Announcements:

Instructor:

Teaching assistants for recitation sections:
Ji Hyeok Choi, Carver 489, jchoi@iastate.edu, Sections A1, C1, J2, L1
Dimitris Kontogiannis, Carver 489, dkontog@iastate.edu, Sections B2, D2, H1, K1
Ahmet Ozkan Ozer, Carver 231, oozer@iastate.edu, Sections B1, D1, J1, L2

Regular class meetings:

Exceptions and additional meeting times: Holidays Monday, September 3 and Monday - Friday, November 19 - 23. No class Friday, October 5 (day after midterm exam)
Midterm exam 8:00 - 9:30 PM, October 4, Lecture Section A in LeBaron 1210, Section B, H in MacKay 117. Final exam Wednesday, December 12, 4:30 - 6:30 PM, Lecture Section A in Hoover 2055, Section B, H in Curtiss 0127

Text, syllabus, test dates:

August 20 - 29 lectures: Limits, Sections 1.1, 1.3 - 1.6

August 31 - September 26 lectures: The Derivative, Sections 2.1 - 2.9
Test One, Friday, September 7, covers Chapter One and Section 2.1
Test Two, Friday, September 21, covers Sections 2.2 - 2.6

September 28 - Ocotber 22 lectures: Applications of the Derivative, Sections 3.1- 3.5, 3.7, 3.8, 3.9
Midterm, Thursday, October 4, 8 PM, special location above, covers Sections 1.1, 1.3 - 1.6, 2.1 - 2.8, 3.1, 3.2
Test Four, Monday, October 15, covers Sections 2.9, 3.3, 3.4

October 24 - November 7 lectures: The Definite Integral, Sections 4.1 - 4.5, 4.6
Test Five, Wednesday, October 31, covers Sections 3.5, 3.8, 3.9, 4.1
Test Six, Monday, November 12, covers Sections 3.7, 4.2 - 4.5

November 9 - November 30 lectures: Applications of the Integral, Sections 6.1 - 6.5, 6.8
Test Seven, Monday, December 3, covers Sections 4.6, 6.1 - 6.4, 6.8

December 5 - December 7 lectures: Review
Final Exam, Wednesday, December 12, 4:30 - 6:30 PM, Lecture Section A in Hoover 2055, Section B, H in Curtiss 0127

Recommended homework & preparation for tests:

The important ideas, techniques, and terms, by section:
Section 1.1: Limit (the central idea that characterizes calculus) understood intuitively, recognized in graphs, guessed from numerical evidence), right- and left-hand limits
Section 1.3: The basic limit theorems that justify the expectations of our intuition, the Squeeze Theorem, manipulation of expressions to help evaluate limits.
Section 1.4: Calculation of trig function limits, manipulation of experessions to use the known limit of (sinx)/x as x approaches 0
Section 1.5: Intuitive understanding and calculation of limits involving infinity (no need to memorize precise definition or use it in proofs), relation of these limits to horizonatal and vertical asymptotes, limits as integer variable n approaches infinity
Section 1.6: Continuity at a point, understood both through the equation in the definition and through the graphical interpretation, removable and nonremovable discontiunities,continunity from one side, continuity on an interval, continuity of combinations of functions, Intermediate Value Theorem, recognizing contiunuous functions through (1) list of elementary functions known to be continuous, (2) combinations of contiunous functions that produce contiunuous functions, (3) definition of continuity
Section 2.1: Slope of a curve at a point, instantaneous velocity, other rates of change, all understood and calculated as limits of approximations, tangent line equations
Section 2.2: Defining formulas for the derivative at a point, interpretation of derivative as a rate and as a slope of a graph, the derivative as a function, the many notations for derivative, the terms such as "differentiation" related to the derivative, differentiability implies continuity
Section 2.3: Rules for efficient calculation of derivatives, the derivative as an operator, recognizing differentiable functions
Section 2.4: Derivatives of trigonometric functions
Section 2.5: Chain Rule for differentiating compositions, expressed in various notations, applied to composition chains of more than two functions
Section 2.6: Higher order derivatives, meaning, various notations, and calculation, acceleration as second derivative of position (or displacement).
Section 2.7: Implicit versus explicit description of functions, implicit differentiation
Section 2.8: Related rates problems
Section 3.1: Extreme values of two kinds: maxima and minima; critical points of three kinds: boundary points, stationary points, and singular points; theorems on max-min existence and on critical points; use of the theory to find maximum and minimum values
Section 3.2: Monotonic functions of two kinds: increasing and decreasing, concave up and concave down functions and graphs, inflection points, interpretation of those concepts in applications, use of the theorems on monotonicity and concavity to investigate the shapes of graphs and sketch the graphs
Section 3.3: Local extreme values, locating them by use of the Critical Point Theorem and the First and Second Dervivative Tests
Section 3.4: Setting up mathematical max/min problems from word problems and solving by using calculus techniques
Section 3.5: Graphing functions using calculus (three main steps are (1) behavior at ends of intervals, (2) info from first derifative, (3) info from second derivative)
Section 3.8: Antiderivatives (indefinite integrals), integral notation, generalized power rule
Section 3.9: First order separable differential equations, technique of separation of variables
Section 4.1: Sigma notation, linearity of summation, collapsing sums, special sum formulas, use of inscribed and circumscribed polygons and limits in calculation of area
Section 4.2: Riemann sums, definite integral definition, definite integral interpretation as area or displacement, integrability of bounded continuous functions on [a,b], interval additive property
Section 3.7: Newton's Method for root finding using calculator only for simple operations and function evaluations, basis of Newton's Method in the tangent line equation
Section 4.3: First Fundamental Theorem of Calculus on the derivative on an accumulation function, comparison property and linearity of the definite integral
Section 4.4: Second Fundamental Theorem of Calculus for evaluation of definite integrals, use of Substitution for calculating definite and indefinite integrals
Section 4.5: Average value of a function, the integral Mean Value Theorem, the use of symmetry in integration
Section 4.6: Formulas and use of Midpoint Rule, Trapezoidal Rule, and Parabolic Rule approximations to the definite integral, and certain features of their errors: En goes to 0 like 1/n^2 or 1/n^4, formulas are exact for polynomials of certain degrees
Section 6.1: The natural logarithm: definition as a definite integral, derivative, notation, graph, properties. Use of the natural logarithm in integration. Logarithmic differentiation.
Section 6.2, 6.8: Review of basic facts about inverse functions, the inverse function theorem, application to inverse trigonometric functions, use of inverse trig functions in integration
Section 6.3: The natural exponential function and the number e: definitions using natural log, properties, derivative, graph, use in integration
Section 6.4: General exponential and log functions: definitions using natural exponential and log, properties, conversion of problems to natural exponential and log problems
Section 6.5: Exponential growth and decay, radioactive decay, crude model of population growth: the differential equation, general solution, use of additional data

For Midterm and Final Exam samples, also see the calculus sequence web site: Calculus I,II,III

Test Solutions:

Grading:

Attendance points are counted for fourteen weeks, beginning week two. Ten points are earned each day of attendance, up to a total of 100. So, attending ten of the fourteen weeks will earn the full 100 points attendance credit. This allows for four absences without penalty. No excuses will be considered for further absence.

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