the derivative function.
Recognize points of non-differentiability from the graph of the original function.
Calculate the second derivative function as an iterated derivative function of a specified function.
- Week 5, September 19 September 23
Section 3.1 Derivatives of polynomials and exponential functions
Section 3.2 The product and quotient rules
Paper Homework 4 due in recitation. - Week 5 Topics. Students should be able to:
Calculate the derivatives of polynomials, sums, products, and quotients.
Know the derivatives of exponential functions. - Week 6, September 26 September 30
Section 3.3 Derivatives of trigonometric functions
Section 3.4 The chain rule
MIDTERM 1 on Wednesday, September 28 at 7:50 PM.
No WebAssign homework due this week. No paper homework due this week. - Week 6 Topics. Students should be able to:
Understand via a geometric argument the proof that sin(x)/x limits to 1 as x approaches 0.
Know the derivatives of the standard trigonometric functions.
Understand the chain rule, and apply it in many situations.
- Week 7, October 3 October 7
Section 3.5 Implicit differentiation
Section 3.6 Inverse trigonometric functions and their derivatives
Section 3.7 Derivatives of logarithmic functions
Paper Homework 5 due in recitation.
Last date to drop-down to another calculus course is Friday, October 7. - Week 7 Topics. Students should be able to:
Calculate derivatives implicitly.
Use implicit differentiation to calculate slopes of implicitly defined curves and find tangent lines.
Know the derivatives of the standard inverse trigonometric functions.
Know the derivatives of radical functions.
Know the derivatives of logarithmic functions.
Use the technique of logarithmic differentiation to find derivatives of large products, quotients, exponentials, etc.
- Week 8, October 10 October 14
Section 3.8 Linear approximations and differentials
Section 4.1 Related rates
Paper Homework 6 due in recitation. No class on October 10-11. - Week 8 Topics. Students should be able to:
Apply linear approximations in calculations (e.g., to approximate the cube root of 9).
Estimate how errors in measurement propagate in calculations.
Solve related-rates problems as an application of the chain rule and implicit differentiation.
- Week 9, October 17 October 21
Section 4.2 Maximum and minimum values
Section 4.3 Derivatives and the shapes of curves
Paper Homework 7 due in recitation. - Week 9 Topics. Students should be able to:
Locate critical points of a function; classify as to local maximum or minimum or neither.
Determine the maximum value of a function on a closed interval.
Know the statement of the Mean Value Theorem and its consequences.
Understand the relation between the second derivative and concavity of a graph.
Make accurate sketches of graphs of functions, including critical points, concavity, and inflection points.
Be able to sketch the graph of a function given the graph of the derivative function (and one point on the graph).
Use relative maxima and minima and limit information to understand functions and sketch their graphs.
- Week 10, October 25 October 29
Section 4.5 Indeterminate forms and l'Hospital's rule
Section 4.6 Optimization problems
Paper Homework 8 due in recitation. - Week 10 Topics. Students should be able to:
Understand when l'Hospitals rule can be used and how to use it (iterating if necessary).
Translate an optimization problem into a search for the maxima/minima of a function on an interval, and translate the solution back to the original problem.
- Week 11, October 31 November 4
Section 4.7 Newton's method
MIDTERM 2 on Thursday, Nov 3 at 8:15 PM.
No WebAssign homework due this week. No paper homework due this week. - Week 11 Topics. Students should be able to:
Understand the formulation of Newton's method, and apply it to approximate the zero of a function. Recognize when it may fail.
- Week 12, November 7 November 11
Section 5.1 Areas and distances
Section 5.2 The definite integral
Paper Homework 9 due in recitation. - Week 12 Topics. Students should be able to:
Estimate the area under the graph of piecewise-linear function.
Estimate areas of more general (positive) functions using (finite) right-hand and left-hand sums.
Use Sigma notation for sums.
Understand the general definition of a (finite) Riemann sum.
Represent a definite integral as a limit a Riemann sum.
Extend the notion of area to "signed area" so as to include functions with negative values.
- Week 13, November 14 November 18
Section 4.8 Antiderivatives
Section 5.3 Evaluating definite integrals
Section 5.4 The fundamental theorem of calculus
Paper Homework 10 due in recitation. - Week 13 Topics. Students should be able to:
Understand the definition of an antiderivative as a differentiable function whose associated derivative function is a specified function.
Recognize many antiderivative functions from derivatives studied in this course.
Understand the statement of the Fundamental Theorem of Calculus, including the formulation as the "Net Change Theorem".
Define functions in terms of definite integral, and understand the derivatives of these functions.
Combine definite integral functions with other functions, e.g., via composition, and use derivative rules and the Fundamental Theorem of Calculus to compute the derivative of the resulting functions.
Given the graph of a function, answer questions about the graph of the associated definite integral function.
Set up integrals to evaluate areas and signed areas.
Estimate distance and displacement from velocity information in a graph or table.
Compute simple integrals involving standard functions, including trigonomentric and exponential functions.
Compute integrals which result in logarithms and inverse trigonometric functions.
- Week 14, November 21 November 25
Section 5.5 The substitution rule
No WebAssign homework due this week. No paper homework due this week.
No class on November 23-25. - Week 14 Topics. Students should be able to:
Compute integrals using substitution.
Use definite integrals and antiderivatives to solve simple initial-value differential equations.
- Week 15, November 28 December 2
REVIEW
Paper Homework 11 due in recitation.
Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr